What do you think?
Rate this book
Mindstorms: Children, Computers, And Powerful Ideas
Computers have completely changed the way we teach children. We have Mindstorms to thank for that. In this book, pioneering computer scientist Seymour Papert uses the invention of LOGO, the first child-friendly programming language, to make the case for the value of teaching children with computers. Papert argues that children are more than capable of mastering computers, and that teaching computational processes like de-bugging in the classroom can change the way we learn everything else. He also shows that schools saturated with technology can actually improve socialization and interaction among students and between students and teachers.
252 pages, Paperback
First published January 1, 1980
Ratings & Reviews
Friends & Following
Create a free account to discover what your friends think of this book!
Community Reviews
Displaying 1 - 30 of 92 reviews
June 24, 2019
This review is cross-posted from my personal site: Computers As Objects To Think With
Bret Victor wrote an essay in 2012 that left me desperately wishing I were a computer engineer. "Learnable Programming" was a critique of 1) Khan Academy's newly released intro course on programming, 2) the Processing language the course focused on, and 3) decades of stagnation in programming pedagogy. The essay was funny, visually stunning, provocative, and so convincing in its presentation of an effective foundation for how to teach programming to learners by showing them what their code was actually doing that one could easily be led to believe that anyone who'd even considered the question of how to teach programming before was asleep at the pedagogical wheel. The intellectual effect was something akin to a first encounter with Edward Tufte's suggestion that graphs should show information instead of junky non-information. It was brilliant in a way that makes your temples burn and you mouth keep murmuring "Yes. Yes. Yes!" Computers are awesome. Education is awesome. Teaching students how to do powerful things with computers = Best. Thing. Ever.
Ergo, I desperately wished that I knew enough about programming join whatever project Victor was about to suggest.
Pivotal to the essay was the (brief) intellectual history of older languages and computer environments explicitly designed to teach students about programming. In this, Victor was unequivocal on the importance of Mindstorms:
Given the brainy rush induced by Victor's essay, I had no other choice that to follow his direct instructions, "For fuck's sake, read 'Mindstorms.'" So I ordered a used copy within minutes of reaching the bottom of his article.
Mindstorms was published in 1980, while Papert worked at MIT, so he uses terms like "cybernetics" in earnest and offers astounding facts like "in the past two years, over 200,000 personal computers have entered the lives of Americans" (p 181). So in that sense, the jargon and computational enthusiasm resonates with Tracy Kidder's The Soul of a New Machine. Now set this in concert with Papert's vision for the role of computers in building learning environments for children: it is grounded firmly in his years of work with developmental psychologist Jean Piaget, a pioneer of constructivist education theory. The "build it yourself" and "ask lots of questions" spirit resonates with my 80s memories of LEGO sets and Sesame Street. Taken together, Papert's ideas, read three decades later, crystalize for me a certain utopian fetish for the intellectual, cultural, and political possibilities of kids screwing around with boxy, green-screened Apple IIes.
But on a more practical level, the book is full of clear-eyed distillations of how tinkering with computers can help teachers and students make thinking visible. Take, for instance, Papert's ideas here about the pedagogical power of "debugging" a computer program as a special case of tenacious learning-by-experiment:
Thirty years on, there's a profusion of non-profits, projects, and start-ups trying to teach kids and adults alike to code. But what often goes unstated in the breathlessness about how cool it is to learn how to code is that fact that learning to code is, like learning to read and write, an extension of learning how to think. And learning how to think requires learning how to be "metacognitive"--that is, able to think about how your own ideas and thought processes work, so that you can find problems and correct them.
The LOGO interface allows users to draw using simple commands. Here's one way to draw a square:
This code it easy enough to decipher: go forward 100 units, turn right 90 degrees, repeat 4 times, and you've drawn 4 straight sides at right angles to one another.
But I believe that part of Victor's fascination with LOGO as a teaching tool lies in the simple metaphor of the Turtle. The Turtle is the stylus implied in the lines of code above. In LOGO, the "cursor" that moves around the screen, drawing your square (or whatever other shape) is called the "Turtle," and all the written commands in the code are simply instructions to the Turtle for where to go and what to do. The Turtle is a little metaphor that helps to crystalize the fact that writing an effective program is nothing more than figuring out how to provide a cute, determined animal with the right set of instructions.
(Screengrab from the LOGO Foundation site)
But here's were things get cooler. Papert's team didn't just build LOGO software and use it to help students experiment with mathematical principals while drawing shapes on green computer screens. The were also real Turtles students could control using the exact same instructions. These real Turtles were dome-shaped motorized robots with retractable styluses in them that would draw programed shapes and images on swaths of paper laid out on the classroom floor.
(Image from bfoit.org)
The link between the simple mathematics of a computer program and the real images a student could create is a perfect example of constructivist learning. Tinker with something abstract, see the results in the real world. Repeat over and over and the learner's understanding improves.
Furthermore, the conceptual link between the instructions a student writes in a computer program and the visual results of that code is another fundamental element of how students learn. "An important part of becoming a good learner is learning how to push out the frontier of what we can express with words," Papert writes (p 96). Essentially, he's arguing that part of expanding what a student knows is forcing them to encounter the edges of their explanatory powers: the link between code and image is itself pushing that expansion. When a student's words are insufficient to explain what he or she knows, a key element of the learning process is acquiring new words, new concepts, and new grammars to explain it. And when there is such an intimate link between the new words (code) and the concepts they express (the program output), the boundaries of what the student can express expand.
The illustrate this point, consider another example from the LOGO Foundation's web page introducing the basics of the language. After explaining foundational concepts like how to draw a line and a square, the example introduces how to combine and repeat instructions to create a picture made by iterating a a drawing of a square over and over on top of itself, creating a pinwheel design that is difficult to describe in pure words, but which explodes onto the screen with just a few lines of code:
(Screengrab from the LOGO Foundation site)
Papert's walks through several different analogies for how computational thinking can illuminate instructional situations. There's an extended discussion of how learning to juggle is a process of "debugging"--correcting many small isolated errors to get a sequence of actions to work. There's explanations of how computer environments to shape better physics instruction that helps students make connections between physical principles and their own experience of objects in the world--as opposed to simply forcing them to encounter physics through a set of abstract equations. But he also anticipates criticism of this push for teaching "computational thinking" with a powerful argument for how it expands cognitive ability:
And perhaps most importantly, Papert believes that the process of learning computational thinking is necessarily a social process that facilitates and depends upon the interplay between student, learning objective, and teacher. Again, the process of debugging is powerful because it re-writes concepts about what it means to be "wrong" and helps students think metacognitively, but it also creates questions and topics of conversation for student/teacher interactions, where the student practices pushing out the frontiers of what he or she can express with words.
"In my vision the computer acts as a transitional object to mediate relationships that are ultimately between person and person," Papert writes in one of the concluding chapters (p 183). In this case, Victor's essay on Learnable Programming did just that: a maze of networked computers served up his ideas and enthusiasm for Mindstorms, and hopefully I've been able to capture some of that excitement for you, dear reader, on your computer.
Bret Victor wrote an essay in 2012 that left me desperately wishing I were a computer engineer. "Learnable Programming" was a critique of 1) Khan Academy's newly released intro course on programming, 2) the Processing language the course focused on, and 3) decades of stagnation in programming pedagogy. The essay was funny, visually stunning, provocative, and so convincing in its presentation of an effective foundation for how to teach programming to learners by showing them what their code was actually doing that one could easily be led to believe that anyone who'd even considered the question of how to teach programming before was asleep at the pedagogical wheel. The intellectual effect was something akin to a first encounter with Edward Tufte's suggestion that graphs should show information instead of junky non-information. It was brilliant in a way that makes your temples burn and you mouth keep murmuring "Yes. Yes. Yes!" Computers are awesome. Education is awesome. Teaching students how to do powerful things with computers = Best. Thing. Ever.
Ergo, I desperately wished that I knew enough about programming join whatever project Victor was about to suggest.
Pivotal to the essay was the (brief) intellectual history of older languages and computer environments explicitly designed to teach students about programming. In this, Victor was unequivocal on the importance of Mindstorms:
The canonical work on designing programming systems for learning, and perhaps the greatest book ever written on learning in general, is Seymour Papert's 'Mindstorms.'
Given the brainy rush induced by Victor's essay, I had no other choice that to follow his direct instructions, "For fuck's sake, read 'Mindstorms.'" So I ordered a used copy within minutes of reaching the bottom of his article.
Mindstorms was published in 1980, while Papert worked at MIT, so he uses terms like "cybernetics" in earnest and offers astounding facts like "in the past two years, over 200,000 personal computers have entered the lives of Americans" (p 181). So in that sense, the jargon and computational enthusiasm resonates with Tracy Kidder's The Soul of a New Machine. Now set this in concert with Papert's vision for the role of computers in building learning environments for children: it is grounded firmly in his years of work with developmental psychologist Jean Piaget, a pioneer of constructivist education theory. The "build it yourself" and "ask lots of questions" spirit resonates with my 80s memories of LEGO sets and Sesame Street. Taken together, Papert's ideas, read three decades later, crystalize for me a certain utopian fetish for the intellectual, cultural, and political possibilities of kids screwing around with boxy, green-screened Apple IIes.
But on a more practical level, the book is full of clear-eyed distillations of how tinkering with computers can help teachers and students make thinking visible. Take, for instance, Papert's ideas here about the pedagogical power of "debugging" a computer program as a special case of tenacious learning-by-experiment:
The question to ask about the program is not whether it is right or wrong, but if it is fixable. If this way of looking at intellectual products were generalized to how the larger culture thinks about knowledge and its acquisition, we all might be less intimidated by our fears of "being wrong." This potential influence of the computer on changing our notion of a black and white version of our successes and failures is an example of using the computer as an "object-to-think-with." It is obviously not necessary to work with computers in order to acquire good strategies for learning. Surely "debugging" strategies were developed by successful learners long before computers existed. But thinking about learning by analogy with developing a program is a powerful and accessible way to get started on becoming more articulate about one's debugging strategies and more deliberate about improving them (p 23).
Thirty years on, there's a profusion of non-profits, projects, and start-ups trying to teach kids and adults alike to code. But what often goes unstated in the breathlessness about how cool it is to learn how to code is that fact that learning to code is, like learning to read and write, an extension of learning how to think. And learning how to think requires learning how to be "metacognitive"--that is, able to think about how your own ideas and thought processes work, so that you can find problems and correct them.
The LOGO interface allows users to draw using simple commands. Here's one way to draw a square:
FORWARD 100
RIGHT 90
FORWARD 100
RIGHT 90
FORWARD 100
RIGHT 90
FORWARD 100
RIGHT 90
This code it easy enough to decipher: go forward 100 units, turn right 90 degrees, repeat 4 times, and you've drawn 4 straight sides at right angles to one another.
But I believe that part of Victor's fascination with LOGO as a teaching tool lies in the simple metaphor of the Turtle. The Turtle is the stylus implied in the lines of code above. In LOGO, the "cursor" that moves around the screen, drawing your square (or whatever other shape) is called the "Turtle," and all the written commands in the code are simply instructions to the Turtle for where to go and what to do. The Turtle is a little metaphor that helps to crystalize the fact that writing an effective program is nothing more than figuring out how to provide a cute, determined animal with the right set of instructions.
(Screengrab from the LOGO Foundation site)
But here's were things get cooler. Papert's team didn't just build LOGO software and use it to help students experiment with mathematical principals while drawing shapes on green computer screens. The were also real Turtles students could control using the exact same instructions. These real Turtles were dome-shaped motorized robots with retractable styluses in them that would draw programed shapes and images on swaths of paper laid out on the classroom floor.
(Image from bfoit.org)
The link between the simple mathematics of a computer program and the real images a student could create is a perfect example of constructivist learning. Tinker with something abstract, see the results in the real world. Repeat over and over and the learner's understanding improves.
Furthermore, the conceptual link between the instructions a student writes in a computer program and the visual results of that code is another fundamental element of how students learn. "An important part of becoming a good learner is learning how to push out the frontier of what we can express with words," Papert writes (p 96). Essentially, he's arguing that part of expanding what a student knows is forcing them to encounter the edges of their explanatory powers: the link between code and image is itself pushing that expansion. When a student's words are insufficient to explain what he or she knows, a key element of the learning process is acquiring new words, new concepts, and new grammars to explain it. And when there is such an intimate link between the new words (code) and the concepts they express (the program output), the boundaries of what the student can express expand.
The illustrate this point, consider another example from the LOGO Foundation's web page introducing the basics of the language. After explaining foundational concepts like how to draw a line and a square, the example introduces how to combine and repeat instructions to create a picture made by iterating a a drawing of a square over and over on top of itself, creating a pinwheel design that is difficult to describe in pure words, but which explodes onto the screen with just a few lines of code:
(Screengrab from the LOGO Foundation site)
Papert's walks through several different analogies for how computational thinking can illuminate instructional situations. There's an extended discussion of how learning to juggle is a process of "debugging"--correcting many small isolated errors to get a sequence of actions to work. There's explanations of how computer environments to shape better physics instruction that helps students make connections between physical principles and their own experience of objects in the world--as opposed to simply forcing them to encounter physics through a set of abstract equations. But he also anticipates criticism of this push for teaching "computational thinking" with a powerful argument for how it expands cognitive ability:
In my view a salient feature of human intelligence is the ability to operate with many ways of knowing, often in parallel, so that something can be understood on many levels. In my experience, the fact that I ask myself to 'think like a computer' does not close off other epistemologies. It simply opens new ways for approaching thinking. … But true computer literacy is not just knowing how to make use of computer and computational ideas. It is knowing when it is appropriate to do so (p 155).
And perhaps most importantly, Papert believes that the process of learning computational thinking is necessarily a social process that facilitates and depends upon the interplay between student, learning objective, and teacher. Again, the process of debugging is powerful because it re-writes concepts about what it means to be "wrong" and helps students think metacognitively, but it also creates questions and topics of conversation for student/teacher interactions, where the student practices pushing out the frontiers of what he or she can express with words.
"In my vision the computer acts as a transitional object to mediate relationships that are ultimately between person and person," Papert writes in one of the concluding chapters (p 183). In this case, Victor's essay on Learnable Programming did just that: a maze of networked computers served up his ideas and enthusiasm for Mindstorms, and hopefully I've been able to capture some of that excitement for you, dear reader, on your computer.
November 26, 2012
I am in agreement with Papert's theories of child learning. In particular, while reading Chapter Two ("Mathophobia: The Fear of Learning"), I had to suppress the urge to open the windows and shout, "Yes, dammit! This!" to anyone who would listen.
You see, I was one of those kids who thought math just wasn't for them. I did fine when we were learning whole new subjects like geometry or algebra for the first time. But when things devolved into endless repetition and (seemingly) mindless rote work, I loathed it - could only just barely force myself to do the bare minimum to get by. I always kind of felt bad about it because somewhere deep in the back of my mind I believed that I did have the aptitude. But if this was what math was all about, I wanted nothing to do with it.
Later in life, after teaching myself so many different things that my confidence in my ability to learn is very high, I've come to understand how very right I was about math (it's real-world purpose and applications) and how utterly wrong my teachers were. I guess I could feel vindicated. But mostly the whole thing is just sad. All of those classroom hours, completely wasted...
Anyway, Papert believes that children learn most effectively when they’re trying to solve a problem - and when they’re genuinely interested in the outcome of the problem. I believe that too. I know that’s true for me as a learner. He also believes that computers allow us to examine and learn subjects such as mathematics and physics in intuitive ways which simply are not possible with pencil and paper. Computers encourage experimentation, problem-solving, and iterative attempts at a problem until the desired outcome is finally achieved. Again, I know my programming and writing on computers are what have gotten me where I am now. I believe it would work for others as well.
I do have a bit of a bone to pick with Mindstorms. The cover claims that it’s about, “Logo - How it was invented and how it works.” But that really isn’t the case. Logo (the computer language Papert developed for child learning) is certainly featured in this book. But it’s not at all the central subject. And unless I accidentally skipped a paragraph or something, the “how it was invented” part doesn’t even exist except for some brief mentions in the Afterward and Acknowledgments at the very end of the book. That’s strange - and unfortunate since I would have been very interested, indeed, to read about the development of the Logo language and was looking forward to that part.
While it’s not horrendous, I found Mindstorms to be redundant towards the end. The last couple chapters seemed to contain an awful lot of the same arguments made in the beginning and middle parts of the book. I would have been much happier if the text had been pruned and more concrete examples of Logo being used to teach various subjects had been added.
Something else to note: for a book that was first published in 1980, the content has hardly aged a day. In fact, many of Papert’s prognostications are so dead-on correct that it’s really quite amazing. I feel that his uncanny ability to have forseen the future of technology so accurately lends a lot of credibility to his ideas and abilities as a thinker in general.
I highly recommend this book to anyone with an interest in the subject. Just be warned that it’s much more concerned with the theories of child learning than it is about the Logo language.
I also wish I could force educators to read this, understand it, and act upon it.
You see, I was one of those kids who thought math just wasn't for them. I did fine when we were learning whole new subjects like geometry or algebra for the first time. But when things devolved into endless repetition and (seemingly) mindless rote work, I loathed it - could only just barely force myself to do the bare minimum to get by. I always kind of felt bad about it because somewhere deep in the back of my mind I believed that I did have the aptitude. But if this was what math was all about, I wanted nothing to do with it.
Later in life, after teaching myself so many different things that my confidence in my ability to learn is very high, I've come to understand how very right I was about math (it's real-world purpose and applications) and how utterly wrong my teachers were. I guess I could feel vindicated. But mostly the whole thing is just sad. All of those classroom hours, completely wasted...
Anyway, Papert believes that children learn most effectively when they’re trying to solve a problem - and when they’re genuinely interested in the outcome of the problem. I believe that too. I know that’s true for me as a learner. He also believes that computers allow us to examine and learn subjects such as mathematics and physics in intuitive ways which simply are not possible with pencil and paper. Computers encourage experimentation, problem-solving, and iterative attempts at a problem until the desired outcome is finally achieved. Again, I know my programming and writing on computers are what have gotten me where I am now. I believe it would work for others as well.
I do have a bit of a bone to pick with Mindstorms. The cover claims that it’s about, “Logo - How it was invented and how it works.” But that really isn’t the case. Logo (the computer language Papert developed for child learning) is certainly featured in this book. But it’s not at all the central subject. And unless I accidentally skipped a paragraph or something, the “how it was invented” part doesn’t even exist except for some brief mentions in the Afterward and Acknowledgments at the very end of the book. That’s strange - and unfortunate since I would have been very interested, indeed, to read about the development of the Logo language and was looking forward to that part.
While it’s not horrendous, I found Mindstorms to be redundant towards the end. The last couple chapters seemed to contain an awful lot of the same arguments made in the beginning and middle parts of the book. I would have been much happier if the text had been pruned and more concrete examples of Logo being used to teach various subjects had been added.
Something else to note: for a book that was first published in 1980, the content has hardly aged a day. In fact, many of Papert’s prognostications are so dead-on correct that it’s really quite amazing. I feel that his uncanny ability to have forseen the future of technology so accurately lends a lot of credibility to his ideas and abilities as a thinker in general.
I highly recommend this book to anyone with an interest in the subject. Just be warned that it’s much more concerned with the theories of child learning than it is about the Logo language.
I also wish I could force educators to read this, understand it, and act upon it.
November 14, 2023
One of the best books ever written about learning.
Read
October 25, 2011This book provides persuasive explanations deriving what had only been intuitions for a great number of my long-held vague suspicions. Which is critical, of course, to building on these ideas: we can't compose or leap well without error correction, and an explanatory framework allows us the ready error-checking of emergent ideas which dogmatic belief does not.
Papert's epistemological ideas are radical but convincing: that derivational learning trumps the mechanical (for the reasons I describe above!); that students have difficulty deriving the principles of abstraction for themselves because their environments lack the raw materials; that computers may be a useful vector for supplying this material.
I don't think we even understand how important it is that we be skilled with abstraction. Consider, for instance, that one faces similar problems when studying a computer program to those involved in genomics. A generation which has been thinking in the abstract since childhood could substantially affect the life expectancy of its progenitors.
Papert's epistemological ideas are radical but convincing: that derivational learning trumps the mechanical (for the reasons I describe above!); that students have difficulty deriving the principles of abstraction for themselves because their environments lack the raw materials; that computers may be a useful vector for supplying this material.
I don't think we even understand how important it is that we be skilled with abstraction. Consider, for instance, that one faces similar problems when studying a computer program to those involved in genomics. A generation which has been thinking in the abstract since childhood could substantially affect the life expectancy of its progenitors.
March 1, 2020
Mindstorms: Children, Computers, And Powerful Ideas by Seymour Papert
—
Книжке 40 лет, но она актуальна как никогда. Сеймур предлагает радикально изменить подходы к преподаванию разных предметов, в основном естественных наук.
Пейперт безжалостно критикует современную систему образования, но, в отличие от многих критиков, он предлагает свой подход. Его не так-то просто уместить в одном предложении, но я попробую:
^ Давайте дадим детям среду, в которой они будут исследовать микро-миры (модели), находить закономерности и создавать новые модели.
Что мне запомнилось:
1. В школе детей не учат правильно работать с ошибками. Ошибки — это плохо. Вот что есть в школе. Рукописный текст плохо поддается правкам, поэтому конечно дети не будут корректировать сочинение. Программирование учит дебаггингу, ошибки — это неотьемлемая часть работы. К ним нужно относится спокойно, искать и исправлять. Это часть пути. Отчасти это можно исправить, убрав рукописные тексты со средней школы. Но нужно изменять и сам подход преподавания предметов.
2. В школе предметы практически не связаны между собой. Я это прекрасно прочувствовал на себе в старших классах, когда вообще не понимал роль дифференциального исчисления в физике. Учебные программы должны размывать все это. Нужно связывать предметы вместе. Показывать геометрию в физике и химии. Показывать роль симметрии в мире. Показывать глубину дифференциального исчисления на примерах ускорения и прочих процессов. Пейперт утверждает, что это реализуемо через модели в компьютерах.
3. Уже в 70х он предвидел, что персональные компьютеры будут везде. Этот прогноз с блеском оправдался. Но Сеймур был излишне оптимистичен по поводу их роли в образовании. Мало что изменилось. Компьютеры используются только на уроках информатики.
4. Основная идея — давать детям микро-миры, которые можно исследовать. Несколько команд для изучения скорости и ускорения — и через часок дети начинают интуитивно чувствовать что значат эти понятия. Без всяких формул, просто меняя переменные и скриптуя простые действия двигающейся черепашки. Задача системы образования — сделать правильный набор базовых моделей, в которых дети могут исследовать мир. Что из этого есть сейчас в школе? Ни-че-го.
5. Изучая модели и вырабатывая интуитивное понимание, дети гораздо проще схватывают формализм. Когда ты уже поигрался с моделью, где есть инерция и масса, гораздо проще понять законы Ньютона. В школе сразу пихают в детей формализм, выбивая напрочь способность к интуиции и любопытству. Некоторые выживают и сохраняют в себе дух познания, но это все вопреки системе.
6. Путь познания часто лежит через неправильные модели и неправильные выводы. В школе все это перечеркивается и дается только правильная, конечная точка. Нужно давать детям возможность создавать неверные модели, учить находить в них ошибки и постепенно приходить к правильным моделям.
7. Детей в школе не учат алгоритмам. А это базовое понятие многих дисциплин. Разбивая навыки на алгоритмы можно освоить его гораздо быстрее. Пример — жонглирование. На самом деле понятие алгоритма и умение разбить решение проблемы на шаги — совершенно фундаментальная вещь. Как с этим в школе? Никак.
8. Его язык LOGO очень простой и одновременно мощный. В наше время есть Scratch, который впитал многие идеи LOGO. Конструктор ЛЕГО Mindstorms назван в честь этой книги.
Я не буду здесь приводить любимые цитаты, потому что у меня четверть книги желтая от хайлайтов. Если вы вдруг касаетесь сферы образования — прочитайте эту книгу. Возможно, она изменит вашу жизнь.
—
Книжке 40 лет, но она актуальна как никогда. Сеймур предлагает радикально изменить подходы к преподаванию разных предметов, в основном естественных наук.
Пейперт безжалостно критикует современную систему образования, но, в отличие от многих критиков, он предлагает свой подход. Его не так-то просто уместить в одном предложении, но я попробую:
^ Давайте дадим детям среду, в которой они будут исследовать микро-миры (модели), находить закономерности и создавать новые модели.
Что мне запомнилось:
1. В школе детей не учат правильно работать с ошибками. Ошибки — это плохо. Вот что есть в школе. Рукописный текст плохо поддается правкам, поэтому конечно дети не будут корректировать сочинение. Программирование учит дебаггингу, ошибки — это неотьемлемая часть работы. К ним нужно относится спокойно, искать и исправлять. Это часть пути. Отчасти это можно исправить, убрав рукописные тексты со средней школы. Но нужно изменять и сам подход преподавания предметов.
2. В школе предметы практически не связаны между собой. Я это прекрасно прочувствовал на себе в старших классах, когда вообще не понимал роль дифференциального исчисления в физике. Учебные программы должны размывать все это. Нужно связывать предметы вместе. Показывать геометрию в физике и химии. Показывать роль симметрии в мире. Показывать глубину дифференциального исчисления на примерах ускорения и прочих процессов. Пейперт утверждает, что это реализуемо через модели в компьютерах.
3. Уже в 70х он предвидел, что персональные компьютеры будут везде. Этот прогноз с блеском оправдался. Но Сеймур был излишне оптимистичен по поводу их роли в образовании. Мало что изменилось. Компьютеры используются только на уроках информатики.
4. Основная идея — давать детям микро-миры, которые можно исследовать. Несколько команд для изучения скорости и ускорения — и через часок дети начинают интуитивно чувствовать что значат эти понятия. Без всяких формул, просто меняя переменные и скриптуя простые действия двигающейся черепашки. Задача системы образования — сделать правильный набор базовых моделей, в которых дети могут исследовать мир. Что из этого есть сейчас в школе? Ни-че-го.
5. Изучая модели и вырабатывая интуитивное понимание, дети гораздо проще схватывают формализм. Когда ты уже поигрался с моделью, где есть инерция и масса, гораздо проще понять законы Ньютона. В школе сразу пихают в детей формализм, выбивая напрочь способность к интуиции и любопытству. Некоторые выживают и сохраняют в себе дух познания, но это все вопреки системе.
6. Путь познания часто лежит через неправильные модели и неправильные выводы. В школе все это перечеркивается и дается только правильная, конечная точка. Нужно давать детям возможность создавать неверные модели, учить находить в них ошибки и постепенно приходить к правильным моделям.
7. Детей в школе не учат алгоритмам. А это базовое понятие многих дисциплин. Разбивая навыки на алгоритмы можно освоить его гораздо быстрее. Пример — жонглирование. На самом деле понятие алгоритма и умение разбить решение проблемы на шаги — совершенно фундаментальная вещь. Как с этим в школе? Никак.
8. Его язык LOGO очень простой и одновременно мощный. В наше время есть Scratch, который впитал многие идеи LOGO. Конструктор ЛЕГО Mindstorms назван в честь этой книги.
Я не буду здесь приводить любимые цитаты, потому что у меня четверть книги желтая от хайлайтов. Если вы вдруг касаетесь сферы образования — прочитайте эту книгу. Возможно, она изменит вашу жизнь.
January 27, 2019
*4.5
(Note that I’ve liberally repurposed some quotes from the book in my notes to self, which I then copied here. No plagiarism is intended.)
Raising an eyebrow at the description, I approached this book cautiously, unconvinced by the “algorithmic thinking” craze in education and fully unenthused by the prospect of teaching small children to program a “turtle” to draw shapes on a screen. (For some context, I was underwhelmed with my own experiences in LOGO, and was generally wary of another nonfiction book wherein the author hits the reader repeatedly with his sledgehammer of a thesis without regard to objectivity or good epistemic practice.)
TL;DR, Papert argues for an educational paradigm shift that can be catalyzed [only] by computers. His thesis is actually twofold: (1) learning happens through the improvement of our mental models and (2) computers are the best/a very good way to mediate this kind of learning.
Everything Papert went on to say about (1) resonated with me; what he said about (2) had either already come true, or I was (initially) quite skeptical about. Yet though Mindstorms was published in 1980, the accuracy of some of its predictions lent the rest of his reasoning much credibility. [For instance, he spends much time defending ideas like: programming need not be a recondite discipline; computers would catalyze the emergence of new ideas; computers would carry these ideas into a world larger than a research lab (e.g. via the ubiquitousness of today’s Internet).] So I read on.
*I. Learning in general*
Epistemology is the theory of knowledge. Usually, the term describes the study of the conditions of validity of knowledge. Here though, Papert talks of Piaget’s epistemology, concerned not with the validity of knowledge but rather with its origin and growth – what he terms “genetic epistemology.”
Basically, the claim is that people have a collection of models in their heads. These models/heuristics constitute what they know about the world. Accordingly, learning anything is easy if one can assimilate it to their collection of models. It further follows that what an individual can learn (and how he learns it) depends on what models and real-world data they have available. Papert argues for more “Piagetian learning” in schools, optimizing for conditions under which new models can take root.
Educators should understand the nature of this “natural” learning. It notably does not mean regurgitating information, or any kind of tabula rasa/teacher-filling-empty-minds-of-students model. These natural learning paths include “false” theories. New and old knowledge sometimes contradict, and effective learning requires strategies to deal with this conflict. That is, sometimes we encounter data inconsistent with our expectations, or when our intuition fails us. In these situations we need to improve our intuition. Education is about learning to improve this intuition/mental model collection. Sometimes the conflicting pieces of knowledge can be reconciled, sometimes one or the other must be abandoned, and sometimes the two can both be safely kept around in separate mental compartments – and all this is normal.
In traditional schools, though, children are being force-fed “correct” theories well before they are ready to invent them, before their intuition says anything at all, and well before they care about the question the facts are addressing. After all, it’s easy to take truth for granted (in a “well, that obvious” way) without having had to derive it in the first place. For instance, natural selection seems “obvious” when it’s taught in an introductory biology class, but many very smart people didn’t believe it back in the 1800s, and nobody verbalized before Darwin either. Or how about when Descartes invented his grid? I don’t think about coordinates non-Cartesianly anymore, but even this was apparently once unintuitive enough that it had to be invented. (I’ll come back to this point in a bit.)
It’s also worth noting that timescales of this learning are very hard to measure. In particular, there are experiences we have that have disproportionately large or far-reaching consequences, but only many years later. At the end of the day, an educator ought to remember that what they see is not the learning itself; they can never access the full picture. What’s going on in students’ minds is often hard to access. Students need practice becoming aware of and communicating their thought process. After all, the root of “education” is Latin’s ēdūcere – to draw out the existing knowledge (and models) in children’s heads (as opposed to “teaching how to think” per se – students already do this naturally!). Yet in a system centered around test results and measurable outcomes, Piagetian learning is all but ignored.
*II. The Context of learning*
How we think about knowledge affects how we think about ourselves. Students are exposed to a range of (potentially arbitrary) labels: STEM/humanities; smart/dumb; freshman/senior.
People who believe they are “good at X” and [therefore] “bad at Y” may then view Y as foreign and “other”. These students self-report “making their head go blank” to memorize Y. In doing so, they encode a factoid in isolation, missing out on potential connections. Yet to learn something, one must 1) relate new thing to something they already know and then 2) make the new thing their own. Imagine learning a foreign language by only memorizing a random list of vocabulary without building sentences or conversing! How pointless that seems, and how transient the knowledge. And to draw links between things, they must seem meaningful instead of arbitrary.
There’s an overall lack of genuineness in traditional schooling. Why learn the parts of speech in elementary school? The distinction is pretty pointless, unless, for instance, you’re going to try to make a program produce reasonable sentences. The reasons must be real. When a teacher tells a student that the reason for those many hours of arithmetic is to check change or calculate tip, or that “math is used in all jobs”, that’s ridiculous. It’s just another instance of that unnecessary dishonesty in the educational relationship (along the lines of “let’s do that together” when the teacher already knows the answer). Discovery cannot be a setup; invention cannot be scheduled. The flow of ideas should not be one way street. How long I waited for “growing up”, only to find that real-world adults (or researchers!) didn’t really know better, and were nearly as confused as the rest of us.
It’s worth noting that “genuine” doesn’t have to mean “real-world”. For some, the game is scoring grades; for others it is outsmarting the system. For many, school math is enjoyable in its repetitiveness, precisely because it is so mindless and dissociated. But just because people can find meaning in intrinsic dullness is not a reason to avoid improving. Papert claims a good learning environment is where real, socially cohesive, and where experts and novices are all learning together. Learning should not feel compartmentalized or arbitrarily partitioned, and “in-school” time should be as enjoyable as “out of school” time (e.g. clubs, the things people choose to work on on their own).
As a final story, imagine that children were forced to spend an hour a day drawing dance steps on squared paper and had to pass tests in these “dance facts” before they were allowed to dance physically. Would we not expect the world to be full of “dance-phobes”? Would we say that those who made it to the dance floor and music had the greatest “aptitude for dance”? It is no more appropriate to draw conclusions about mathematical aptitude from children’s unwillingness to spend hundreds of hours doing sums.
*III. The traditional system sucks*
Papert forewarns that the human-computer interface needs to be implemented with care and intent, lest historical accidents lead to strange side effects. That is, in developing a new system/technology, it’s worth putting some time into making sure it’s actually doing what’s intended before wider implementation. For instance, BASIC is a lot less readable than Python, and if it became the standard (as it was for some years), programming might look very different today. He also talks about how QWERTY sucks (though maybe this is an urban legend), and how humanity was a bit hasty during the Industrial Revolution. Education is no different.
School is a set of historical accidents. A committee of 10 people decided the standard curriculum; it’s said that we often learn science in the order “biology, chemistry, physics” only because these were listed in alphabetical order. Likewise, a major factor that determined what math went into the standards was what could be done in a classroom with pencil and paper (e.g. I’d agree graphing parabolas is not particularly fundamental to understanding math).
To avoid this, Papert advocates identifying for every subject X the difference between “school X”, “proto X” (knowledge about X presupposed by school X), and “missing X” (what students should understand about X that is not in school X). He notes that education should probably be rethought entirely; the car was not made by gradually trying to improve the horse and carriage. Only looking at what already exists is insufficient.
Not only is school bad, but research to improve it also in a rough spot. There is no recognized place in academia for e.g. people whose research is really physics, but in educationally meaningful directions. Such people are not particularly welcome in a physics department, as their education goals trivialize their work in the eyes of other physicists. Nor are they welcome in the education school, where their highly technical language is not understood and their research criteria are out of step. These hypothetical physicists will see their work very differently, as a theoretical contribution to physics that in the long run will make knowledge of the physical universe more accessible, but which in the short run would not be expected to improve performance of students in a physics course. The concept of a serious enterprise of making science for the people was, at the time of writing, quite alien. (And perhaps still is. That makes me very sad – for once, research that would interest me! but apparently nobody’s hiring.)
*IV. Computers can help*
Okay, I was on board so far. But Papert argues that the computer in particular is a likely panacea. Computers, he argue, cross cultural barriers and make scientific knowledge intimately part of individuals’ lives, personalizing otherwise obscure facts. Initially, I viewed his comments akin to how famous physicists fell in love with radio sets or cars. Because of the computer’s simulation capabilities, he considers them universal vectors for cultural seeds, and cultural assimilation is inculcation of a way fo thinking.. (Perhaps he foretells the Internet.) Children appropriate all the things in their environments (e.g. the models cherished, the metaphors and connections drawn) to build their own, and when the computer becomes ubiquitous, children will have access to better data for better models.
His argument became convincing with the following line: “in teaching the computer how to think, children embark on an exploration about how they themselves think…Thinking about thinking turns the child into an epistemologist”. He continues drawing more connections between good learning and programming: debugging gives students a growth mindset (turning the dichotomy from “right/wrong” into “fixable/not”), and also forces students to verbalize what exactly the next step is or should be. (That is, getting a computer to do something requires the underlying process be described with enough precision to be carried out by the machine.) Students may learn to have the discipline to think before mindlessly calculating (pseudocoding, at least to some extent, before typing). Even if computers are not the only way to learn this skill, I admit it’s a pretty transparent and accessible way to start being articulate about debugging strategies.
As learners become experts in any field, they have not just the object-level facts, but the connections/network between them. Papert speaks of how “expert learners” use certain metaphors to talk about important learning experiences. They talk about “getting to know” an idea, “exploring” a field, and acquiring sensitivity to distinctions that seemed ungraspably subtle just a moment ago. That is, learning about developing aesthetic and taste! But to do that, one needs many examples to “machine learn” off of. Computers can provide those simulation worlds, giving children the relevant data/training set.
But computers don’t just help by simulating. Papert believes the computer is much more than a tool for pre-programmed instruction – and thus fundamentally different from the fuss the invention of the radio or TV created in education. Instead, he says that its importance is computing culture and computational thinking. Computers facilitate the Piagetian learning that takes places as a child grows up. But “teaching without curriculum” does not mean spontaneous, freeform classrooms or simply leaving a child alone. In this model, educational intervention means supporting children as they build their own intellectual structures with materials drawn from the surrounding culture, a culture educators can add constructive elements to and eliminate noxious ones from. (That is, educators ought to feed the student-evidentialist good data.)
He adds that the vocabulary CS introduced is a key part of its culture. In general, people need more structured ways to talk and think about the learning of skills. Many scientific and mathematical advances have served a similar linguistic function by giving us words and concepts (models) to describe what had previously seemed too amorphous for systematic thought. Why is it, he asks, that children are unable to systematically and accurately list all the possible combinations of colored beads until 5th or 6th grade [citation needed]? (This was shocking.) He claims this is because there was no commonly used vocabulary for things like “bug”, “nested loops”, or “double-counting”. Our culture, he claims, is poor in models of systematic procedures. With computers, children can learn to be systematic before they learn to be quantitative.
[I’m a fan of the argument that vocabulary influences thinking (weak Sapir-Whorf). Much of the value in reading TFaS, for instance, was getting a library of labels for cognitive biases. CFAR vocabulary (“debugging”) is suggestive of the impacts CS has had on “rationality”. But can you acquire such vocabulary through some metacognatively rich approach that doesn’t so heavily rely on computers? I’m not against computers per se – just unconvinced they’re a necessary or even optimal ingredient).]
So is learning systematic/”algorithmic” thinking the only way forward? No. While curriculum reformers are often concerned about making the choice between learning strategies X and Y choice from above and building it into the curriculum, what Papert hopes for is for learners to learn how to make that choice for themselves. He considers algorithmic thinking a tool among many, and wants learners to become expert in recognizing and choosing among varying styles of thought. No knowledge is entirely reducible to words, and no knowledge is entirely ineffable – having the vocabulary for this mode of thinking isn’t a panacea after all. But still, an important part of becoming a good learner is learning how to push out the frontier of what we can express with words.
*V. Lingering inchoate thoughts*
Throughout, I wondered about other ways to introduce algorithmic thinking. Math was an obvious one. But I also wondered how much of my anti-algorithmic-thinking view was just viewing CS as bashy and math as elegant – after all, whenever Papert spoke of implementation via math instead of CS, I had no issues. Am I just biased against CS? Why? I don’t even mind casework – in math, at least…
I also wasn’t convinced by the claims that students who learn CS will learn to favor modularity. A working program can certainly be bashy, and I’m not convinced people will clean it up by default. At SSP, students produced some nasty, convoluted code to avoid learning how to e.g. write a for loop. (That is, S1 tries to minimize effort, even if the process ends up taking longer.) I grudgingly agree this is fine insofar as students will always produce stuff they understand instead of regurgitating things they don’t, but I’m not sure they’ll push themselves to do it better. Papert depicts what I agree an optimal learning situation looks like, and I agree that subdividing problems into simpler steps is a good metacognitive technique that CS might, in the right circumstances, promote. But how does theory translate to practice? How should educators implement these ideas? Ah well, I suppose that’s beyond the scope of his book.
Papert’s computer “microwords” and simulations are artificial – that is, deliberately invented – Piagetian material. Indeed, they function as carriers of powerful ideas for learners, separating the powerful big ideas from their inaccessible formalisms. His microworlds are stripped of complexity and is graspable. Debugging is most effective when the modules are small enough for it to be unlikely that any one contains more than one bug. Skills and discrete facts are easy to teach and learn one at a time. [E.g. it’s easy to teach people to associate “protein” with “amino acid”, but hard to give them the whole network of knowledge without throwing the (not-necessarily-proverbial) textbook at them.] In some ways, this feels similar to replacing Shakespeare with simplified text. Do I agree with this technique in general? Not sure. (My literature sensibilities scream no, but I admit I do this when teaching biology and chemistry.) Distilling something to its core & stripping away all the exceptions makes the inaccessible (to the point of arcane, really) enjoyable for a larger audience, which seems at the very least like a reasonable entry point.
A big concern throughout was this notion of “over-scaffolding”, or breaking things down for learners too much. In coming up with the perfect analogy or model for a learner, I’m doing the cognitive lifting, leaving them only the bite-sized, standards-focused, overly-predigested pieces. Am I oversimplifying? Do students just chalk the existence of such models to magic? – Then again, is that not what we do with real world phenomena? At some layer, perhaps it gets axiomatic…
Maybe more struggle would be better: there’s benefit in things that are just hard. I think [some] SSP students build character (or at least learn something valuable) in their struggles.
And what if students break the concept down into small parts and understand the units but never chunk upward? – if they understand each line without seeing the bigger picture. How do you make students generalize reflect upon what they’ve learned? Is it really as simple as feeding evidentialists good evidence? Are people even good evidentialists to begin with?! Do people really strive to be logically consistent by default??
Blah. I suppose some of this depends on what the learning goal is. In general, scaffolds should support the goal and clear away unnecessary underbrush. Thus, it's worth keeping in mind that the point isn't teaching the content, but rather improving students' metacognitive skills. This is why I can't make learning e.g. astrophysics too easy for SSPers. This way, students can practice their own meta-skills and figure out how to learn better themselves, in situations beyond the models given in the classroom.
(Note that I’ve liberally repurposed some quotes from the book in my notes to self, which I then copied here. No plagiarism is intended.)
Raising an eyebrow at the description, I approached this book cautiously, unconvinced by the “algorithmic thinking” craze in education and fully unenthused by the prospect of teaching small children to program a “turtle” to draw shapes on a screen. (For some context, I was underwhelmed with my own experiences in LOGO, and was generally wary of another nonfiction book wherein the author hits the reader repeatedly with his sledgehammer of a thesis without regard to objectivity or good epistemic practice.)
TL;DR, Papert argues for an educational paradigm shift that can be catalyzed [only] by computers. His thesis is actually twofold: (1) learning happens through the improvement of our mental models and (2) computers are the best/a very good way to mediate this kind of learning.
Everything Papert went on to say about (1) resonated with me; what he said about (2) had either already come true, or I was (initially) quite skeptical about. Yet though Mindstorms was published in 1980, the accuracy of some of its predictions lent the rest of his reasoning much credibility. [For instance, he spends much time defending ideas like: programming need not be a recondite discipline; computers would catalyze the emergence of new ideas; computers would carry these ideas into a world larger than a research lab (e.g. via the ubiquitousness of today’s Internet).] So I read on.
*I. Learning in general*
Epistemology is the theory of knowledge. Usually, the term describes the study of the conditions of validity of knowledge. Here though, Papert talks of Piaget’s epistemology, concerned not with the validity of knowledge but rather with its origin and growth – what he terms “genetic epistemology.”
Basically, the claim is that people have a collection of models in their heads. These models/heuristics constitute what they know about the world. Accordingly, learning anything is easy if one can assimilate it to their collection of models. It further follows that what an individual can learn (and how he learns it) depends on what models and real-world data they have available. Papert argues for more “Piagetian learning” in schools, optimizing for conditions under which new models can take root.
Educators should understand the nature of this “natural” learning. It notably does not mean regurgitating information, or any kind of tabula rasa/teacher-filling-empty-minds-of-students model. These natural learning paths include “false” theories. New and old knowledge sometimes contradict, and effective learning requires strategies to deal with this conflict. That is, sometimes we encounter data inconsistent with our expectations, or when our intuition fails us. In these situations we need to improve our intuition. Education is about learning to improve this intuition/mental model collection. Sometimes the conflicting pieces of knowledge can be reconciled, sometimes one or the other must be abandoned, and sometimes the two can both be safely kept around in separate mental compartments – and all this is normal.
In traditional schools, though, children are being force-fed “correct” theories well before they are ready to invent them, before their intuition says anything at all, and well before they care about the question the facts are addressing. After all, it’s easy to take truth for granted (in a “well, that obvious” way) without having had to derive it in the first place. For instance, natural selection seems “obvious” when it’s taught in an introductory biology class, but many very smart people didn’t believe it back in the 1800s, and nobody verbalized before Darwin either. Or how about when Descartes invented his grid? I don’t think about coordinates non-Cartesianly anymore, but even this was apparently once unintuitive enough that it had to be invented. (I’ll come back to this point in a bit.)
It’s also worth noting that timescales of this learning are very hard to measure. In particular, there are experiences we have that have disproportionately large or far-reaching consequences, but only many years later. At the end of the day, an educator ought to remember that what they see is not the learning itself; they can never access the full picture. What’s going on in students’ minds is often hard to access. Students need practice becoming aware of and communicating their thought process. After all, the root of “education” is Latin’s ēdūcere – to draw out the existing knowledge (and models) in children’s heads (as opposed to “teaching how to think” per se – students already do this naturally!). Yet in a system centered around test results and measurable outcomes, Piagetian learning is all but ignored.
*II. The Context of learning*
How we think about knowledge affects how we think about ourselves. Students are exposed to a range of (potentially arbitrary) labels: STEM/humanities; smart/dumb; freshman/senior.
People who believe they are “good at X” and [therefore] “bad at Y” may then view Y as foreign and “other”. These students self-report “making their head go blank” to memorize Y. In doing so, they encode a factoid in isolation, missing out on potential connections. Yet to learn something, one must 1) relate new thing to something they already know and then 2) make the new thing their own. Imagine learning a foreign language by only memorizing a random list of vocabulary without building sentences or conversing! How pointless that seems, and how transient the knowledge. And to draw links between things, they must seem meaningful instead of arbitrary.
There’s an overall lack of genuineness in traditional schooling. Why learn the parts of speech in elementary school? The distinction is pretty pointless, unless, for instance, you’re going to try to make a program produce reasonable sentences. The reasons must be real. When a teacher tells a student that the reason for those many hours of arithmetic is to check change or calculate tip, or that “math is used in all jobs”, that’s ridiculous. It’s just another instance of that unnecessary dishonesty in the educational relationship (along the lines of “let’s do that together” when the teacher already knows the answer). Discovery cannot be a setup; invention cannot be scheduled. The flow of ideas should not be one way street. How long I waited for “growing up”, only to find that real-world adults (or researchers!) didn’t really know better, and were nearly as confused as the rest of us.
It’s worth noting that “genuine” doesn’t have to mean “real-world”. For some, the game is scoring grades; for others it is outsmarting the system. For many, school math is enjoyable in its repetitiveness, precisely because it is so mindless and dissociated. But just because people can find meaning in intrinsic dullness is not a reason to avoid improving. Papert claims a good learning environment is where real, socially cohesive, and where experts and novices are all learning together. Learning should not feel compartmentalized or arbitrarily partitioned, and “in-school” time should be as enjoyable as “out of school” time (e.g. clubs, the things people choose to work on on their own).
As a final story, imagine that children were forced to spend an hour a day drawing dance steps on squared paper and had to pass tests in these “dance facts” before they were allowed to dance physically. Would we not expect the world to be full of “dance-phobes”? Would we say that those who made it to the dance floor and music had the greatest “aptitude for dance”? It is no more appropriate to draw conclusions about mathematical aptitude from children’s unwillingness to spend hundreds of hours doing sums.
*III. The traditional system sucks*
Papert forewarns that the human-computer interface needs to be implemented with care and intent, lest historical accidents lead to strange side effects. That is, in developing a new system/technology, it’s worth putting some time into making sure it’s actually doing what’s intended before wider implementation. For instance, BASIC is a lot less readable than Python, and if it became the standard (as it was for some years), programming might look very different today. He also talks about how QWERTY sucks (though maybe this is an urban legend), and how humanity was a bit hasty during the Industrial Revolution. Education is no different.
School is a set of historical accidents. A committee of 10 people decided the standard curriculum; it’s said that we often learn science in the order “biology, chemistry, physics” only because these were listed in alphabetical order. Likewise, a major factor that determined what math went into the standards was what could be done in a classroom with pencil and paper (e.g. I’d agree graphing parabolas is not particularly fundamental to understanding math).
To avoid this, Papert advocates identifying for every subject X the difference between “school X”, “proto X” (knowledge about X presupposed by school X), and “missing X” (what students should understand about X that is not in school X). He notes that education should probably be rethought entirely; the car was not made by gradually trying to improve the horse and carriage. Only looking at what already exists is insufficient.
Not only is school bad, but research to improve it also in a rough spot. There is no recognized place in academia for e.g. people whose research is really physics, but in educationally meaningful directions. Such people are not particularly welcome in a physics department, as their education goals trivialize their work in the eyes of other physicists. Nor are they welcome in the education school, where their highly technical language is not understood and their research criteria are out of step. These hypothetical physicists will see their work very differently, as a theoretical contribution to physics that in the long run will make knowledge of the physical universe more accessible, but which in the short run would not be expected to improve performance of students in a physics course. The concept of a serious enterprise of making science for the people was, at the time of writing, quite alien. (And perhaps still is. That makes me very sad – for once, research that would interest me! but apparently nobody’s hiring.)
*IV. Computers can help*
Okay, I was on board so far. But Papert argues that the computer in particular is a likely panacea. Computers, he argue, cross cultural barriers and make scientific knowledge intimately part of individuals’ lives, personalizing otherwise obscure facts. Initially, I viewed his comments akin to how famous physicists fell in love with radio sets or cars. Because of the computer’s simulation capabilities, he considers them universal vectors for cultural seeds, and cultural assimilation is inculcation of a way fo thinking.. (Perhaps he foretells the Internet.) Children appropriate all the things in their environments (e.g. the models cherished, the metaphors and connections drawn) to build their own, and when the computer becomes ubiquitous, children will have access to better data for better models.
His argument became convincing with the following line: “in teaching the computer how to think, children embark on an exploration about how they themselves think…Thinking about thinking turns the child into an epistemologist”. He continues drawing more connections between good learning and programming: debugging gives students a growth mindset (turning the dichotomy from “right/wrong” into “fixable/not”), and also forces students to verbalize what exactly the next step is or should be. (That is, getting a computer to do something requires the underlying process be described with enough precision to be carried out by the machine.) Students may learn to have the discipline to think before mindlessly calculating (pseudocoding, at least to some extent, before typing). Even if computers are not the only way to learn this skill, I admit it’s a pretty transparent and accessible way to start being articulate about debugging strategies.
As learners become experts in any field, they have not just the object-level facts, but the connections/network between them. Papert speaks of how “expert learners” use certain metaphors to talk about important learning experiences. They talk about “getting to know” an idea, “exploring” a field, and acquiring sensitivity to distinctions that seemed ungraspably subtle just a moment ago. That is, learning about developing aesthetic and taste! But to do that, one needs many examples to “machine learn” off of. Computers can provide those simulation worlds, giving children the relevant data/training set.
But computers don’t just help by simulating. Papert believes the computer is much more than a tool for pre-programmed instruction – and thus fundamentally different from the fuss the invention of the radio or TV created in education. Instead, he says that its importance is computing culture and computational thinking. Computers facilitate the Piagetian learning that takes places as a child grows up. But “teaching without curriculum” does not mean spontaneous, freeform classrooms or simply leaving a child alone. In this model, educational intervention means supporting children as they build their own intellectual structures with materials drawn from the surrounding culture, a culture educators can add constructive elements to and eliminate noxious ones from. (That is, educators ought to feed the student-evidentialist good data.)
He adds that the vocabulary CS introduced is a key part of its culture. In general, people need more structured ways to talk and think about the learning of skills. Many scientific and mathematical advances have served a similar linguistic function by giving us words and concepts (models) to describe what had previously seemed too amorphous for systematic thought. Why is it, he asks, that children are unable to systematically and accurately list all the possible combinations of colored beads until 5th or 6th grade [citation needed]? (This was shocking.) He claims this is because there was no commonly used vocabulary for things like “bug”, “nested loops”, or “double-counting”. Our culture, he claims, is poor in models of systematic procedures. With computers, children can learn to be systematic before they learn to be quantitative.
[I’m a fan of the argument that vocabulary influences thinking (weak Sapir-Whorf). Much of the value in reading TFaS, for instance, was getting a library of labels for cognitive biases. CFAR vocabulary (“debugging”) is suggestive of the impacts CS has had on “rationality”. But can you acquire such vocabulary through some metacognatively rich approach that doesn’t so heavily rely on computers? I’m not against computers per se – just unconvinced they’re a necessary or even optimal ingredient).]
So is learning systematic/”algorithmic” thinking the only way forward? No. While curriculum reformers are often concerned about making the choice between learning strategies X and Y choice from above and building it into the curriculum, what Papert hopes for is for learners to learn how to make that choice for themselves. He considers algorithmic thinking a tool among many, and wants learners to become expert in recognizing and choosing among varying styles of thought. No knowledge is entirely reducible to words, and no knowledge is entirely ineffable – having the vocabulary for this mode of thinking isn’t a panacea after all. But still, an important part of becoming a good learner is learning how to push out the frontier of what we can express with words.
*V. Lingering inchoate thoughts*
Throughout, I wondered about other ways to introduce algorithmic thinking. Math was an obvious one. But I also wondered how much of my anti-algorithmic-thinking view was just viewing CS as bashy and math as elegant – after all, whenever Papert spoke of implementation via math instead of CS, I had no issues. Am I just biased against CS? Why? I don’t even mind casework – in math, at least…
I also wasn’t convinced by the claims that students who learn CS will learn to favor modularity. A working program can certainly be bashy, and I’m not convinced people will clean it up by default. At SSP, students produced some nasty, convoluted code to avoid learning how to e.g. write a for loop. (That is, S1 tries to minimize effort, even if the process ends up taking longer.) I grudgingly agree this is fine insofar as students will always produce stuff they understand instead of regurgitating things they don’t, but I’m not sure they’ll push themselves to do it better. Papert depicts what I agree an optimal learning situation looks like, and I agree that subdividing problems into simpler steps is a good metacognitive technique that CS might, in the right circumstances, promote. But how does theory translate to practice? How should educators implement these ideas? Ah well, I suppose that’s beyond the scope of his book.
Papert’s computer “microwords” and simulations are artificial – that is, deliberately invented – Piagetian material. Indeed, they function as carriers of powerful ideas for learners, separating the powerful big ideas from their inaccessible formalisms. His microworlds are stripped of complexity and is graspable. Debugging is most effective when the modules are small enough for it to be unlikely that any one contains more than one bug. Skills and discrete facts are easy to teach and learn one at a time. [E.g. it’s easy to teach people to associate “protein” with “amino acid”, but hard to give them the whole network of knowledge without throwing the (not-necessarily-proverbial) textbook at them.] In some ways, this feels similar to replacing Shakespeare with simplified text. Do I agree with this technique in general? Not sure. (My literature sensibilities scream no, but I admit I do this when teaching biology and chemistry.) Distilling something to its core & stripping away all the exceptions makes the inaccessible (to the point of arcane, really) enjoyable for a larger audience, which seems at the very least like a reasonable entry point.
A big concern throughout was this notion of “over-scaffolding”, or breaking things down for learners too much. In coming up with the perfect analogy or model for a learner, I’m doing the cognitive lifting, leaving them only the bite-sized, standards-focused, overly-predigested pieces. Am I oversimplifying? Do students just chalk the existence of such models to magic? – Then again, is that not what we do with real world phenomena? At some layer, perhaps it gets axiomatic…
Maybe more struggle would be better: there’s benefit in things that are just hard. I think [some] SSP students build character (or at least learn something valuable) in their struggles.
And what if students break the concept down into small parts and understand the units but never chunk upward? – if they understand each line without seeing the bigger picture. How do you make students generalize reflect upon what they’ve learned? Is it really as simple as feeding evidentialists good evidence? Are people even good evidentialists to begin with?! Do people really strive to be logically consistent by default??
Blah. I suppose some of this depends on what the learning goal is. In general, scaffolds should support the goal and clear away unnecessary underbrush. Thus, it's worth keeping in mind that the point isn't teaching the content, but rather improving students' metacognitive skills. This is why I can't make learning e.g. astrophysics too easy for SSPers. This way, students can practice their own meta-skills and figure out how to learn better themselves, in situations beyond the models given in the classroom.
February 7, 2019
When I was in middle school, we had “informatics” classes. I remember that at some point we were shown the Logo environment and were tasked with drawing various objects on the screen. I don’t remember much beside that, but if you had asked me prior to reading this book what I thought about Logo, I would have said that I don’t see how it is better than e.g. python or pascal with imported module for drawing, and Turtle is no more than a gimmick added to make the language “child-friendly.” Turns out, I did not get the ideas behind Turtle and Logo at all.
This book is not about Logo, though. Logo is just a product of the ideas in it, and a useful example to showcase them. “Mindstorms” is about how people learn and think, and what opportunities computers create for helping children with that. Of course, when you hear about computers used for teaching anything besides programming, probably the first image that pops into your mind is the one you would see in many classrooms: using computers to plot graphs of functions so as not to waste time drawing them by hand, using them for calculations, showing presentations or some visualizations, or using them to create documents instead of writing them by hand. Do you notice a thing in common among these examples? They all are not really adding anything fundamentally new—just taking a thing that we were doing before we had computers and using computers to do the same thing faster with a more appealing output. Better ink and paper, more powerful calculator, a slightly more interactive TV, a typewriter on steroids. This does not seem groundbreaking, and you certainly can’t get a radically better education out of that—these all are quantitative changes, not qualitative ones.
Papert shows a way to use computers for a qualitative difference in education: to let children learn about procedural thinking. Surprisingly, until fifth or sixth grade, given a set of beads of different colors children can’t construct a list of all “families” (unordered pairs) of these colors. This requires a systematic way of thinking, and children do not have any examples of that in their environments because our culture is not reach in necessary examples.
Computer allows us to create the only environment which can specifically teach children to think in procedures. Using computers, we could stop hoping that children would accidentally pick the procedural style of thinking up from their environments. And having this style of thinking in their toolbox could help them learn other skills more efficiently. Papert gives an example of a kid who learned to walk on stilts faster than his friend thanks to thinking in procedures and understanding the idea of debugging—he isolated and corrected the part he was doing wrong, instead of trying the same thing over and over again until he accidentally got the right movements like his friend did.
Turns out, Logo’s ultimate goal is not to teach children programming. Its goal is to teach children to think in an important new way, give them a new lens through which to look at the world, themselves, and how they learn. And Turtle itself is no gimmick—it is the main point of contact with the child, an anthropomorphizable object they can pretend to be to see where the program goes wrong, which also at the same time teaches them “powerful” geometric ideas. How do you draw a circle when you can only go forward and turn in place? Pretend to be Turtle yourself and find out how you can walk in a circle, then tell Turtle to do the same.
“Mindstorms” is 39 years old. It makes you wonder how different schools would have been today had its ideas been heard. Computers in various forms are in every home, but mathophobia Papert writes about still permeates our culture thanks to the fact that math is still being taught like it was a century ago, “debugging” is still a specialized word without synonyms, and from the outside it does not look like the situation is changing. Papert has a separate chapter on what would be required for his ideas to be implemented, and he says that the only possible source of change is the culture itself. And it looks like our culture has not been changed much by computers in the domain of education. Is it because there has not been a critical mass of parents that would be interested in such changes? Or because too few people realize that these changes are possible? Many (most?) cultural changes in the last decade happened because of tech startups: is it possible to create a viral educational app that could change our attitude towards education, math, programming? It seems to be a useful question to ponder. How could we help spread these ideas and improve education?
This is a fascinating book. It made me think about thinking, learning, psychology, programming languages, math, and I learned something new about each of these topics and their interplay between each other, and you probably will too. You should definitely read it even if you are interested in just one of these topics, and even if you are afraid of math or programming yourself. I am sure you will have much to think about afterwards.
This book is not about Logo, though. Logo is just a product of the ideas in it, and a useful example to showcase them. “Mindstorms” is about how people learn and think, and what opportunities computers create for helping children with that. Of course, when you hear about computers used for teaching anything besides programming, probably the first image that pops into your mind is the one you would see in many classrooms: using computers to plot graphs of functions so as not to waste time drawing them by hand, using them for calculations, showing presentations or some visualizations, or using them to create documents instead of writing them by hand. Do you notice a thing in common among these examples? They all are not really adding anything fundamentally new—just taking a thing that we were doing before we had computers and using computers to do the same thing faster with a more appealing output. Better ink and paper, more powerful calculator, a slightly more interactive TV, a typewriter on steroids. This does not seem groundbreaking, and you certainly can’t get a radically better education out of that—these all are quantitative changes, not qualitative ones.
It took years before designers of automobiles accepted the idea that they were cars, not “horseless carriages,” and the precursors of modern motion pictures were plays acted as if before a live audience but actually in front of a camera.
Papert shows a way to use computers for a qualitative difference in education: to let children learn about procedural thinking. Surprisingly, until fifth or sixth grade, given a set of beads of different colors children can’t construct a list of all “families” (unordered pairs) of these colors. This requires a systematic way of thinking, and children do not have any examples of that in their environments because our culture is not reach in necessary examples.
There is no word for “nested loops” and no word for double-counting bug. Indeed, there are no words for the powerful ideas computerists refer to as “bug” and “debugging.”
Computer allows us to create the only environment which can specifically teach children to think in procedures. Using computers, we could stop hoping that children would accidentally pick the procedural style of thinking up from their environments. And having this style of thinking in their toolbox could help them learn other skills more efficiently. Papert gives an example of a kid who learned to walk on stilts faster than his friend thanks to thinking in procedures and understanding the idea of debugging—he isolated and corrected the part he was doing wrong, instead of trying the same thing over and over again until he accidentally got the right movements like his friend did.
Turns out, Logo’s ultimate goal is not to teach children programming. Its goal is to teach children to think in an important new way, give them a new lens through which to look at the world, themselves, and how they learn. And Turtle itself is no gimmick—it is the main point of contact with the child, an anthropomorphizable object they can pretend to be to see where the program goes wrong, which also at the same time teaches them “powerful” geometric ideas. How do you draw a circle when you can only go forward and turn in place? Pretend to be Turtle yourself and find out how you can walk in a circle, then tell Turtle to do the same.
“Mindstorms” is 39 years old. It makes you wonder how different schools would have been today had its ideas been heard. Computers in various forms are in every home, but mathophobia Papert writes about still permeates our culture thanks to the fact that math is still being taught like it was a century ago, “debugging” is still a specialized word without synonyms, and from the outside it does not look like the situation is changing. Papert has a separate chapter on what would be required for his ideas to be implemented, and he says that the only possible source of change is the culture itself. And it looks like our culture has not been changed much by computers in the domain of education. Is it because there has not been a critical mass of parents that would be interested in such changes? Or because too few people realize that these changes are possible? Many (most?) cultural changes in the last decade happened because of tech startups: is it possible to create a viral educational app that could change our attitude towards education, math, programming? It seems to be a useful question to ponder. How could we help spread these ideas and improve education?
This is a fascinating book. It made me think about thinking, learning, psychology, programming languages, math, and I learned something new about each of these topics and their interplay between each other, and you probably will too. You should definitely read it even if you are interested in just one of these topics, and even if you are afraid of math or programming yourself. I am sure you will have much to think about afterwards.
June 23, 2020
This book was stunning, just mind blowingly awesome. I'm not going to write a long form review now, as I have to go through and process what just happened... but it's so nice to find someone who's thought out so far along the dimensions I'm interested in, and validated the road. READ MINDSTORMS!
August 2, 2016
Simply wow. People, knowledge and learning and in a book on “recasting powerful ideas that are as important to the poet as to the engineer” in an environment that is made possible thanks to computers.
It's the possibility to tell the computer what to do, to program it, that makes the huge difference (most of its “users” don’t ever use the computer that way): you can create simple and complex worlds, watch them and learn from them in rapid feedback loops—while still being able to go the tiniest detail and play with it. Abstract ideas can be seen in action and even grasped as any other natural object.
I cannot think of anybody who wouldn't benefit from reading this book.
…
“The obstacle to the growth of popular computer cultures is cultural [… and] the remedy must be cultural. The research challenge is clear. We need to advance the art of meshing computers with cultures so that they can serve to unite, hopefully without homogenizing, the fragmented subcultures that coexist counterproductively in contemporary society. For example, the gulf must be bridged between the technical-scientific and humanistic cultures. And I think that the key to constructing this bridge will be learning how to recast powerful ideas in computational form, ideas that are as important to the poet as to the engineer.”
…
“Our commitment to communication is not only expressed through our commitment to modularization, which facilitates it, but through our attempt to find a language for such domains as physics and mathematics, which have as their essence communication between constructed entities. By restating Newton's laws as assertions about how particles (…) communicate with one another, we give it a handle that can be more easily grabbed by a child or by a poet.”
…
“Educators sometimes hold up an ideal of knowledge as having the kind of coherence defined by formal logic. But these ideals bear little resemblance to the way in which most people experience themselves. The subjective experience of knowledge is more similar to the chaos and controversy of competing agents than to the certitude and orderliness of p's implying q's. The discrepancy between our experience of ourselves and our idealizations of knowledge has an effect. It intimidates us, it lessens the sense of our own competence, and it leads us into counterproductive strategies for learning and thinking.”
It's the possibility to tell the computer what to do, to program it, that makes the huge difference (most of its “users” don’t ever use the computer that way): you can create simple and complex worlds, watch them and learn from them in rapid feedback loops—while still being able to go the tiniest detail and play with it. Abstract ideas can be seen in action and even grasped as any other natural object.
“When knowledge can be broken up into ‘mind-size bites,’ it is more communicable, more assimilable, more simply constructable. The fact that we divide knowledge up into scientific and humanistic worlds defines some knowledge as being a priori uncommunicable to certain kinds of people.”
I cannot think of anybody who wouldn't benefit from reading this book.
…
“The obstacle to the growth of popular computer cultures is cultural [… and] the remedy must be cultural. The research challenge is clear. We need to advance the art of meshing computers with cultures so that they can serve to unite, hopefully without homogenizing, the fragmented subcultures that coexist counterproductively in contemporary society. For example, the gulf must be bridged between the technical-scientific and humanistic cultures. And I think that the key to constructing this bridge will be learning how to recast powerful ideas in computational form, ideas that are as important to the poet as to the engineer.”
…
“Our commitment to communication is not only expressed through our commitment to modularization, which facilitates it, but through our attempt to find a language for such domains as physics and mathematics, which have as their essence communication between constructed entities. By restating Newton's laws as assertions about how particles (…) communicate with one another, we give it a handle that can be more easily grabbed by a child or by a poet.”
…
“Educators sometimes hold up an ideal of knowledge as having the kind of coherence defined by formal logic. But these ideals bear little resemblance to the way in which most people experience themselves. The subjective experience of knowledge is more similar to the chaos and controversy of competing agents than to the certitude and orderliness of p's implying q's. The discrepancy between our experience of ourselves and our idealizations of knowledge has an effect. It intimidates us, it lessens the sense of our own competence, and it leads us into counterproductive strategies for learning and thinking.”
March 18, 2013
Really inspiring book about learning and teaching and computers. The author, Seymour Papert, invented LOGO and wrote this book about how he thinks we think and how we can learn to think better by building knowledge cumulatively.
He describes the mind as essentially a multitude of small rules that generally add to much more than we prune, or even modify. Understanding then is mostly a processes of apply old rules to new situations, and deciding which ones are useful in thinking about this new thing and which ones aren't.
This is illustrated in the book with a story about how children learn about preservation of volumes. It is a developmental milestone when a child can watch the water in a skinny glass poured into a fat glass and say "there is the same amount of water in the big glass as there was in the small one". We don't unlearn the rule "higher water level means more water" we just add "if we don't add or subtract water, then there must be the same amount of water".
He presents this all more elegantly than I, but there you go. His whole thesis really jells well with my current theory that the most basic thing the human brain can do is determine how two things are alike and unalike.
He describes the mind as essentially a multitude of small rules that generally add to much more than we prune, or even modify. Understanding then is mostly a processes of apply old rules to new situations, and deciding which ones are useful in thinking about this new thing and which ones aren't.
This is illustrated in the book with a story about how children learn about preservation of volumes. It is a developmental milestone when a child can watch the water in a skinny glass poured into a fat glass and say "there is the same amount of water in the big glass as there was in the small one". We don't unlearn the rule "higher water level means more water" we just add "if we don't add or subtract water, then there must be the same amount of water".
He presents this all more elegantly than I, but there you go. His whole thesis really jells well with my current theory that the most basic thing the human brain can do is determine how two things are alike and unalike.
July 23, 2019
There are few books inspiring enough that they can define a reader's career. Mindstorms presents a deep, fundamental problem in the education system of now, and provides a grounded toolkit and beautiful vision to construct what education could become. The book's age only speaks to the timelessness of its vastly unimplemented ideas. It is remarkable how much work is left to be done in this space.
April 1, 2013
Educators, read this.
March 25, 2017
Non potrei essere più d'accordo!
July 6, 2021
FORWARD by Mitchel Resnick
In Mindstorms, Seymour offered a radically different vision. For Seymour, computers were not a replacement for the teacher but a new medium that children could use for making things and expressing themselves.
Seymour was certainly interested in machines and new technologies, but only insofar as they could support learning or lead to new insights about learning. P.viii
The theory [constructionism] builds on the work of Jean Piaget, the great child-development pioneer, who Seymour had collaborated with in the early 1960s. Piaget’s great insight was that knowledge in not delivered from teacher to learner; rather, children are constantly constructing knowledge through their everyday interactions with people and objects around them...children construct knowledge most effectively when they are actively engaged in constructing things in the world….and computational technologies can greatly expand the range of what and how children create. P.ix
He wanted to support children not only in developing their thinking but also in developing their voice. Seymour saw the computer not just as a problem-solving tool but as an expressive medium. Seymour wanted to help all children, from all backgrounds, have opportunities to express and share their ideas so that they could be full and active participants in society. P.x
Seymour was interested in applying ideas from AI to engage children in thinking about their own thinking-and learning about their own learning.
Four guiding principles:
Projects: (EP?) Seymour argued that it is best for children to learn new ideas through working on projects, not before working on projects.
Passion: “Education has very little to do with explanation, it has to do with engagement, with falling in love with the material.”
Peers: Importance of social dimension of learning.
Play: Play is experimenting, taking risks, testing the boundaries, and iteratively adapting when things go wrong. Play is “hard fun”...children are very willing to work hard on things that they find meaningful.
Seymour’s ideas provide children with more opportunities to explore, experiment, and express themselves, so that they can develop as creative thinkers.
PREFACE (Seymour Papert)
When I read Piaget I was struck by the fact that his discussion does not do full justice to his own idea. He talks almost entirely about cognitive aspects of assimilation. But there is also an affective component. p.xvi
Anything is easy if you can assimilate it to your collection of models. p.xvii
It is the double relationship of the abstract and sensory that give the gear the power to carry powerful mathematics into the mind. In a terminology I shall develop in later chapters, the gear acts here as a transitional object.
The computer is the Proteus of machines. Its essence is its universality, its power to simulate. Because it can take on a thousand forms and can serve a thousand functions, it can appeal to a thousand tastes. This book is the result of my own attempts over the past decade to turn computers into instruments flexible enough so that many children can each create for themselves something like what the gears were for me. p.xvii
INTRODUCTION
In this book I discuss ways in which the computer presence could contribute to mental processes not only instrumentally but in more essential, conceptual ways, influencing how people think even when they are far removed from physical contact with a computer.
This book is about how computers can be carriers of powerful ideas and of the seeds of cultural change, how they can help people form new relationships with knowledge.
...can we construct intellectual environments in which people who today think of themselves as “humanists” will feel part of, not alienated from, the process of constructing computational cultures.
My image does not go beyond: It goes in the opposite direction. p.3
[technology IS affective---how are we noticing that?]
Two fundamental ideas run through this book. The first is that it is possible to design computers so that learning to communicate with them can be a natural process. Second, learning to communicate with a computer man change the way other learning takes place. p.4
I believe that the computer presence will enable us to so modify the learning environment outside the classroom that much if not all the knowledge schools presently try to teach with such pain and expense and such limited success will be learned, as the child learns to talk, painlessly, successfully, and without organized instruction. This obviously implies that schools as we know them today will have no place in the future. But it is an open question whether they will adapt by transforming themselves into something new or wither away and be replaced.
Although technology will play an essential role in the realization of my vision of the future of education, my central focus is not on the machine but on the mind, and particularly on the way in which intellectual movements and cultures define themselves and grow. Indeed, the role I give to the computer is that of a carrier of cultural “germs” or “seeds” whose intellectual products will not need technological support once they take root in an actively growing mind. p.8
Thus this book is really about how a culture, a way of thinning, an idea comes to inhabit a young mind. p.9 [gears]
My goal has been the design of other objects that children can make theirs for themselves and in their own ways. p.10
[The “turtle” is his “object-to-think-with”...could EP function as “turtle”...transitional object?]
My interest is in the process of invention of “objects-to-think-with”, objects in which there is an intersection of cultural presence, embedded knowledge, and the possibility for personal identification. p.11
My vision of a new kind of learning environment demands free contact between children and computers. p.16
...and can provide children with new possibilities for learning, thinking, and growing emotionally as well as cognitively. I want my readers to be very clear that what is “utopian” in my vision and in this book is particular way of using computers, of forging new relationships between computers and people. p.18
CHAPTER 1
When a child learns to program [build EP], the process of learning is transformed. It becomes more active and self-directed. In particular, the knowledge is acquired for a recognizable personal purpose. The child does something with it. The new knowledge is a source of power and is experienced as such from the moment it begins to form in the child’s mind. p.21
Knowledge that was accessible only through formal processes can now be approached concretely. And the real magic comes from the fact that this knowledge includes those elements one needs to become a formal thinker. [model+content] p.22
[Building an EP] children are learning to think articulately about thinking.
Programming the [EP] starts by making one reflect on how one does oneself what one would like the [EP] to do. p.29
[How has technology shaped children’s identity as writers? Thinkers? Actual cognition?]p.32
I believe that the computer as a writing instrument offers children an opportunity to become more like adults, indeed like advanced professionals, in their relationship to their intellectual products and to themselves. p.33
The first use of the new technology is quite naturally to do in a slightly different way what had been done before without it. It took years before designers of automoviles accepted the idea that they were cars, not “horseless carriages”, and the precursors of modern motion pictures were plays acted as if before a live audience but actually in front of a camera. A whole generation was needed for the new art of motion pictures to emerge as something quite different from a linear mix of theatre plus photography. Most of what has been done up to now under the name “educational technology” or “computers in education” is still at the stage of the linear mis of old instructional methods with new technologies. p.40
Very few with the imagination, creativity, and drive to make great new inventions enter the field of education. Most of those who do are soon driven out in frustration. Conservatism in the world of education has become a self-perpetuating social phenomenon….but computers are able to offer an open marketplace directly to consumers. There will be new opportunities for imagination and originality. There might be a renaissance of thinking about education. p.41
CHAPTER 2
All this is done through what I have called Piagetian learning, a learning process that has many features the schools should envy: It is effective (all children get there), it is inexpensive (it seems to require neither teacher or curriculum development), and it is humane (the children seem to do it in a carefree spirit without explicit external rewards and punishment). p.47
[If one’s strength is language, but lack mathematical vocabulary or a sense of purpose grows a hatred of math.] I am convinced that what shows up as intellectual weakness very often grows out of intellectual strengths. And it is not only verbal strengths that undermine others. Every careful observer of children must have seen similar processes working in different directions: For example, a child who has become enamored of logical order is set up to be turned off by English spelling and to go on from there to develop a global dislike for writing. p.52
Some of the historical reasons for school math had to do with what was learnable and teachable in the precomputer epoch. [WHY DO WE LEARN WHAT WE LEARN IN MATH?!] p.59
Very few people ever suspect that the reason for what is included and what is not included in school math might be as crudely technological as the ease of production of parabolas with pencils! p.60
A dignified mathematics for children cannot be something we permit ourselves to inflict on children, like unpleasant medicine, although we see no reason to take it ourselves. p.62
CHAPTER 3
For most children numbers have to be explored, and doing so is an exciting and playful process. p.65
How can we write about math, and science...in language arts? To develop a language for math...THERE ARE WORDS FOR MATH!
CHAPTER 4
[We will be better able to teach the problems and purposes of the EP when we have learned its language ourselves.]
An important part of becoming a good learner is learning how to push out the frontier of what we can express with words. The central theme of this chapter is the development of descriptive languages for talking about learning. p.106
If we can find an honest place for scientific thinking in activities that the child feels are important and personal, we shall open the doors to a more coherent, syntonic pattern of learning. p.107
The use of programming concepts as a descriptive language facilitates debugging. p.125
Errors benefit us because they lead us to study what happened, to understand what went wrong and, through understanding, to fix it. Experience with computer programming leads children more effectively than any other activity to “believe in” debugging. p.126
[MISTAKES AS LEARNING OPPORTUNITIES]
[BUILDING AN EP INVOLVED CORRECTING MISTAKES - THE TEST PROCESS IS LEARNING]
The LOGO environment [or the learning environment created when building an EP] is special because it provides numerous problems that elementary school children can understand with a kind of completeness that is rare in ordinary life. p.128
DEPTH AND COMPLEXITY
The internal intelligibility of computer worlds offers children the opportunity to carry out projects of greater complexity that are usually possible in the physical world. Many children imagine complex structures they might build with an erector set or fantasize about organizing friends into complex enterprises. But when they try to realize such projects, they too soon run into the unintelligible limitations of matter and people. Because computer programs can in principle be made to behave exactly as they are intended to, they can be combined more safely into complex systems. Thus, children are able to acquire a feel for complexity.p.131
CHAPTER 5
First, relate what is new and to be learned to something you already know. Second, take what is mew and make it your own. P.133
CHAPTER 6
Learning that vs. learning how.
Working in [EP] microworlds is a model for what it is to get to know an idea the way you get to know a person. [could the EP be even more?] p.153
Everyone must acquire skill at getting to know and a personal style for doing it.
The idea is that early experience with [EPs] is a good way to ‘get to know’ what it is like to learn a formal subject by ‘getting to know’ its powerful ideas.
[The EP as epistemology?] p.154
It is of a kind with the intuitive and informal, but often very powerful, ideas that inhabit all of our heads whether we are children or physicists.
The need for drill and practice in arithmetic is a symptom of the absence of conditions for the syntonic learning of mathematics.
Traditional physics teaching is forced to overemphasize the quantitative by the accidents of a paper-and-pencil technology which favors work that can produce a definite “answer”. p.156
[Importance of understanding intuition.] What the student needs is a better understanding of himself...to know why his intuition gives him a wrong expectation. He needs to know how to work on his intuitions in order to change them when they are wrong. p.162
I want you to go away from this book with a new sense of a child’s value as a thinker, even as an ‘epistemologist’ with a notion of the power of powerful ideas. p.169
As educators we can help by creating the conditions for children to use procedural thinking effectively and joyfully. p.173
CHAPTER 7
The aim of AI is to give concrete form to ideas about thinking that previously might have seemed abstract, even metaphysical.
I believe the ability to articulate the processes of thinking enables us to improve them. p.177
In my own thinking I have placed a greater emphasis on two dimensions implicit but not elaborated in Piaget’s own work: an interest in intellectual structures that could develop as opposed to those that actually at present do develop in the child, and the design of learning environments that are resonant with them. The [EP] can be used to illustrate both of these interests; first, the identification of powerful set of [linguistic]ideas that we do not presume to be represented, at least not in a developed form, in children; second, the creation of a transitional object, the [EP], that can exist in the child’s environment and make contact with the ideas. p.181
Working with computers can make it more apparent that children construct their own personal microworlds. p.182
Traditional epistemology has often been taken as a branch of philosophy Genetic epistemology worlds to assert itself as a science. Its students gather data and develop theories about how knowledge developed, sometimes focusing on the evolution of knowledge in history, sometimes on the evolution of knowledge in the individual. But it does not see the two realms as distinct: It seeks to understand relations between them. These relations can take different forms. p.183
Genetic epistemology!!!! Thus, the importance of studying the structure of knowledge is not just to better understand the knowledge itself, but to understand the person.
Research on the structure of this dialectical process translates into the belief that neither people nor knowledge-including mathematics-can be fully grasped separately from the other. The study of people and the study of what they learn and think are inseparable. p.184
The important question is not whether the brain or the computer is discrete but whether knowledge is modularizable. For me, our ability to use computational metaphors in this way, as carriers for new psychological theories, has implications concerning where theories of knowledge are going and where we are going as producers and carriers of knowledge. p.193
The discrepancy between our experience of ourselves and our idealizations of knowledge has an effect: It intimidates us, it lessens the sense of our own competence, and it leads us into counterproductive strategies for learning and thinking. P.194
[BUT THE EP COULD MITIGATE THAT DISCREPANCY.]
[How could using an EP overtime change children epistemologically? If we affect their idealization of knowledge to their experience of themselves - if constructing knowledge and constant reflection becomes their experience of self? Can the EP effect the way they construct knowledge and think about their own construction, because the EP is constructive.]
CHAPTER 8
We are brought back to seeing the necessity for the educator to be an anthropologist. Educational innovators must be aware that in order to be successful they must be sensitive to what is happening in the surrounding culture and use dynamic cultural trends as a medium to carry their educational interventions. p.204
[Researchers] will be manifestations of a social movement of people interested in personal computation, interested in their own children, and interested in education. p.205
For people interested in education in general, it will be important to trace the life histories of these efforts: How will they affect the intellectual development of their school-age participants? Will we see reversals of piagetian stages? Will they develop pressures to withdraw from traditional schools? What kind of computer culture can grow in communities where there is not already a rich technophilic soil.
In my vision the computer acts as a transitional object to mediate relationships that are ultimately between person and person. P.206
By creating an intellectual environment in which the emphasis is on process, we give people with different skills and interests something to talk about. What is more important is understanding the recasting of knowledge into new forms. p.207
EXAMPLE OF SKI SCHOOL TECHNIQUE CHANGING: At the heart of the change is a reconceptualization of skiing, not a mere change in pedagogy or technology. p.208
The revolution I envision is of ideas, not technology. It consists of new understandings of specific subject domains and new understandings of the process of learning itself.
The computer presence has catalyzed the emergence of ideas. The computer will carry ideas into a world larger than the research centers where they have incubated up to now. p.210
The fact that we will be in a period of rapid evolution will produce footholds for institutional changes that might have been impossible in a more stable period. [DISRUPTION OF 2020]
In Mindstorms, Seymour offered a radically different vision. For Seymour, computers were not a replacement for the teacher but a new medium that children could use for making things and expressing themselves.
Seymour was certainly interested in machines and new technologies, but only insofar as they could support learning or lead to new insights about learning. P.viii
The theory [constructionism] builds on the work of Jean Piaget, the great child-development pioneer, who Seymour had collaborated with in the early 1960s. Piaget’s great insight was that knowledge in not delivered from teacher to learner; rather, children are constantly constructing knowledge through their everyday interactions with people and objects around them...children construct knowledge most effectively when they are actively engaged in constructing things in the world….and computational technologies can greatly expand the range of what and how children create. P.ix
He wanted to support children not only in developing their thinking but also in developing their voice. Seymour saw the computer not just as a problem-solving tool but as an expressive medium. Seymour wanted to help all children, from all backgrounds, have opportunities to express and share their ideas so that they could be full and active participants in society. P.x
Seymour was interested in applying ideas from AI to engage children in thinking about their own thinking-and learning about their own learning.
Four guiding principles:
Projects: (EP?) Seymour argued that it is best for children to learn new ideas through working on projects, not before working on projects.
Passion: “Education has very little to do with explanation, it has to do with engagement, with falling in love with the material.”
Peers: Importance of social dimension of learning.
Play: Play is experimenting, taking risks, testing the boundaries, and iteratively adapting when things go wrong. Play is “hard fun”...children are very willing to work hard on things that they find meaningful.
Seymour’s ideas provide children with more opportunities to explore, experiment, and express themselves, so that they can develop as creative thinkers.
PREFACE (Seymour Papert)
When I read Piaget I was struck by the fact that his discussion does not do full justice to his own idea. He talks almost entirely about cognitive aspects of assimilation. But there is also an affective component. p.xvi
Anything is easy if you can assimilate it to your collection of models. p.xvii
It is the double relationship of the abstract and sensory that give the gear the power to carry powerful mathematics into the mind. In a terminology I shall develop in later chapters, the gear acts here as a transitional object.
The computer is the Proteus of machines. Its essence is its universality, its power to simulate. Because it can take on a thousand forms and can serve a thousand functions, it can appeal to a thousand tastes. This book is the result of my own attempts over the past decade to turn computers into instruments flexible enough so that many children can each create for themselves something like what the gears were for me. p.xvii
INTRODUCTION
In this book I discuss ways in which the computer presence could contribute to mental processes not only instrumentally but in more essential, conceptual ways, influencing how people think even when they are far removed from physical contact with a computer.
This book is about how computers can be carriers of powerful ideas and of the seeds of cultural change, how they can help people form new relationships with knowledge.
...can we construct intellectual environments in which people who today think of themselves as “humanists” will feel part of, not alienated from, the process of constructing computational cultures.
My image does not go beyond: It goes in the opposite direction. p.3
[technology IS affective---how are we noticing that?]
Two fundamental ideas run through this book. The first is that it is possible to design computers so that learning to communicate with them can be a natural process. Second, learning to communicate with a computer man change the way other learning takes place. p.4
I believe that the computer presence will enable us to so modify the learning environment outside the classroom that much if not all the knowledge schools presently try to teach with such pain and expense and such limited success will be learned, as the child learns to talk, painlessly, successfully, and without organized instruction. This obviously implies that schools as we know them today will have no place in the future. But it is an open question whether they will adapt by transforming themselves into something new or wither away and be replaced.
Although technology will play an essential role in the realization of my vision of the future of education, my central focus is not on the machine but on the mind, and particularly on the way in which intellectual movements and cultures define themselves and grow. Indeed, the role I give to the computer is that of a carrier of cultural “germs” or “seeds” whose intellectual products will not need technological support once they take root in an actively growing mind. p.8
Thus this book is really about how a culture, a way of thinning, an idea comes to inhabit a young mind. p.9 [gears]
My goal has been the design of other objects that children can make theirs for themselves and in their own ways. p.10
[The “turtle” is his “object-to-think-with”...could EP function as “turtle”...transitional object?]
My interest is in the process of invention of “objects-to-think-with”, objects in which there is an intersection of cultural presence, embedded knowledge, and the possibility for personal identification. p.11
My vision of a new kind of learning environment demands free contact between children and computers. p.16
...and can provide children with new possibilities for learning, thinking, and growing emotionally as well as cognitively. I want my readers to be very clear that what is “utopian” in my vision and in this book is particular way of using computers, of forging new relationships between computers and people. p.18
CHAPTER 1
When a child learns to program [build EP], the process of learning is transformed. It becomes more active and self-directed. In particular, the knowledge is acquired for a recognizable personal purpose. The child does something with it. The new knowledge is a source of power and is experienced as such from the moment it begins to form in the child’s mind. p.21
Knowledge that was accessible only through formal processes can now be approached concretely. And the real magic comes from the fact that this knowledge includes those elements one needs to become a formal thinker. [model+content] p.22
[Building an EP] children are learning to think articulately about thinking.
Programming the [EP] starts by making one reflect on how one does oneself what one would like the [EP] to do. p.29
[How has technology shaped children’s identity as writers? Thinkers? Actual cognition?]p.32
I believe that the computer as a writing instrument offers children an opportunity to become more like adults, indeed like advanced professionals, in their relationship to their intellectual products and to themselves. p.33
The first use of the new technology is quite naturally to do in a slightly different way what had been done before without it. It took years before designers of automoviles accepted the idea that they were cars, not “horseless carriages”, and the precursors of modern motion pictures were plays acted as if before a live audience but actually in front of a camera. A whole generation was needed for the new art of motion pictures to emerge as something quite different from a linear mix of theatre plus photography. Most of what has been done up to now under the name “educational technology” or “computers in education” is still at the stage of the linear mis of old instructional methods with new technologies. p.40
Very few with the imagination, creativity, and drive to make great new inventions enter the field of education. Most of those who do are soon driven out in frustration. Conservatism in the world of education has become a self-perpetuating social phenomenon….but computers are able to offer an open marketplace directly to consumers. There will be new opportunities for imagination and originality. There might be a renaissance of thinking about education. p.41
CHAPTER 2
All this is done through what I have called Piagetian learning, a learning process that has many features the schools should envy: It is effective (all children get there), it is inexpensive (it seems to require neither teacher or curriculum development), and it is humane (the children seem to do it in a carefree spirit without explicit external rewards and punishment). p.47
[If one’s strength is language, but lack mathematical vocabulary or a sense of purpose grows a hatred of math.] I am convinced that what shows up as intellectual weakness very often grows out of intellectual strengths. And it is not only verbal strengths that undermine others. Every careful observer of children must have seen similar processes working in different directions: For example, a child who has become enamored of logical order is set up to be turned off by English spelling and to go on from there to develop a global dislike for writing. p.52
Some of the historical reasons for school math had to do with what was learnable and teachable in the precomputer epoch. [WHY DO WE LEARN WHAT WE LEARN IN MATH?!] p.59
Very few people ever suspect that the reason for what is included and what is not included in school math might be as crudely technological as the ease of production of parabolas with pencils! p.60
A dignified mathematics for children cannot be something we permit ourselves to inflict on children, like unpleasant medicine, although we see no reason to take it ourselves. p.62
CHAPTER 3
For most children numbers have to be explored, and doing so is an exciting and playful process. p.65
How can we write about math, and science...in language arts? To develop a language for math...THERE ARE WORDS FOR MATH!
CHAPTER 4
[We will be better able to teach the problems and purposes of the EP when we have learned its language ourselves.]
An important part of becoming a good learner is learning how to push out the frontier of what we can express with words. The central theme of this chapter is the development of descriptive languages for talking about learning. p.106
If we can find an honest place for scientific thinking in activities that the child feels are important and personal, we shall open the doors to a more coherent, syntonic pattern of learning. p.107
The use of programming concepts as a descriptive language facilitates debugging. p.125
Errors benefit us because they lead us to study what happened, to understand what went wrong and, through understanding, to fix it. Experience with computer programming leads children more effectively than any other activity to “believe in” debugging. p.126
[MISTAKES AS LEARNING OPPORTUNITIES]
[BUILDING AN EP INVOLVED CORRECTING MISTAKES - THE TEST PROCESS IS LEARNING]
The LOGO environment [or the learning environment created when building an EP] is special because it provides numerous problems that elementary school children can understand with a kind of completeness that is rare in ordinary life. p.128
DEPTH AND COMPLEXITY
The internal intelligibility of computer worlds offers children the opportunity to carry out projects of greater complexity that are usually possible in the physical world. Many children imagine complex structures they might build with an erector set or fantasize about organizing friends into complex enterprises. But when they try to realize such projects, they too soon run into the unintelligible limitations of matter and people. Because computer programs can in principle be made to behave exactly as they are intended to, they can be combined more safely into complex systems. Thus, children are able to acquire a feel for complexity.p.131
CHAPTER 5
First, relate what is new and to be learned to something you already know. Second, take what is mew and make it your own. P.133
CHAPTER 6
Learning that vs. learning how.
Working in [EP] microworlds is a model for what it is to get to know an idea the way you get to know a person. [could the EP be even more?] p.153
Everyone must acquire skill at getting to know and a personal style for doing it.
The idea is that early experience with [EPs] is a good way to ‘get to know’ what it is like to learn a formal subject by ‘getting to know’ its powerful ideas.
[The EP as epistemology?] p.154
It is of a kind with the intuitive and informal, but often very powerful, ideas that inhabit all of our heads whether we are children or physicists.
The need for drill and practice in arithmetic is a symptom of the absence of conditions for the syntonic learning of mathematics.
Traditional physics teaching is forced to overemphasize the quantitative by the accidents of a paper-and-pencil technology which favors work that can produce a definite “answer”. p.156
[Importance of understanding intuition.] What the student needs is a better understanding of himself...to know why his intuition gives him a wrong expectation. He needs to know how to work on his intuitions in order to change them when they are wrong. p.162
I want you to go away from this book with a new sense of a child’s value as a thinker, even as an ‘epistemologist’ with a notion of the power of powerful ideas. p.169
As educators we can help by creating the conditions for children to use procedural thinking effectively and joyfully. p.173
CHAPTER 7
The aim of AI is to give concrete form to ideas about thinking that previously might have seemed abstract, even metaphysical.
I believe the ability to articulate the processes of thinking enables us to improve them. p.177
In my own thinking I have placed a greater emphasis on two dimensions implicit but not elaborated in Piaget’s own work: an interest in intellectual structures that could develop as opposed to those that actually at present do develop in the child, and the design of learning environments that are resonant with them. The [EP] can be used to illustrate both of these interests; first, the identification of powerful set of [linguistic]ideas that we do not presume to be represented, at least not in a developed form, in children; second, the creation of a transitional object, the [EP], that can exist in the child’s environment and make contact with the ideas. p.181
Working with computers can make it more apparent that children construct their own personal microworlds. p.182
Traditional epistemology has often been taken as a branch of philosophy Genetic epistemology worlds to assert itself as a science. Its students gather data and develop theories about how knowledge developed, sometimes focusing on the evolution of knowledge in history, sometimes on the evolution of knowledge in the individual. But it does not see the two realms as distinct: It seeks to understand relations between them. These relations can take different forms. p.183
Genetic epistemology!!!! Thus, the importance of studying the structure of knowledge is not just to better understand the knowledge itself, but to understand the person.
Research on the structure of this dialectical process translates into the belief that neither people nor knowledge-including mathematics-can be fully grasped separately from the other. The study of people and the study of what they learn and think are inseparable. p.184
The important question is not whether the brain or the computer is discrete but whether knowledge is modularizable. For me, our ability to use computational metaphors in this way, as carriers for new psychological theories, has implications concerning where theories of knowledge are going and where we are going as producers and carriers of knowledge. p.193
The discrepancy between our experience of ourselves and our idealizations of knowledge has an effect: It intimidates us, it lessens the sense of our own competence, and it leads us into counterproductive strategies for learning and thinking. P.194
[BUT THE EP COULD MITIGATE THAT DISCREPANCY.]
[How could using an EP overtime change children epistemologically? If we affect their idealization of knowledge to their experience of themselves - if constructing knowledge and constant reflection becomes their experience of self? Can the EP effect the way they construct knowledge and think about their own construction, because the EP is constructive.]
CHAPTER 8
We are brought back to seeing the necessity for the educator to be an anthropologist. Educational innovators must be aware that in order to be successful they must be sensitive to what is happening in the surrounding culture and use dynamic cultural trends as a medium to carry their educational interventions. p.204
[Researchers] will be manifestations of a social movement of people interested in personal computation, interested in their own children, and interested in education. p.205
For people interested in education in general, it will be important to trace the life histories of these efforts: How will they affect the intellectual development of their school-age participants? Will we see reversals of piagetian stages? Will they develop pressures to withdraw from traditional schools? What kind of computer culture can grow in communities where there is not already a rich technophilic soil.
In my vision the computer acts as a transitional object to mediate relationships that are ultimately between person and person. P.206
By creating an intellectual environment in which the emphasis is on process, we give people with different skills and interests something to talk about. What is more important is understanding the recasting of knowledge into new forms. p.207
EXAMPLE OF SKI SCHOOL TECHNIQUE CHANGING: At the heart of the change is a reconceptualization of skiing, not a mere change in pedagogy or technology. p.208
The revolution I envision is of ideas, not technology. It consists of new understandings of specific subject domains and new understandings of the process of learning itself.
The computer presence has catalyzed the emergence of ideas. The computer will carry ideas into a world larger than the research centers where they have incubated up to now. p.210
The fact that we will be in a period of rapid evolution will produce footholds for institutional changes that might have been impossible in a more stable period. [DISRUPTION OF 2020]
January 26, 2024
It’s good— I think it’s undeniable that Papert contributed a lot of revolutionary ideas to how we think of how kids interact with and learn from computers. I might quibble a bit with the ordering of the chapters and the inclusion of content that seems to dip too closely to high-level transfer, though (particularly with the dyna-turtles).
November 2, 2019
I really wanted to like this book because it's considered the book to read for anyone interested in the use of computers in education. However, this book fell short of my expectations. I found the writing style somewhat difficult to read, though I did have some takeaways, all of which came from the chapter on turtle geometry.
Syntonic learning = learning that is coherent with children’s sense of themselves as people with intentions, goals, desires, likes, and dislikes
In LOGO, the [mathematical] concept empowers the child, and the child experienced what it is like for mathematics to enable whole cultures to do what no one could do before.
The most powerful idea of all is the idea of powerful ideas.
October 28, 2018
This book explores different approaches for reconceptualizing learning. It shifts the focus on debugging and encourages not to fear mistakes, but recognize it as an intrinsic part of the learning process. Papert remains loyal to the Piagetian theory of cognitive development throughout the text. He pushes for learning that takes place as naturally as possible vs. through dissociated learning, which we are very accustomed to in the classroom. He argues that dissociated learning often detaches the learner who may lose personal interest thus limiting the ability to grasp the material.
The reader is introduced to the Turtle environment, a programming application that teaches kids basic geometry. Through this application, he provides many examples how being in control of the learning process and interacting with concepts dramatically improves a kid's attitude and ability to learn. Papert pushes for an increase of computer-mediated learning (a controversial topic at the time) and explains why advancements in that area might be beneficial.
Although the book was published in 1980, there's a lot of insightful ideas presented making it a relevant read.
The reader is introduced to the Turtle environment, a programming application that teaches kids basic geometry. Through this application, he provides many examples how being in control of the learning process and interacting with concepts dramatically improves a kid's attitude and ability to learn. Papert pushes for an increase of computer-mediated learning (a controversial topic at the time) and explains why advancements in that area might be beneficial.
Although the book was published in 1980, there's a lot of insightful ideas presented making it a relevant read.
August 7, 2012
Papert created the computer language, LOGO, and discusses how the use of LOGO enhances problem solving and the learning of mathematics for children. He describes the book as "an exercise in an applied genetic epistemology expanded beyond Piaget’s cognitive emphasis to include a concern with the affective." In his studies he noticed how children who had learned to program computers could use concrete models to think about thinking and to learn about learning, enhancing their power as psychologists and epistemologists. Papert describes the "Turtle geometry" of the LOGO language through examples of LOGO programming and pictures of the program results. He suggests that in Turtle geometry an environment is created in which the child’s task is not to learn formal rules but to develop insight into the way spatial moves allow transposition of self-knowledge that will cause a Turtle to move. The application of this computer language has proven to be significant, with Disney programmers now creating computer activities that allow elementary-aged students to play with calculus.
December 31, 2017
While playing Lego Mindstorms with my kids, I wondered about the origin of that amazing project. A quick online search led me to the MIT Media Lab, and then to this book. It was not as entertaining as I thought it would and it took me several months to finish. The author uses highly technical terms coming from mathematics, psychology and philosophy, making it really a treatise on early cognitive development. It's "vintage" and at first, I was taken back by the long tutorial pieces on the LOGO programming language, until I found out that this language is still in use. I will now test it with my kids, so that's a real plus! At the end, the most interesting for me was the afterword, with the short history of the Media Lab and of early AI work. There were many mind-blowing ideas distilled in that book about the future of education and the combined role of maths and computers. The writing style was the difficult part.
February 7, 2013
A good book. I decided to read it from the programming essay by bret victor. At times a bit long-winded, but motivates the problem well. I'm truly blown away about when this book was written, because it seems very ahead of its time. Many things that seemed obvious to Papert then I think are much more obvious now, but still not all are realized. It is strangely more philosophical than I would have expected.
Read
January 25, 2015Very interesting and educational. Even though a book is about programming language LOGO it's much more than that. It is a book on how computers can be used not only to revolutionize the education, but to improve how children learn. It is quite philosophical and I believe I'll need to read it couple of times more before I get the full grasp of it.
Highly recommended for passionate about education and/or math.
Highly recommended for passionate about education and/or math.
February 17, 2013
The philosophy behind the LOGO programming language as a method for teaching mathematical thought to children -- I remember doing some of these exercises in Grade 3 or 4. Look up Bret Victor to see some very interesting contemporary programming tools/UI inspired by this work.
May 20, 2016
A protégé of Piaget, Papert was one of the first to espouse the benefits of teaching though computer programming. He suggests learning through tinkering and approaching concepts in smaller "mindbites".
December 15, 2016
Some interesting insights, but ultimately fails to move beyond the premise introduced in the first few pages. Classic example of a non-fiction book that would have been a much more effective fifteen page article.
January 7, 2013
Good ideas. Needlessly philosophically complicated writing style. I wanted something more concrete.
April 4, 2017
First-stop book for teachers in IT and Math
June 5, 2018
This book is seriously good.
See my full review here: https://medium.com/@amanagarwal/book-...
See my full review here: https://medium.com/@amanagarwal/book-...
November 5, 2021
I read this book concurrently to Free For All, which showed science as it was practiced in the time this book was written in. In the RAND Health Insurance Experiment, there was a disconnect that they found between the 'action' and 'research' team. Like other disconnects that people complained about in the 20th century, this begins to point to a problem at the heart of the 20th century's conception of culture within the free world. However, something new was happening, in 1980, when Paper wrote; the personal computer revolution. Video games were still 2 years away from being pronounced a "fad", children by and large did not have access to computers, and there was pervasive mathophobia. This mathophobia did not just pervade general society, but also teachers and the education system. Papert made the case that this mathophobia limited the capacity of people to do undirected, independent and 'unstructured' thought. That this fear of math was, in fact, a mind killer and an unnecessary one in the new age of personal computing. We often aren't able to articulate what we are missing, but this book, and the style education it suggests are an attempt at doing so.
Papert looked into the future. He saw the problems we face today, and attempted to propose a way for the children about to be born(people like me, born 1982) to avoid or overcome them. These problems included mass surveillance, thought control, balkanization of culture(ie the precursors to filter bubbles). So the potential risks and benefits were high. The key to defeating these problems was to set the children free, especially free from the fear and mathophobia.
The mathophobia Paper describes still lives and thrives. 2017 is a year that the UK, US, France, Australia, Canada and other countries are all having serious discussions of banning the teaching, use and knowledge of certain math. There's even rumours of extending this ban via international trade agreements that would bind national governments so that even if citizens voted to undo these bans, that they would be cut out of the international economy for their doing so. The cost of losing this battle to keep math legal to future generations would be incalculable. Copyright, recent attacks on code sharing in Europe and the lack of a flourishing public domain through this lens serves to cripple our children's ability to learn by denying them a social universe that so obviously can exist with the by now worldwide ubiquitous and cheap computers.
In 2009 I argued in a Copyright Consultation submission that the future could be bright if only the children were allowed to seize it. Mindstorms very much supports this position, and is practically a manifesto written in that direction. (Sadly this submission seems to have vanished from the internet.)
The permission culture that copyright represents actually cuts deeper, and though Papert didn't explicitly spell it out there was some explicit discussion about thinking about how to make culture "resonate" with children *so that they can appropriate it for their own ends, and broader understanding*. He was talking about mathematics...but mathematics is a placeholder for an understanding of everything else(not the only one, but one that he argues should be explored more). This resonance was meant to be for both student and teacher, youth and adult. The problem of making mathematics make sense and making computers humane for children to use is how to *maximize*, not mimize cultural appropriation. It is to *minimize* permission culture and copyright as part of that.
There was a dialogue that was basically a shorthand for the larger details of the debate found in Galileo Courtier.
"Science begins to be puzzled when we questioned *why* things move to their natural place, they begin to ask why"-Noam Chomsky
This is related to the copyfight above, not just on the question of 'how do we fund creators/science so that we do not bias the results' but also on the level of how to deal with the question of a fundamental disconnect between the Old Views of a world without technology and revolutionary new data that technology allows(in Galileo's case, telescopes and math itself). Also, the question of experimenting with ideas by using the mask of Anonymous is relevant here, as well. Copyright is crippling our children if this book is any indication. Likewise, one aspect of the struggle between Galilean programs and Aristotelian ones is that it's a struggle between formalist and those who might escape formalism. This struggle is by far not over, and the fruit from undertaking it will not only bring more fruit for my generation, but also the next.
Pappert is not a psychologist, he's an epistemologist. so he takes a neutral view on psychology, and does not pick sides in the many branches of psychology ranging from the (by the 1980s discredited) freudian school to plato to somewhat modern cognitive science, and everything in between. This makes for strange, if revolutionary, reading.
This book builds a lot on the shoulders of giants. It tries to take a step towards understanding knowledge, language and math *as children are actually capable of learning it*, phrased in terms of (primitively recursive) programs so that it's one step closer to testable. But much of the work of producing such a theory is punted to *our* generation. I wonder how far those who read this took him up on that. Part of the answer here is understanding our emotions on this programmatic level, and Steven Pinker's description of how utterly *functional* they are to social problems inherent in our history as a species. The very same social problems that, say Parfit looks at.
Part of the endgame though is to bring a new understanding of existing fields, like physics. I couldn't help but think after skimming some older works about the generalizing of motion and differentials suggested in mindstorms. It kind of makes me wish I had more and freer access to children who might be the source of important questions that can lead us to have a deeper understanding on issues like, say, morpheogenesis.
In particular the formal PoV tends to be missing an intuitive 'what does this mean in response to me' view. It also seems to harbour within it a type of confirmation bias in practice to show that things have to be a certain way rather than to show how to construct the situation intuitively. Especially when we're talking children, "the purpose of working on the problem is not to get the right answer, but to look sensitively for conflict between different ways of thinking about the problem". Ie not to prove yourself *right* but to do something fruitful.
Conflict points, unstable points, points of contention can lead to Teachable Moments.
Seriously though, there is a gap in our culture that we do not have an institution or incentive to fill - "it seems to be nobody's business to think in a fundamental way about science in relation to the way people think and learn it. Although lip service has been paid to the importance of sicence and society, the underlying methodology is like that of traditional education: one of delivering elements of ready-made science to a special audience. The concept of a serious enterprise of making science for the people is quite alien." Hackerspaces are partway there, and so are some groups who investigate existential risks...but there's a lack of a systematic approach here that uses as a starting point not excluding children. Also relevant here: ScienceMart.
"does this allow us to conjecture that mathematics shares more with jokes, dreams, and hysteria than is commonly recognized?"
The rethinking of culture that is called for doesn't just mean broadening our ability for datalove. It means a much deeper rethinking of the structures and perhaps broadening our expectation of the transgressions that was to come, from the perspective of the world of 1980:
"the emergence of motion pictures as a new art form went hand in hand with the emergence of a new subculture, a new set of professions made up with people whose skills, sensitivities and philosophies of like were unlike anything that had existed before. The story of the evolution of the wold of movies is inseperable from the story of the evolution of the communities of people. Similarly a new world of personal computing is about to come into being, and its history will be inseparable from the story of the people who will make it".
Downside: Like many geeks of the early PC revolution, there's perhaps an overlooking of the social connection to computing, political power, and non-platonic relationships (say, between students). The ideas in this book certainly have broader implications in terms of these interpersonal and personal-group/state relationships, up to and including NSA/Facebook, but this is not really the book to learn about these. Perhaps a sequel to mindstorms could be written that delves into these topics.
But one thing is for sure, it is *possible* to leverage computers/education into these topics, and the key may very well be locating them as meaningful to the student using something very much like LOGO.
Anyways, in short, the book seemed very much like a manifesto...not the thorough treatment that I was looking for. Part of the excitement in the book I was already infected with by virtue of just being born in the 1980s, part of it was by virtue of my participation in the cyberculture. But it's an extra hit of this infectious meme that maybe, things *could* be better if we don't ignore the obvious new tool in our toolkit, if we use the distraction rectangles more instead of allowing ourselves to be used *by* them.
"One might even say that computer science is wrongly so called: Most of it is not the science of computers, but the science of descriptions and descriptive languages."
It turns out Ada Lovelace had it right, all along. It's not computer science, it's *poetic* science. Poetry is essentially *human*, and it's through poetry and poetic science that a humane world can perhaps be built.
Papert looked into the future. He saw the problems we face today, and attempted to propose a way for the children about to be born(people like me, born 1982) to avoid or overcome them. These problems included mass surveillance, thought control, balkanization of culture(ie the precursors to filter bubbles). So the potential risks and benefits were high. The key to defeating these problems was to set the children free, especially free from the fear and mathophobia.
The mathophobia Paper describes still lives and thrives. 2017 is a year that the UK, US, France, Australia, Canada and other countries are all having serious discussions of banning the teaching, use and knowledge of certain math. There's even rumours of extending this ban via international trade agreements that would bind national governments so that even if citizens voted to undo these bans, that they would be cut out of the international economy for their doing so. The cost of losing this battle to keep math legal to future generations would be incalculable. Copyright, recent attacks on code sharing in Europe and the lack of a flourishing public domain through this lens serves to cripple our children's ability to learn by denying them a social universe that so obviously can exist with the by now worldwide ubiquitous and cheap computers.
In 2009 I argued in a Copyright Consultation submission that the future could be bright if only the children were allowed to seize it. Mindstorms very much supports this position, and is practically a manifesto written in that direction. (Sadly this submission seems to have vanished from the internet.)
The permission culture that copyright represents actually cuts deeper, and though Papert didn't explicitly spell it out there was some explicit discussion about thinking about how to make culture "resonate" with children *so that they can appropriate it for their own ends, and broader understanding*. He was talking about mathematics...but mathematics is a placeholder for an understanding of everything else(not the only one, but one that he argues should be explored more). This resonance was meant to be for both student and teacher, youth and adult. The problem of making mathematics make sense and making computers humane for children to use is how to *maximize*, not mimize cultural appropriation. It is to *minimize* permission culture and copyright as part of that.
There was a dialogue that was basically a shorthand for the larger details of the debate found in Galileo Courtier.
"Science begins to be puzzled when we questioned *why* things move to their natural place, they begin to ask why"-Noam Chomsky
This is related to the copyfight above, not just on the question of 'how do we fund creators/science so that we do not bias the results' but also on the level of how to deal with the question of a fundamental disconnect between the Old Views of a world without technology and revolutionary new data that technology allows(in Galileo's case, telescopes and math itself). Also, the question of experimenting with ideas by using the mask of Anonymous is relevant here, as well. Copyright is crippling our children if this book is any indication. Likewise, one aspect of the struggle between Galilean programs and Aristotelian ones is that it's a struggle between formalist and those who might escape formalism. This struggle is by far not over, and the fruit from undertaking it will not only bring more fruit for my generation, but also the next.
Pappert is not a psychologist, he's an epistemologist. so he takes a neutral view on psychology, and does not pick sides in the many branches of psychology ranging from the (by the 1980s discredited) freudian school to plato to somewhat modern cognitive science, and everything in between. This makes for strange, if revolutionary, reading.
This book builds a lot on the shoulders of giants. It tries to take a step towards understanding knowledge, language and math *as children are actually capable of learning it*, phrased in terms of (primitively recursive) programs so that it's one step closer to testable. But much of the work of producing such a theory is punted to *our* generation. I wonder how far those who read this took him up on that. Part of the answer here is understanding our emotions on this programmatic level, and Steven Pinker's description of how utterly *functional* they are to social problems inherent in our history as a species. The very same social problems that, say Parfit looks at.
Part of the endgame though is to bring a new understanding of existing fields, like physics. I couldn't help but think after skimming some older works about the generalizing of motion and differentials suggested in mindstorms. It kind of makes me wish I had more and freer access to children who might be the source of important questions that can lead us to have a deeper understanding on issues like, say, morpheogenesis.
In particular the formal PoV tends to be missing an intuitive 'what does this mean in response to me' view. It also seems to harbour within it a type of confirmation bias in practice to show that things have to be a certain way rather than to show how to construct the situation intuitively. Especially when we're talking children, "the purpose of working on the problem is not to get the right answer, but to look sensitively for conflict between different ways of thinking about the problem". Ie not to prove yourself *right* but to do something fruitful.
Conflict points, unstable points, points of contention can lead to Teachable Moments.
Seriously though, there is a gap in our culture that we do not have an institution or incentive to fill - "it seems to be nobody's business to think in a fundamental way about science in relation to the way people think and learn it. Although lip service has been paid to the importance of sicence and society, the underlying methodology is like that of traditional education: one of delivering elements of ready-made science to a special audience. The concept of a serious enterprise of making science for the people is quite alien." Hackerspaces are partway there, and so are some groups who investigate existential risks...but there's a lack of a systematic approach here that uses as a starting point not excluding children. Also relevant here: ScienceMart.
"does this allow us to conjecture that mathematics shares more with jokes, dreams, and hysteria than is commonly recognized?"
The rethinking of culture that is called for doesn't just mean broadening our ability for datalove. It means a much deeper rethinking of the structures and perhaps broadening our expectation of the transgressions that was to come, from the perspective of the world of 1980:
"the emergence of motion pictures as a new art form went hand in hand with the emergence of a new subculture, a new set of professions made up with people whose skills, sensitivities and philosophies of like were unlike anything that had existed before. The story of the evolution of the wold of movies is inseperable from the story of the evolution of the communities of people. Similarly a new world of personal computing is about to come into being, and its history will be inseparable from the story of the people who will make it".
Downside: Like many geeks of the early PC revolution, there's perhaps an overlooking of the social connection to computing, political power, and non-platonic relationships (say, between students). The ideas in this book certainly have broader implications in terms of these interpersonal and personal-group/state relationships, up to and including NSA/Facebook, but this is not really the book to learn about these. Perhaps a sequel to mindstorms could be written that delves into these topics.
But one thing is for sure, it is *possible* to leverage computers/education into these topics, and the key may very well be locating them as meaningful to the student using something very much like LOGO.
Anyways, in short, the book seemed very much like a manifesto...not the thorough treatment that I was looking for. Part of the excitement in the book I was already infected with by virtue of just being born in the 1980s, part of it was by virtue of my participation in the cyberculture. But it's an extra hit of this infectious meme that maybe, things *could* be better if we don't ignore the obvious new tool in our toolkit, if we use the distraction rectangles more instead of allowing ourselves to be used *by* them.
"One might even say that computer science is wrongly so called: Most of it is not the science of computers, but the science of descriptions and descriptive languages."
It turns out Ada Lovelace had it right, all along. It's not computer science, it's *poetic* science. Poetry is essentially *human*, and it's through poetry and poetic science that a humane world can perhaps be built.
July 1, 2018
It’s incredible to me that this book was originally published in 1980. When I was only 10 this guy was already predicting the future of education—what we now have the gall to call 21st Century education, he described 20 years before. And here I am nearly 40 years later, reading his ideas with awe, and they are as relevant and as contemporary as anything else I’ve read in the intervening years.
The insight of this man was nothing short of astounding. I’ve believe fervently, that counter to popular understanding, tech in its essence has not changed very much it all since it’s inception in the 1980s, and reading this book is yet more evidence of this. What Papert describes in terms of the potential for computers to revolutionise education is as true now as it was then, if he could have seen the iPad, he would have been gratified to behold the device that would be the embodiment of so much he believed would and could be true of classrooms where digital technologies are integrated effectively. I gave this book 3 stars, as really only the first third offers much of any great import; after that it becomes bogged down in excessively convoluted theorising and desperate attempts to appeal to the use of LOGO as the means by which the revolution would or could be realised. To be fair, the tag line on the cover does highlight this, but LOGO was far from the reason I chose to read this book—so why did I? For insightful observations like these:
“The computer is the Proteus of machines. Its essence is its universality, its power to simulate. Because it can take on a thousand forms and can serve a thousand functions, it can appeal to a thousand tastes.”
“computers can be carriers of powerful ideas and of the seeds of cultural change, how they can help people form new relationships with knowledge that cut across the traditional lines separating humanities from sciences and knowledge of the self from both of these. It is about using computers to challenge current beliefs about who can understand what and at what age.”
“it is possible to design computers so that learning to communicate with them can be a natural process, more like learning French by living in France than like trying to learn it through the unnatural process of American foreign-language instruction in classrooms. Second, learning to communicate with a computer may change the way other learning takes place.”
“children can learn to use computers in a masterful way, and learning to use computers can change the way they learn everything else.”
“many children are held back in their learning because they have a model of learning in which you have either "got it" or "got it wrong." But when you learn to program a computer you almost never get it right the first time. Learning to be a master programmer is learning to become highly skilled at isolating and correcting "bugs," the parts that keep the program from working. The question to ask about the program is not whether it is right or wrong, but if it is fixable. If this way of looking at intellectual products were generalised to how the larger culture thinks about knowledge and its acquisition, we all might be less intimidated by our fears of "being wrong." This potential influence of the computer on changing our notion of a black and white version of our successes and failures is an example of using the computer as an "object-to-think-with."
“the computer as writing instrument offers children an opportunity to become more like adults, indeed like advanced professionals, in their relationship to their intellectual products and to themselves. In doing so, it comes into head- on collision with the many aspects of school whose effect, if not whose intention, is to "infantilize" the child.”
The insight of this man was nothing short of astounding. I’ve believe fervently, that counter to popular understanding, tech in its essence has not changed very much it all since it’s inception in the 1980s, and reading this book is yet more evidence of this. What Papert describes in terms of the potential for computers to revolutionise education is as true now as it was then, if he could have seen the iPad, he would have been gratified to behold the device that would be the embodiment of so much he believed would and could be true of classrooms where digital technologies are integrated effectively. I gave this book 3 stars, as really only the first third offers much of any great import; after that it becomes bogged down in excessively convoluted theorising and desperate attempts to appeal to the use of LOGO as the means by which the revolution would or could be realised. To be fair, the tag line on the cover does highlight this, but LOGO was far from the reason I chose to read this book—so why did I? For insightful observations like these:
“The computer is the Proteus of machines. Its essence is its universality, its power to simulate. Because it can take on a thousand forms and can serve a thousand functions, it can appeal to a thousand tastes.”
“computers can be carriers of powerful ideas and of the seeds of cultural change, how they can help people form new relationships with knowledge that cut across the traditional lines separating humanities from sciences and knowledge of the self from both of these. It is about using computers to challenge current beliefs about who can understand what and at what age.”
“it is possible to design computers so that learning to communicate with them can be a natural process, more like learning French by living in France than like trying to learn it through the unnatural process of American foreign-language instruction in classrooms. Second, learning to communicate with a computer may change the way other learning takes place.”
“children can learn to use computers in a masterful way, and learning to use computers can change the way they learn everything else.”
“many children are held back in their learning because they have a model of learning in which you have either "got it" or "got it wrong." But when you learn to program a computer you almost never get it right the first time. Learning to be a master programmer is learning to become highly skilled at isolating and correcting "bugs," the parts that keep the program from working. The question to ask about the program is not whether it is right or wrong, but if it is fixable. If this way of looking at intellectual products were generalised to how the larger culture thinks about knowledge and its acquisition, we all might be less intimidated by our fears of "being wrong." This potential influence of the computer on changing our notion of a black and white version of our successes and failures is an example of using the computer as an "object-to-think-with."
“the computer as writing instrument offers children an opportunity to become more like adults, indeed like advanced professionals, in their relationship to their intellectual products and to themselves. In doing so, it comes into head- on collision with the many aspects of school whose effect, if not whose intention, is to "infantilize" the child.”
November 19, 2017
This book is about how children learn "a way of thinking". Seymour Papert has a background as "a mathematician and Piagetian psychologist" (p.166). He writes about "what kinds of nurturance are needed for intellectual growth" and "what can be done to create such nurturance" (p.10). The book is about children, but the "ideas" are relevant to "how people learn at any age" (p.213).
Two "ideas run through" the book: 1) change in "patterns of intellectual development" come about through "cultural change", and 2) the "likely bearer" of this "cultural change" is the "increasingly pervasive computer presence" (p.216). It's worth noting that the book was originally published in 1980.
Seymour Papert defines "mathetics as being to learning as heuristics is to problem solving". Principles of mathetics "illuminate and facilitate" learning: 1) Relate "what is new" to "something you already know", and 2) take "what is new" and "make it your own" (p.120). Different metaphors can be used to talk "mathetically" about "learning experiences": 1) "Getting to know " an idea, 2) "exploring an area of knowledge", and 3) "acquiring sensitivity to [subtle] distinctions" (p.136).
Jean Piaget's contribution to Seymour Papert's work has been deep. Piaget's ideas have "contributed toward the knowledge-based theory of learning" that Papert describes (p.156). "For Piaget, the separation between the learning process and what is being learned is a mistake" (p.158). It's not unusual that Piaget, at the same time, refers to "the behavior of small children", and to "the concerns of theoretical mathematicians" (p.158).
Seymour Papert uses "learning to ride a bicycle" to make more concrete "the idea of studying learning by focusing on the structure of what is learned" (p.158). The conclusion is that "learning to ride does not mean learning to balance, it means learning not to unbalance, learning not to interfere" (p.159). A deeper understanding of the "process of learning" is, in other words, acquired through a "deeper insight into what is being learned" (p.159).
Another example is that we can "understand how children learn number" through a "deeper understanding of what number is" (p.159). The Bourbaki school of mathematics sees more "complex structures" as combinations of "simpler structures" of which the most important are three "mother structures" (p.160).
Interestingly, the "theory of mother structures" is a "theory of learning" (p.160). The "knowledge of how to work the world" is the "mother structure of order" (p.160). Jean Piaget observed that children develop "intellectual structures" that are similar to the "mother structures" (p.160).
Seymour Papert presents a "mathetic" vision in his book, one that helps us to "learn about learning" (p.177). He shows how a mathetic culture can humanize the learning experience and make it more personal. Papert's philosophy is "revolutionary rather than reformist" (p.186). He thinks "seriously about a world without schools" (p.178) and discusses settings that are "socially cohesive, and where experts and novices are all learning" (p.179). It is the "very youngest who stand to gain the most from changes in the conditions of learning" (p.213).
Many of Seymour Papert's ideas are still valid today!
Two "ideas run through" the book: 1) change in "patterns of intellectual development" come about through "cultural change", and 2) the "likely bearer" of this "cultural change" is the "increasingly pervasive computer presence" (p.216). It's worth noting that the book was originally published in 1980.
Seymour Papert defines "mathetics as being to learning as heuristics is to problem solving". Principles of mathetics "illuminate and facilitate" learning: 1) Relate "what is new" to "something you already know", and 2) take "what is new" and "make it your own" (p.120). Different metaphors can be used to talk "mathetically" about "learning experiences": 1) "Getting to know " an idea, 2) "exploring an area of knowledge", and 3) "acquiring sensitivity to [subtle] distinctions" (p.136).
Jean Piaget's contribution to Seymour Papert's work has been deep. Piaget's ideas have "contributed toward the knowledge-based theory of learning" that Papert describes (p.156). "For Piaget, the separation between the learning process and what is being learned is a mistake" (p.158). It's not unusual that Piaget, at the same time, refers to "the behavior of small children", and to "the concerns of theoretical mathematicians" (p.158).
Seymour Papert uses "learning to ride a bicycle" to make more concrete "the idea of studying learning by focusing on the structure of what is learned" (p.158). The conclusion is that "learning to ride does not mean learning to balance, it means learning not to unbalance, learning not to interfere" (p.159). A deeper understanding of the "process of learning" is, in other words, acquired through a "deeper insight into what is being learned" (p.159).
Another example is that we can "understand how children learn number" through a "deeper understanding of what number is" (p.159). The Bourbaki school of mathematics sees more "complex structures" as combinations of "simpler structures" of which the most important are three "mother structures" (p.160).
Interestingly, the "theory of mother structures" is a "theory of learning" (p.160). The "knowledge of how to work the world" is the "mother structure of order" (p.160). Jean Piaget observed that children develop "intellectual structures" that are similar to the "mother structures" (p.160).
Seymour Papert presents a "mathetic" vision in his book, one that helps us to "learn about learning" (p.177). He shows how a mathetic culture can humanize the learning experience and make it more personal. Papert's philosophy is "revolutionary rather than reformist" (p.186). He thinks "seriously about a world without schools" (p.178) and discusses settings that are "socially cohesive, and where experts and novices are all learning" (p.179). It is the "very youngest who stand to gain the most from changes in the conditions of learning" (p.213).
Many of Seymour Papert's ideas are still valid today!
Displaying 1 - 30 of 92 reviews