Mindstorms: what did Papert argue and what does it mean for learning and education?

I turned 37 years old today. People like to point out that I don’t really look my age, and so I leverage this to act younger and feel younger than I am. And yet, despite my youthful looks, I’ve have lived nearly four decades on Earth. And if there’s anything notable about the period of 1980–2017, it’s not my life, it’s the rapid proliferation of personal computing and it’s profound effects on my generation.

To put this in perspective, I was born in a year that people had just started buying computers for their homes. Having one for a whole family was a luxury, and a mostly unrealized promise of a more enriching future of work and play. Now I live in a world in which supercomputers are in every pocket and purse, where the promise of computing is almost too realized. Living through this change has given me a lived perspective that’s not only defined my academic interests, but the course of my personal and professional entire life. It defined who I am and what I’ve given back to the world through my scholarship.

Seymour Papert

By no coincidence, 1980 was also the year Seymour Papert published Mindstorms, in which he conveyed a vision for how to leverage the democratization of computing for learning. In a way, Papert’s book didn’t affect my life at all. It didn’t change my schools, it didn’t change my education, and up to this point in time, it has barely informed my research. I might have used Logo for an hour in 4th grade. It clearly wasn’t memorable enough to have transformed my life. And yet, Mindstorms is a book inherently about my life at school, my life as a professor, and my research on computing education.

The first time I read Mindstorms was in my second year of college. I barely got past the first few chapters. I found it dense, impenetrable, and boring. For a book about powerful ideas in “mind-sized bites,” it was a 200-page epic argument woven from threads of mathematics, epistemology, the culture of science and education, and social critique. This was a book written for people with Ph.D.’s, not a 19-year old barely capable of theorizing about himself, let alone learning. It was like the Master Sword in Zelda: powerful and necessary tool for achieving my ultimate quest, but only accessible after first proving my courage and wisdom. I wasn’t worthy of it yet. (Sorry for the random Zelda reference, I’m currently absorbed in Breath of the Wild!)

Mindstorms’ inaccessibility is its biggest problem: I can’t just give the book to anyone and have them understand it’s biggest ideas. It’s not the right shape or the right size. To understand it, I’ve had to live the life I lived, earned the Ph.D. I earned, and read what I’ve read to comprehend it’s foundations. I can’t expect others to do the same.

So this year I decided to re-read it. But my goal wasn’t just to understand it, it was to translate it—for my students, my collaborators, and for you, to make it’s ideas more accessible. To this end, below I present my articulation of Papert’s ideas in as simple and accessible a form as I can muster. Tell me if I got it wrong.

We “build” knowledge

“All of us learn by constructing, exploring, or theory building, but most of the theory building on which we cut our teeth resulted in theories we would have to give up later.” — Papert, Mindstorms (Chapter 5)

The central premise of Papert’s ideas about learning is that we “construct” knowledge. His claim here is not that we literally do this out of bricks, blocks, code, or paper, but that our process of learning as humans is an iterative, cumulative one, not one of “absorbing” knowledge fully formed.

From this follows Papert’s central critique of modern education: it assumes that the end product of academic discoveries—say, Newton’s F=ma—is something that is meaningfully digestible by human minds. Papert rejects this. In fact, he believed that Newton himself only understood his second law in it’s mathematical form after a tortured decade with other representations of his ideas. So why would anyone arrive at his same intuition by just encountering it’s propositional form?

Papert further argued that the very scientists and engineers who depend on Newton’s formula also didn’t learn it by absorbing it directly into their minds, but rather, they had to develop their own personal understanding of the formula’s meaning by building upon their prior knowledge, such as their physical experiences with bicycle riding or playing billiards. You may remember sitting in a physics class doing just this, wracking you mind trying to get an intuitive sense of the math, but only having your eureka moment when you found the right non-mathematical representation of the idea that was deeply linked to something you already understood. Only then could you link you prior knowledge to Newton’s formal representation. This is Papert’s “construction” of knowledge in action.

That is not to say that Papert believed the formal notations we find in science are not useful, but that they are not useful for learning. Instead Papert proposed that education must make room for the iterative development and improvement of ideas. In that sense, we all converge toward F=ma, only after beginning with many brittle but useful theories about the relationship between mass and acceleration, much like Newton did on his path to discovering it.

Abstract and impersonal knowledge makes us hate education

A key corollary of Papert’s critique of modern education is that by learning academic’s formal representations of knowledge, students come to hate learning. Papert believed that learning to memorize and compute F=ma, completely divorced from it’s meaning in the world and in a person’s life, essentially requires teachers to lie to children about it’s relevance. He lamented that teachers around the world must regularly argue, “This formula is important and valuable to you,” when teachers know it is not, and don’t even believe it is personally valuable to them. Papert believed that this deception erodes the relationship between teachers and children, and ultimately erodes the trust and respect of educational institutions. (I see this regularly in my daughter’s reaction to school and it’s excruciating; I hopelessly try to fill the gaps that teachers leave unaddressed, such as why Newton wanted so badly to discover mechanics).

Additionally, Papert was critical of educational institutions resistance to the inevitable need for children to refine their theories of ideas over time. Papert believed that if it is true that people learn by essentially “debugging” their beliefs, school should be a place in which debugging is viewed as essential, encouraged, and supported. Yet, because of the obsession with teaching the knowledge academics view as most correct, students get the idea that there is “right” knowledge and “wrong” knowledge, rather than just useful personal knowledge that is to be improved. Just as the teachers’ lie about relevance erodes learning, Papert viewed education’s resistance to supporting the iterative construction of knowledge as invalidating the natural process by which children learn.

Some representations of ideas are more powerful than others

Papert argued that instead of teaching our most “correct” forms of knowledge to children—Newton’s F=ma—we should be crafting representations of those ideas that are more easily linked to children’s prior knowledge and more easily appropriated by children to engage their interests. Papert’s exploration of this idea was Logo, a programming language designed to develop children’s nascent theories about geometry upon their already developed personal experiences of egocentric position, movement, and command. Papert observed that every child has the experience of where they are in space, what it means to move in space, and what it means to tell other people how to move in space. Papert believed that offering children a notation that leveraged this universal knowledge, children would be able to build more robust, intuitive theories of geometry that were more powerful than our mathematical theories of geometry. These theories of geometry would of course be temporary and eventually replaced with better, more formal ones, but Papert believed this more personal construction of knowledge would prevent children from coming to hate geometry. They might even love it.

A simple Logo program

Logo was essentially a simple imperative programming language that commanded a “turtle” to move and turn in space, drawing lines as it did. In that sense, it was simple. But Papert didn’t so much care about what it was as a programming language, but what ideas the programming language contained, and how those ideas helped children form new ideas about geometry.

Papert didn’t view Logo as the only powerful representation. To him, it was just an example suitable for geometry and physics, used to illustrate a broader point about how some representations are more powerful than others for learning. He envisioned a world in which there were hundreds of powerful representations spanning all kinds of knowledge, carefully crafted by researchers and educators as personally meaningful, powerful representations serving as entry points into everything humanity has learned.

Computing is necessary to make powerful representations personal and concrete

Papert saw one problem with representations such as the Logo turtle: they were still abstract. You couldn’t walk into a classroom, have people command each other to behave like the Logo turtle, and empower each student to explore the world of geometry in personally meaningful ways. Kids would be waiting around, unable to develop their own ideas, watching as those who engaged most deeply had all the fun. It wouldn’t scale and it wouldn’t be personal, because whatever that turtle was drawing would be socially determined, not personally determined.

With a computer, however, the world defined by the Logo turtle could be simulated not only for each individual student, but also simulated at a much higher fidelity and speed, producing output that a child might fine personally meaningful. One could write commands for the turtle and immediately see the effects, rather than having to imagine the effects, or wait for a human to play out the effects on a student’s behalf. And one could write their own programs that produced personally relevant output, exploring the world made possible by Logo’s big ideas of ego-centric positioning. To Papert, personal computers were therefore the perfect medium in which to engage students with powerful representations:

“Before computers there were very few good points of contact between what is most fundamental and engaging in mathematics and anything firmly planted in everyday life. But the computer —mathematics speak being in the midst of the everyday life of the home, school, and workplace — is able to provide such links. The challenge to education is to find ways to exploit them.” — Papert, Mindstorms (Chapter 2)

But it wasn’t just computers that Papert viewed as necessary for realizing his vision. It was also computing, and in particular, concrete expressions of systematic procedures, which we now call algorithms. Papert viewed algorithms as descriptions of action in the world and a means for reflecting on action. By encouraging children to write down algorithms as part of their learning, he believed we might help them learn to better reflect concretely on their ideas, accelerating their construction of knowledge.

Because of the power of algorithms, Papert lamented that schools taught so much about numbers but so little about procedures:

“In our culture number is richly represented, systematic procedure is poorly represented” — Papert, Mindstorms (Chapter 7)

He imagined a world in which children learned just as much about algorithmic thinking as they did about numerical thinking, evening coining the widely used phrase “computational thinking,” in the hopes that thinking like a computer, combined with more powerful representations for making that thinking explicit, would be a path to better learning of all subjects.

Education should be facilitation, not recitation

Some of the biggest critics of Papert’s ideas were teachers themselves: they could not comprehend a world without curriculum, pedagogy, learning objectives, and assessments.

Papert responded with a vision of education as facilitating bricolage, which is the construction new things out of what is available, namely, the knowledge a child has available:

“But ‘teaching without curriculum‘ does not mean spontaneous, free-form classrooms or simply “leaving the child alone.” It means supporting children as they build their own intellectual structures with materials drawn from the surrounding culture. In this model, educational intervention means changing the culture, planting new constructive elements in it and eliminating noxious ones. This is a more ambitious undertaking than introducing a curriculum change…” — Papert, Mindstorms (Chapter 1)

Papert’s vision of teachers was therefore not as someone “presenting” knowledge and guiding their “acquisition” toward it, but as someone understanding a child’s prior knowledge, intuitively understanding the opportunities to build on top of that knowledge in a manner that results in a deeper understanding of a concept.

Papert went further, arguing that because children must view knowledge as relevant to want to know it, educators must also understand the cultures in which children are embedded:

“Thus 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.” — Papert, Mindstorms (Chapter 8)

This demanded that teachers and education researchers be more than just experts on a subject: it demanded that they be experts on the social worlds in which their children live, so they could make culturally meaningful representations of ideas.

Where will the powerful representations come from?

When describing his vision, Papert worried a lot about where all of the powerful representations like Logo’s turtle would come from:

“…the essential remaining problem in regard to the future of computers and education: the problem of the supply of people who will develop these [powerful representations]. The problem goes much deeper than a mere short supply of such people… there is a role but no place for them. In current professional definitions physicists think about how to do physics, educators think about how to teach it. There is no recognized place for people whose research is really physics, but physics oriented in directions that will be educationally meaningful.”—Papert, Mindstorms (Chapter 8)

Here, Papert is essentially concerned about what institutions would support the work of physics education researchers, as they weren’t likely to be recognized as either physicists or education researchers. While this problem has been overcome in some domains (by coincidence, math and physics education are quite mature and have found homes in education, math, and physics), it remains a major issue for most other areas of education. It’s a particular issue for my doctoral students who study computing education: will they join CS departments or Education departments or rejected by both?

My reflections on Papert’s ideas

For the most part, I agree with most of Papert’s claims. I agree with his fundamental view of knowledge as constructed. I agree with his view of computers as a powerful medium for creating contexts for constructing knowledge. I also see explicit representations of algorithms as powerful in facilitating reflection on ideas.

That said, I struggle with Papert’s utopian vision of education. In a small class, it’s not too hard to scale feedback, help, and facilitation, and if Papert’s ideas about learning are right, it might even be possible to sustain engagement for most children over long periods of time. These matters of classroom management are not so much of a barrier in principle, but ensuring classes are small enough is a still a monumental resource challenge. More fundamentally, however, Papert’s ideas demand breaking the fundamental assumption of school, that children of similar ages learn similar things. It’s hard to imagine an educational institution that would actually realize Papert’s ideas about learning without violating this constraint, allowing children to follow their interests, learn different things at different paces. I do believe that this would be an ideal context for learning, but I don’t buy that it’s feasible. Teachers would have to be virtuosos of many domains and representations, and would have to scale the facilitation of so many diverse student interests. That’s a lot of teacher training and a lot of research to build new representations. I’m skeptical that any country would invest in such a wholesale reinvention of learning and I’m uncertain that we could teach teachers to succeed in this model.

Finally, there’s a lot that Papert didn’t talk about that I also think is critical to learning. Most notably, he really said nothing about the need for explicit instruction and guidance to bootstrap the kind of personal construction of knowledge. I’ve taught too many children and adults to believe that all people need to learn is a fascinating powerful representation: at some point, Papert had to explain the commands FORWARD, BACK, RIGHT, LEFT, PENUP, PENDOWN, and so on. Children would not have discovered the meaning of these ideas independently without a teacher providing an example, an explanation, and a motivating context. As Kirschner, Sweller, and Clark argued in their article “Why Minimal Guidance During Instruction Does Not Work: An Analysis of the Failure of Constructivist, Discovery, Problem-Based, Experiential, and Inquiry-Based Teaching”:

The advantage of guidance begins to recede only when learners have sufficiently high prior knowledge to provide “internal” guidance. Recent developments in instructional research and instructional design models that support guidance during instruction are briefly described. (Kirschner et al. 2006)

That said, arguing for or against Papert is false dichotomy. I believe that high quality, engaging, and explicit instruction is necessary to bootstrap learning, but that personally relevant exploration is also inevitable and necessary. The grand challenge for any teacher, and any researcher of education, is to envision ways of weaving guidance and exploration together throughout a child’s education.

What do Papert’s ideas mean for computing education?

I’m a bit uncertain what Papert would think about the efforts to integrate ideas about algorithms in K-12 education throughout the world. On one side, he might be overjoyed that the idea of every child might learn how to think about “systematic procedures.” On the other side, he makes clear in Mindstorms that he was no fan of curriculum, of learning objectives, and of standards. Recent efforts like the CSTA’s K-12 Computer Science Standards might seem to him worse than teaching nothing about computing at all, because he might fear it would only create a similar disdain for computing that children find with math and science in school. I have the same fear.

I think the unique challenge for those of us interested in applying Papert’s ideas to K-12 education is to think of new CS classes in middle and high school as a constructionist refuge in inherently anti-constructionist institutions. After all, understanding through algorithms is at the heart of computer science, and so a classroom culture build upon that ideal would be authentic to both Papert and to computing. And Papert is partly to thank for that.

Seymour Papert died last year on July 31st, 2016. Whatever you think of his ideas, and however right or wrong they are, they are worth grappling with in our search for a more empowered, enlightened future for humanity.

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