TITLE: Teaching Science and Math to Young Children AUTHOR: Eugene Wallingford DATE: June 19, 2007 3:46 PM DESC: ----- BODY: After commenting on Alan Kay's thesis, I decided to read a more recent paper by Alan that was already in my stack, Thoughts About Teaching Science and Mathematics To Young Children. This paper is pretty informal, written in a conversational voice and marked by occasional typos. It some ways, it felt like a long blog entry, in which Kay could speak to a larger audience about some of the ideas that motivate his current work at the Viewpoints Research Institute. It's short -- barely more than four pages -- so you should read it yourself, but I'll share a few thoughts that came to mind as I read this morning in between bouts of advising incoming CS freshmen. Kay describes one of the key challenges to teaching children to become scientists: we must help students to distinguish between empiricism and modeling on one hand and belief- based acceptance of dogma on the other. This is difficult for at least three reasons: The last of these is a problem because most of us don't understand very well how children think, and most of us are prone to organize instruction in a way that conforms with how we think. As a parent who has watched one daughter pass through middle school and who has another just entering, I have seen children grok some ideas much better than older students when the children have an opportunity engage the concepts in a fortuitous way. I wish that I had gleaned from my experience some ideas that would enable me to create just the right opportunities for children to learn, but I'm still in the hit-or-miss phase. This brings out a second-order effect of understanding how children think, which Kay points out: "the younger the children, the more adept need to be their mentors (and the opposite is more often the case)". To help someone learn to think and act like a scientist, it is at least valuable and more likely essential for the teacher (to be able) to think and act like a scientist. Sadly, this is all to rare among elementary-school and even middle-school teachers. I also see this issue operating at the level of university CS education. Being a good CS1 teacher requires both knowing a lot about how students' minds work and being an active computer scientist (or software developer). Whatever drawbacks you may find in a university system that emphasizes research even for teaching faculty, I think that this phenomenon speaks to the value of the teacher-scholar. And by "scholar", I mean someone who is actively engaged doing the discipline, but the fluffy smokescreen that the term sometimes signifies for faculty who have decided to "focus on their teaching". For Kay, it is essential that children encounter "real science". He uses the phrase "above the threshold" to emphasize that what students do must be authentic, and not circumscribed in a way that cripples asking questions and building testable models. At the end of this paper, he singles out for criticism Interactive Physics and SimCity:
Both of these packages have won many "educational awards" from the pop culture, but in many ways they are anti-real-education because they miss what modern knowledge and thinking and epistemology are all about. This is why being "above threshold" and really understanding what this means is the deep key to making modern curricula and computer environments that will really help children lift themselves.
I found particularly useful Kay's summary of Papert's seminal contribution to this enterprise and of his own contribution. Papert combined an understanding of science and math "with important insights of Piaget to realize that children could learn certain kinds of powerful math quite readily, whereas other forms of mathematics would be quite difficult." In particular, Papert showed that children could understand in a powerful way the differential geometry of vectors and that the computer could play an essential role in abetting this understanding by doing the integral calculus that is beyond them -- and which performance is not necessary for the first-order understanding of the science. Kay claims himself to have made only two small contributions: What must the design of these tools be like? It must hide gratuitous complexity while exposing essential complexity, doing "the best job possible to make all difficulties be important ones whose overcoming is the whole point of the educational process". Learning involves overcoming difficulties, but we want learners to overcome difficulties that matter, not defects in the tools or pedagogy that we design for them. This is a common theme in the never-ending discussion of which language to use to teach CS majors to write programs -- if, say, C introduces too many unnecessary or inconsistent difficulties, should we use it to teach people to program? Certainly not children, would say Kay, and he says the same thing about most of the languages we use in our universities. Unfortunately, the set of languages that are usually part of the CS1 discussion don't really differ in ways that matter... we are discussing something that matters a lot but not in a way that matters at all. Getting the environment and language right do matter, because students who encounter unnecessary difficulties will usually blame themselves for their failure, and even when they don't they are turned off to the discipline. Kay says it this way:
In programming language design in a UI, especially for beginners, this is especially crucial.... Many users will interpret [failure] as "I am stupid and can't do this" rather than the more correct "The UI and language designers are stupid and they can't do this".
This echoes a piece of advice by Paul Graham from an entirely different context, described here recently: "So when you get rejected by investors, don't think 'we suck,' but instead ask 'do we suck?' Rejection is a question, not an answer." Questions, not answers. Kay spends some time talking about how language design can provide the right sort of scaffolding for learning. As students learn, we need to be able to open up the black boxes that are primitive processes and primitive language constructs in their learning to expose a new level of learning that is continuous with the previous. As Kay once wrote elsewhere, one of the beautiful things about how children learn natural language is that the language learned by two-year-olds and elementary school students is fundamentally the same language used by our great authors. The language children use to teach science and math, and the language they use to build their models, should have the same feature. But designing these languages is a challenge, because we have to strike a balance between matching how learners think and providing avenues to greater expressiveness:
Finding the balance between these is critical, because it governs how much brain is left to the learner to think about content rather than form. And for most learners, it is the initial experiences that make the difference for whether they want to dive in or try to avoid future encounters.
Kay is writing about children, but he could just as well be describing the problem we face at the university level. Of course, we may well have been handicapped by an education system that has already lost most students to the sciences by teaching math and science as rules and routine and dogma not to be questioned. That is ultimately what drives Kay and his team to discover something better. If you enjoy this paper -- and there is more there than I've discussed here, including a neat paragraph on how children understand variables and parameters -- check out some more of his team's recent work on VPRI's Writings page. -----