- Piaget’s great insight was that knowledge is not delivered from teacher to learner; rather, children are constantly constructing knowledge through their everyday interactions with people and objects around them. Seymour’s constructionism theory adds a second type of construction, arguing that children construct knowledge most effectively when they are actively engaged in constructing things in the world. As children construct things in the world, they construct new ideas and theories in their minds, which motivates them to construct new things in the world, and on and on.
- Seymour provocatively argued for “projects over problems.” Of course, Seymour understood the importance of problem solving. But he believed that people learn to solve problems (and learn new concepts and strategies) most effectively while they are actively engaged in meaningful projects. Too often, schools start by teaching concepts to students, and only then give students a chance to work on projects. Seymour argued that it is best for children to learn new ideas through working on projects, not before working on projects.
- Slowly I began to formulate what I still consider the fundamental fact about learning: Anything is easy if you can assimilate it to your collection of models. If you can’t, anything can be painfully difficult.
- The understanding of learning must be genetic. It must refer to the genesis of knowledge. What an individual can learn, and how he learns it, depends on what models he has available. This raises, recursively, the question of how he learned these models. Thus the “laws of learning” must be about how intellectual structures grow out of one another and about how, in the process, they acquire both logical and emotional form.
- 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 (just as the gears shaped my understanding of algebra although they were not physically present in the math class).
- 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, 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. The computer can be a mathematics-speaking and an alphabetic-speaking entity. We are learning how to make computers with which children love to communicate. When this communication occurs, children learn mathematics as a living language.
- Like other builders, children appropriate to their own use materials they find about them, most saliently the models and metaphors suggested by the surrounding culture.
- I began to see how children who had learned to program computers could use very concrete computer models to think about thinking and to learn about learning and, in doing so, enhance their powers as psychologists and as epistemologists.
- 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.”
- Plato wrote over his door, "let only geometers enter." Times have changed. Most of those who now seek to enter Plato’s intellectual world neither know mathematics nor sense the least contradiction in their disregard for his injunction. Our culture’s schizophrenic split between “humanities” and “science” supports their sense of security. Plato was a philosopher, and philosophy belongs to the humanities as surely as mathematics belongs to the sciences. This great divide is thoroughly built into our language, our worldview, our social organization, our educational system, and, most recently, even our theories of neurophysiology. It is self-perpetuating: The more the culture is divided, the more each side builds separation into its new growth. I have already suggested that the computer may serve as a force to break down the line between the “two cultures.”
- Our children grow up in a culture permeated with the idea that there are “smart people” and “dumb people.” The social construction of the individual is as a bundle of aptitudes. There are people who are “good at math” and people who “can’t do math.” Everything is set up for children to attribute their first unsuccessful or unpleasant learning experiences to their own disabilities. As a result, children perceive failure as relegating them either to the group of “dumb people” or, more often, to a group of people “dumb at x” (where, as we have pointed out, x often equals mathematics). Within this framework children will define themselves in terms of their limitations, and this definition will be consolidated and reinforced throughout their lives. Only rarely does some exceptional event lead people to reorganize their intellectual self-image in such a way as to open up new perspectives on what is learnable.
- In retrospect, we know that the road that led from nineteenth-century transportation was quite different. The invention of the automobile and the airplane did not come from a detailed study of how their predecessors, such as horse-drawn carriages, worked or did not work. Yet, this is the model for contemporary educational research.
- The analogy of the dance class without music or dance floor is a serious one. Our education culture gives mathematics learners scarce resources for making sense of what they are learning. As a result our children are forced to follow the very worst model for learning mathematics. This is the model of rote learning, where material is treated as meaningless; it is a dissociated model. Some of our difficulties in teaching a more culturally integrable mathematics have been due to an objective problem: Before we had 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—a mathematics-speaking 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.
- First, there was the continuity principle: The mathematics must be continuous with well-established personal knowledge from which it can inherit a sense of warmth and value as well as “cognitive” competence. Then there was the power principle: It must empower the learner to perform personally meaningful projects that could not be done without it. Finally there was a principle of cultural resonance: The topic must make sense in terms of a larger social context.
What I got out of it
- Some of the examples are a bit outdated at this point, but the principles remain the same. Breaking ideas down into their smallest, simplest units is a great way to proceed. Think of learning as an iterative game to be played and improved upon, not something that is right/wrong, static.
