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!