The Roseberry Family - 2009

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book notes: The Glass Wall - Why Mathematics Can Seem Difficult

From time to time I enjoy reading books on how people - especially children - learn. Recently I read The Glass Wall by Frank Smith. Here are a couple of quotes I thought were notable:

One would think that language is something that is discovered by every child (or taught to every child). Yet studies of the rapidly efficient manner in which language skill and knowledge develop in children has led many researchers to assert that language is invented (or reinvented) by children rather than discovered by them or revealed to them. And no less a psychologist that Jean Piaget has asserted that children have to invent or reinvent mathematics in order to learn it. In a sense, the wheel is reinvented every time someone discovers what a wheel can do. p14-15

Memory, like understanding, is unavoidable in mathematics and everything else. Although mathematics might seem to be a constant process of "working things out", the foundation of any kind of mathematical enterprise is memory, and a great deal of learning mathematics involves committing mathematical facts and procedures to memory. Memory eases all of our way through mathematics and we can't get started without it. p113

Many kinds of difficulty confront learners. Locating these difficulties in the learner's brain and giving them pseudo-medical names is not helpful. Usually what is needed is more time, more understanding, more sensitivity, less pressure, a fundamentally different approach to mathematics education, stressing comprehension rather than memorization - and sometimes a period of mental convalescence. p135

He boiled mathematics to a relationship between numbers. In the simplest terms "one and one more". The rest of counting, for instance, is just a repeat of that method.

He gave several good reasons why memorization of facts is greatly aided by comprehension of the facts rather than just by rote.