I was browsing the CLAA site today, and was looking at links to an axiom-based arithmetic text (deductive study - CLAA thumbs up) and to an early inductive arithmetic text (CLAA thumbs down). (Deductive study is first learning general principles and then applying them to specific examples; inductive study is first looking at specific examples and then extracting the general principle from them.)
While reading the intro to the inductive text, I was struck by how similar its aims were to most modern math texts. The author emphasized starting with concrete examples, rather than jumping straight into abstract, number-only work. He started with children's innate understanding of the four operations and built from there. He even advocated using manipulatives! He made a point of stating that his book taught math in a way that was aligned to how children naturally thought about math, and thus they could learn easily, even at young ages.
This is the same goal that most modern educators have - to take what we know about how people learn in order to find the best - easiest, most efficient - way to teach the subject. While people may disagree about which way is best, no one disagrees with the goal. Certainly homeschoolers, especially, have embraced the ideal of finding the particular approach to each subject that best fits their student(s) and how they learn. As for myself, I've spent a fair bit of time studying the latest research in cognitive science and second language acquisition, in order to find the best way to teach my kids.
But, as I was thinking about the differences between the two arithmetic books, it hit me just what it means to "train the brain." It's not just teaching via a particular (deductive) approach, but teaching via an approach that *intentionally* does not align with how people naturally learn. After all, if children naturally thought that way, then they wouldn't have to be specifically taught to do it.
So the fact that traditional classical approaches to some subjects (Latin and Greek, math) don't line up with modern research on the way our brains work is not a bug, but a feature. (Not, of course, that you can't use how people learn to help you design the best, most efficient way to teach things via a classical approach, but that will, almost by definition, be harder than (some) non-classical approaches.)
I had never thought about it that way before, even though it seems blindingly obvious, now.
While reading the intro to the inductive text, I was struck by how similar its aims were to most modern math texts. The author emphasized starting with concrete examples, rather than jumping straight into abstract, number-only work. He started with children's innate understanding of the four operations and built from there. He even advocated using manipulatives! He made a point of stating that his book taught math in a way that was aligned to how children naturally thought about math, and thus they could learn easily, even at young ages.
This is the same goal that most modern educators have - to take what we know about how people learn in order to find the best - easiest, most efficient - way to teach the subject. While people may disagree about which way is best, no one disagrees with the goal. Certainly homeschoolers, especially, have embraced the ideal of finding the particular approach to each subject that best fits their student(s) and how they learn. As for myself, I've spent a fair bit of time studying the latest research in cognitive science and second language acquisition, in order to find the best way to teach my kids.
But, as I was thinking about the differences between the two arithmetic books, it hit me just what it means to "train the brain." It's not just teaching via a particular (deductive) approach, but teaching via an approach that *intentionally* does not align with how people naturally learn. After all, if children naturally thought that way, then they wouldn't have to be specifically taught to do it.
So the fact that traditional classical approaches to some subjects (Latin and Greek, math) don't line up with modern research on the way our brains work is not a bug, but a feature. (Not, of course, that you can't use how people learn to help you design the best, most efficient way to teach things via a classical approach, but that will, almost by definition, be harder than (some) non-classical approaches.)
I had never thought about it that way before, even though it seems blindingly obvious, now.
