Here are is the first of many blog posts about my journey towards understanding how children learn math and how I can facilitate that learning.
I am reading Young Children Reinvent Arithmetic: Implications of Piaget's Theory (Second Edition) by Constance Kamii with Leslie Baker Housman, and I am fascinated.
The topic of math has scared the hell out of me for a long, long time. I grew to hate it in school, and was convinced by the education system, and some of my teachers, that I would be better off if I just didn't spend time in a math classroom.
What I'm really getting at is that for me to be blogging about math feels like risky business. So why am I doing this? Like all of my blog posts, I learn a lot through reading, thinking, listening and writing. And then I learn even more through interacting with others like you.
As I read Kamii's book, I am introduced to the idea of constructive abstraction. It's explained as a mental operation where relationships are constructed between objects. For example, if you have two apples, there are only two because they are relating to each other by being the sum of their two wholes. In other words, one whole is created because two wholes come together to become two parts.
I find this fascinating because Kamii uses this logic to explain why there is no such thing as an "addition fact". Kamii points out three objects are observable but the number "three" is not. Three is a relationship created by constructive abstraction. She then goes on to say that if three is not observable then 3 + 5 = 8 is also not observable.
Kamii's playing hardball here, because what she says next won't fly well with the back to basics crowd:
Addition grows out of children's own logic and is not a "fact" that exists in the external world. The objective of "knowing addition facts," which is often advocated by educators, is therefore not a valid objective.Never mind the back to basics crowd, this hardly sits well with me! Not because I don't want to believe her - like I said, I'm fascinated, but here I am - 31 years old with 16 years of formal education that has taught me the opposite of this. I have a lot of unlearning to do...