In the comprehension questions in Algebra I, I ask students to probe several problems consisting of Algebraic Addition. For example:
3a + 4a + 5a = 12a
What I'm primarily concerned with here is: How do we know that the numerical factors in thesequantities can just be added together, as 3 + 4 + 5 = 12 ? How can we know, for certain that 3a + 4a = 7a ? What, exactly, is going on in this operation?
We do not want to just "do what the book says" in Mathematics. This is good enough, usually, for school work tot get done, but it does not prepare students for real problem solving. I won't allow that kind of fake Math in CLAA studies.
William Michael, Headmaster
Classical Liberal Arts Academy