## Monday, May 13, 2013

### Better learning through abstraction..…

There are many barriers to learning and teaching mathematics, some of which include:  anxiety, comprehension, and focus.  How do we get past these?  First, let’s look at anxiety. Why does the mere mention of mathematics strike fear and confusion in students?   It seems there are so many different causes of this to look at, that we are unable to pin point a single method to fix the problem.  In fact to find the solution, we need use the solution.   You will say   “well that sounds impossible”.   If we don’t know the solution, how can we use the solution to find it? There is a simple answer, abstraction.
I touched upon the idea of abstraction in Algebra: the true heart of mathematics.  So rather than just focusing on a solution to all of the different barriers to learning mathematics, we instead use abstraction to find a general solution.  We can then begin teaching abstraction rather than just mathematics.   If we find ways to take the classic “math” out of the picture we avoid the instant fear that many students face.  The statement “Today, class we are going to invent a new dictionary” is much less daunting than “Today, class we are going to learn algebra”.   The first statement will immediately spark a curiosity. The students will begin asking questions, and wanting to know more.
What does inventing a new dictionary have to do with algebra?  To answer this, we first need to think what is algebra?  Algebra is basically a “dictionary” of formulas, theorems, and proofs which apply to a wide range of problems.
How do these relate to each other?  Let’s look at the commutative property of addition. In algebra this is “defined” as   (a + b = b + a) .    To look at this in words rather than algebraic symbols, you get

Commutative property of addition: When adding two numbers together the order of the numbers does not change the result of the addition.