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
Where do we go from here? This seems no different than how algebra is
introduced normally. What I am proposing
is taking the math out of it in the beginning, and then slowly adding the math
in after the concept of abstraction is understood. We ask the students to look at some common
problems they may face in their daily lives.
We will then list out some of the top suggestions. The students will
then be asked to find the commonalities between the problems to group them
together. Then the students are asked to make a name for each of the problem
groups. They can then begin defining the
general solution to those problem types. Keep it simple, only spend about a
week introducing the concept of abstraction with simple problems. After the idea of abstraction seems clear
then you could start adding the Math back into the process. You will begin with
asking the students about math related problems. You could start with something
simple like what is an even number. Many of the students by this point are
familiar with the idea of what an even number is. However, this time you can approach the same
way you approached your dictionary idea. You ask the students to create their
own definition of an even number. Allowing them to create their own mathematical
rules to use empowers them with the ability to not only recognize the steps of
problem solving, but to understand it rather than just memorize it.
Teaching abstraction
leaves a wide open doorway to many different possibilities. The hardest part of
learning math for many students is the daunting amount of formulas and rules to
remember. A student who knows how and why these rules work, and can look at a
problem and devise their own algorithms for solving it, will be way ahead of
the curve when they are faced with solving any problem they encounter. When you
think about it you use this concept every day. As adults we face many different
types of problems, and we solve them by first identifying the problem then abstracting
a set of procedures for solving them. We sometimes have similar problems that
we have solved before, and we encounter new problems that need new solutions. However, being successful in life is dependent
on the solidarity and efficiency of our ability to solve problems. When I say
problems I don’t mean just mathematical, it is the seemingly mundane parts of
life for some and the more perplexing or dire situations we encounter that I call
problems. Abstraction, logic,
deductive and inductive reasoning are so important to a successful life that part
of the curriculum of each grade level should be dedicated to them.
