My winter break this year has
been largely dedicated to recovering from knee replacement surgery, but I also am
preparing for the Spring semester, on the assumption that my class will make.
Like every teacher I know I am always working to improve how I teach, and
adjusting my syllabus, the assignments, and reflecting on what worked and what
didn’t work last semester. Some of this comes from the student evaluations I
get, which I will talk about in another post, but I also look at old tests to
see where the difficulty was and work on how to explain things more clearly.
One thing that has been on my
mind lately is the order that we introduce the most basic material to our
students. In Basic Math Skills and in Pre-Algebra the book is laid out just
like math is taught in elementary school:
Whole
numbers (then integers in Pre-Algebra)
Fractions
(Rational numbers)
Decimals
Percents
& Ratios
The question I have had for a
long time is, does this make sense? Is there a good reason that the subjects
are taught in this order? Is that reason equally valid for children and adults?
I have heard, since I was a tutor
in the late 1980’s that there are two times in primary math teaching where
students have been shown to have the most problems, often leading to them
feeling that they “can’t do math.” One of them is long division, which I
personally remember struggling with, and the other is fractions.
Learning to work with fractions
involves several useful skills. From a strictly math teacher point of view, if
you don’t know how to deal with numerical fractions, then it will be that much
harder for you when you get to ‘algebra fractions’ (i.e. rational expressions).
From a broader, educational point of view fractions, as well as long division,
are what used to be called synthesis problems, where you take several different
parts of prior learning and figure out how to use them all together.
When dealing with adult students,
many of whom come into the class with low confidence in math, as well as often
having memories of past failures in math, does it really make sense to have the
second major topic be one that, as I often feel my students see it, is the “F-word”
of arithmetic?
Perhaps what would be better,
especially when dealing with adult students who have at least a basic, day to
day understanding of money, to do decimals first, and then transition into
fractions from there. I have done this before in Basic Math classes, and anecdotally
it seems to have better results with the students. They have two tests with
good grades overall before they face the more daunting fractions.
What I really need to do is develop
a way to test this hypothesis. Several classes, taught by the same teachers,
some of which do it the traditional way, and some of which would use a modified
order of topics. This is where I would love to put my energies going forward.
