Order of Operation

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.

In trying to find sources for what I "feel" and trying to find out why I did find one interesting source that I am going to want to do some more research on, Dr. Houman Harouni from Harvard University, who did an NPR interview.