# Why study fractions?

November 23, 2017 1 Comment

I googled the question “Why study fractions?” (for reasons I describe later) and found a study (reported in Swanbrow 2012) that invites critical thinking at two levels: 1) the assumptions, evidence, and reasoning warrant scrutiny; and 2) what is it that allows researchers and policy makers to proceed as if there are no alternative interpretations to be drawn from the study?

In brief, the study reports that “understanding fractions and division at age 10 predicted algebra and overall math achievement in high school” and cites an educational researcher concluding that the “findings demonstrate an immediate need to improve the teaching and learning of fractions and division.”

Critical thinking exercise for readers:

Please scrutinize the assumptions, evidence, and reasoning involved in this conclusion.

While you are doing the exercise, let me discuss why I asked the title question.

A: I wanted to see if other educators were questioning the teaching of fractions and putting forward reasons such as the ones to follow:

1. Students find fractions difficult and they get discouraged from math.;

2. If / or – is understood as a symbol for the first number is divided by the second, this is a) easy to calculate in this age of calculators, AND b) easy to visualize, e.g., imagine someone has divided 2 pizzas into 5 equal servings–that’s what 2/5 means;

3. calculators make it is easy to multiply a decimal number by any other decimal number, including answers to a fraction;

4. more generally, we can make use of technology to open up room for thinking that was not previously possible, or for which there was no time left in the curriculum. (Consider, for example, what the uptake of arabic numerals did for mathematical thinkers in regions of the world that had for centuries held to roman numerals. Surely, the back to basics don’t want us to go back to using roman numerals! But, if not back to that basics, then what are the criteria for what counts as a basics that we need to hold onto versus a basics to let go of?)

If you are still doing the critical thinking exercise, don’t read further. If you have completed it, please compare your response to mine to follow and use the comment section to compare/contrast.

An alternative interpretation is that a) students who do not do well at fractions do not study the later math. topics well because they might see themselves as not good at math., be told that by teachers and peers, drop out of those classes; b) fractions may currently be the gateway for some to further math (for the converse of the reasons it is the roadblock for others in #a), but that does not mean there are no other pathways to later topics, let alone, other ways to envisage the mathematical thinking that might be fostered. The study does not seem to have been designed to compare alternative pathways to achievement of mathematical thinking.

More generally, the interpretation reported above, is an instance of what *is* — in the situation studied — being viewed as an *ought* — for how people move forward.

Reference

Swanbrow, D. (2012) “Fractions are the key to math success, new study shows,” http://home.isr.umich.edu/releases/fractions-are-the-key-to-math-success-new-study-shows/

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