Fractions: Not Getting Them is Not Your Fault!

Overview

Here’s the opener of the first chapter on Fractions in ARITHMETIC & ALGEBRA FOR RADICAL COMPRENSION.
Check out Chapters 5 and 6 here for my take on the full story of fractions.

Many people fear fractions. And this fear seems somewhat universal.

I have a theory as to why.

People first experience learning about fractions as youngsters at home, typically from sharing goods and desserts. Understanding portions of items—such as halves, thirds, quarters—is intuitive and natural.

The typical school curriculum then picks up on this intuitive start and over the course of several years next attempts to build a robust and coherent mathematical story of fractions from this start.

But the school curriculum is caught between two contradictory demands: the demand to be age appropriate and to develop “real world” meaning to the mathematics of fractions each step of the way, and to be honest about the mathematics itself, which, for fractions, very quickly steps beyond real world loyalties.

As I said in Section 23,

Mathematics is bigger and bolder than the real world. It is therefore bigger and bolder than all schoolbook attempts to make every part of it concrete and real. Mathematics certainly incorporates real-world models and is immensely powerful in helping describe them. But mathematics sits at a higher plane to them.

The teaching of fractions is particularly challenged by this fact.

As a result, many elementary- and middle-school curriculums on the topic are muddled and confounding. One doesn’t usually see that confusion right away as each step of the curriculum brings in a real-world idea that makes sense for that one step. It is only when you look back and try to make sense of the story as a whole do you say: Hang on! So, what is a fraction really? Which real-world model applies when, and why not to everything?

To see what I mean, what comes next is an overview of how the story of fractions is often presented from grades K to 7.

Read this section, but don’t take it too seriously. The only message I hope you glean from by its end is this:

It is not your fault!

If you are befuddled, confused, and scared by fractions, it is not your fault for not “getting” them.
(Actually, not getting them is a sign of your intelligence: you’ve picked up that something is awry.)

Here’s the school story of fractions as you may well have experienced it.

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