In many of our developmental courses, we focus on building skills with fractions. For some of us, ‘fractions is where we start’. How have fractions earned such a place of honor?<\/p>\n
To understand the place of fractions in our curriculum, think about what we mean when we say ‘fractions’ — identifying types (proper, improper), reducing, building-up, four operations, conversion to decimal form, and word problems. My comments are based on what I see in the vast majority of courses & textbooks on ‘fractions’.<\/p>\n
I see two fundamental problems with the role of fractions in our work. First, the content lacks sufficient justification in the lives of our students. Second, our curriculum focuses on the algorithms to an extent that precludes significant understanding.<\/p>\n
Originally, fractions in our first courses were justified for occupational as well as mathematical reasons — many jobs involved working with fractions, and college mathematics depended on manual skills with fractions. These occupational justifications have diminished to the point of being a specialty affecting a small proportion of students; various technology tools in occupations either perform the calculations or avoid fractions entirely. The college mathematics justification was weak originally, and that target is valid for a small portion of our students; even if we could inspire most of our students to take college mathematics courses, the algorithms in developmental courses have little purpose … the understanding does.<\/p>\n
Our curriculum with fractions is especially ‘procedurally bound’ within our codes of LCM, GCF, and rules. My students get trained to respond correctly to problems with two fractions separated by operation symbols, but can not explain why they do those steps. Addition of fractions is not connected to ‘like terms’ as a general concept; adding ‘3x’ and ‘5x’ is much simpler conceptually than adding ‘3\/4’ and ‘1\/8’, though we insist that students get right answers for the complex problem before we cover the concept behind it. The other operations are also generally done on ‘auto-pilot’; no need to think too much here, just remember the steps that match the operation. Every time we ‘cover’ fractions (say algebraic fractions) we pretty much teach the process over again … because it looks different, students do not connect the procedures. <\/p>\n
We use fractions as filler in the curriculum. I conclude that we think we have more time than needed for any ‘good stuff’, so we use fraction work to fill in the open spots. We certainly do not teach fractions in a way that transfers to other situations within mathematics or outside of mathematics. I believe that we would not hurt anybody, and might help some, if we eliminated all work on fraction operations.<\/p>\n
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