Fractions as Filler

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?

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’.

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.

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.

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. 

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.

Join Dev Math Revival on Facebook:

2 Comments

• 

  By G. Michael Guy, May 21, 2011 @ 10:37 pm

  I think most all rational number arithmetic should be eliminated from developmental curriculum precisely because it does not transfer to rational algebraic fractions. In fact, the most common approach to algebraic rational expressions is to eliminate the fractions altogether by clearing denominators. Equations: clear denominators. Simplifying complex algebraic fractions: yup, eliminate denominators in numerator and denominator, factor and cancel. So why would we waste so much time with fraction arithmetic with arbitrary denominators? It’s a waste of time and an unnecessary hindrance to students who want to continue their education. Education delayed is often education denied for developmental students, and it’s time to stop doing this based on some ideal world mathematicians create about what students “ought to be able to do.”

• 

  By Michael Wolf, June 6, 2011 @ 2:53 am

  I have been teaching a “Fundamentals of Mathematics” course at a two year college for several years now. I have deveeloped lots of materials about teaching fractions (visuals, manipulatives, text) and had modest success in helping some students. However, this yar I have been interviewing program directors at the various programs offered at the college. I have “learned” that fractions are not used in 80-80% of our programs. The fashion design and interior design people use them a bit. However, all of our health related programs do not. My sense is that this is primarily a result of the digitalization of the universe. Calculators and machines for performing calculations and procedures report results as decimals. I hear again and again that students don’t understand ratios and proportions, and that the most important thing to emphasize is proportional reasoning. That interest in proportions has nothing to do with “fractions,” but has to do with things such as how much medication to give to a person who weighs 110 kg if the dosage is 3 mg per 25 kg of body weight. My intention is to reconfigure the course so proportional reasoning is highlighted and work with fractions is added at the end, if there is time.

Other Links to this Post

RSS feed for comments on this post. TrackBack URI

Leave a comment

You must be logged in to post a comment.