Developmental Mathematics Revival!

Stealth Percents

A student experiencing all of our developmental math courses will see quite a few percents, and probably not understand much of this — in spite of obtaining hundreds of correct answers. We cover stealth percents, not real percents.

Percents are stealth when we use rules and do complicated conversions between percents and other forms. The truth is that converting, by itself, is not that useful; we cover conversions in an attempt to build understanding. However, the understanding is submerged — the rules become the content, not the percents.

Percents are stealth when we use “is over of” and solve dozens of problems based on the sentence structure “8 is 20% of what”. Getting correct answers for these problems shows little knowledge of percents.

Percents are stealth when we cover ‘applications’ using specialized vocabulary such as ‘discount’, ‘mark-up’, and others. We create stimulus-response connections, but little knowledge of percents.

Some of this emphasis on percents comes from a time when many of our students would be working in a retail environment without calculators — let alone computers. Those days are gone, for the vast majority of our students.

Yet, percents are important. We need to understand percents to deal with daily life and academics. Understanding percents means that we know how to communicate accurately — that percents always have a base. If two percents share a base, then it might make sense to combine them (like percent of income for different categories); if two percents have a different base, then it never makes sense to combine them directly — we need to compute a common measure (like dollars) before combining.

Understanding percents means that we know that mixing two strengths means a mixture that is intermediate, whether we are talking about chemicals — milk fat — or interest rates.

Understanding percents means that we can connect a percent change to a symbolic representation (algebraic term) and to a table of values. We can deal with a sequence of percent change.

Understanding percents might also deal with the most common use in media — surveys and polls; these are different kinds of percents (though they always have a base!), and the primary use of these percents is to sway public opinion.

If you think your students understand percents, give them this simple problem: In 2010, all employees took a 10% pay cut … in 2011, all employees received a 10% raise. How does their 2011 salary compare to their 2009 salary?

Let’s do percents right — drop almost all of the conversions, and the ‘percent sentence’ problems; focus on really understanding them!