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.<\/p>\n
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.<\/p>\n
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.<\/p>\n
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.<\/p>\n
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.<\/p>\n
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.<\/p>\n
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.<\/p>\n
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.<\/p>\n
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. <\/p>\n
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?<\/p>\n
Let’s do percents right — drop almost all of the conversions, and the ‘percent sentence’ problems; focus on really understanding them!<\/p>\n
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