My Students Don't Know How to Work With Percents

Recently we've moved away from that abstract mumbo-jumbo in the gen-ed class and have been working with numbers and formulas. Ironically, my students prefer to study the computational tasks that they're used to but can not do (and would fail if we spent significant time on) but despise working with the abstract concepts that they are smart enough to do a reasonable job of understanding.

The theme for the rest of the semester is percents.

We did a problem where they were told the price of the item ($20), the sales tax rate (8%), and the percent discount (25%). The question asked whether getting a discount of 25% and then not having to pay the 8% tax could be thought of as a 33% savings from the usual, non-discounted, with-tax price. (This problem was based on an advertisement that I got in the mail claiming just that.) One student couldn't figure out why the $20 item was $21.60 after tax. No one could decide whether or not paying $15 for the item would be a 33% discount from the $21.60 normal (with-tax) price.

We did another problem in which we were calculating what percent of the positive tests from a medical test were patients who actually had the condition. We found that of the 604 patients who tested positive that only 10 of them had the condition (the remaining 594 were false positives). I calculated the rate as 10/604 and stated that it was about 1.7%. One of my students raised her hand and asked why 10/604 is about 1.7%.

In another problem, we were trying to calculate 60% of 495,000. A lot of students in my class didn't know how to do it.

Tomorrow I start on financial math. We give the students all the formulas, and they struggle to enter them into their calculators because they do not know enough about order of operations. I'll bet you money that on the exam that at least one student will calculate the monthly payment on a loan to be a number greater than the principal.