Meeting Them Where They Are

I teach two Financial Math classes.  The first semester is really financial literacy, as there's no math involved, and in the second semester we do a few calculations.

Some of my students are there because they want to learn some financial literacy, how to do their taxes, etc.  Some are there because they need a 2nd year of math in order to meet graduation requirements, and it took them awhile to pass that first year.

Yesterday we were reviewing for the final exam.  Some of the problems (commission, tax rates, employee share of health insurance costs) involve percentages, an elementary school topic that unfortunately more than a couple students never mastered.  Sure, you and I know when to move the decimal point two places to the left or to the right, and why, but to some students that's just magic math they've never truly understood.  And that's sad.

If they haven't learned it some time since 4th grade, I doubt I'd be able to teach it in any meaningful way.  Besides, the rest of the class can handle decimals and percentages, and that's not really my curriculum.  At this point, decimals and percentages are not ends unto themselves but are tools by which we get answers to more meaningful questions.  It's long past the time to be teaching and learning how to use the tool.

But several questions on my final exam do involve percentages (see above), and I want to give my students a fighting chance--and maybe help them in the process.  So I spent several seconds explaining percentages.

"Per cent".  There are 100 cents in a dollar, and 100 years in a century.  "Per cent" means "out of 100".  If you forget that, you can see the 1 and 2 zeroes in the % sign!  So 6% means "6 out of 100", or 6/100.  A realtor's 6% commission on a $500,000 house means we want 6% of 500,000.  To find that, we convert 6% to 6/100 and multiply that by 500,000.  On the calculator: 6 divided by 100 times 500,000.

Most students can handle 6%, even converting to decimals.  What about Medicare's 1.45% tax rate?  That's a little more confusing to those who haven't mastered the use of decimals.  Not anymore!  Per cent means "out of 100", so 1.45 divided by 100 times whatever.  Everything's consistent, everything's easy.

I actually got a couple Zoom chat messages thanking me for explaining it this way, because now it "makes sense".  I don't believe that, really; what they meant was that I've made the tool easier for them to use so they can solve the more meaningful problems and understand the answer to those.  

I doubt they truly understand the math, but they can use it--and for some students, that's enough.