The new school term started yesterday and I’m teaching a course called College Mathematics. Here’s the course description, straight off of the syllabus:

*This course develops problem–solving and decision-making strategies using mathematical tools from arithmetic, algebra, geometry, and statistics. Topics include consumer mathematics, key concepts in statistics and probability, sets of numbers, and geometry. Upon successful completion of this course, students will be able to apply mathematical tools and methods to solve real-world problems.*

So this is intended to be a course in functional numeracy, which can be defined as “here’s math you can actually use”. Based on my work on “We Hate Math”, I decided to approach this class in a very different way than I had previously. So my opening remarks (after going over the syllabus and class policies) was an expanded version of this post. The short version was that I was trying to convince them that math and arithmetic are not the same thing and when people think they hate math, what they actually hate is arithmetic (and that’s completely normal).

While I was doing my patter (teaching is one quarter preparation and three-quarters live theater), one of my students raised her hand and asked, “So what’s the difference between math and arithmetic?”

This question stopped me in my tracks. I considered for a moment and this is the explanation I gave her.

Let’s suppose I want to drive to the pet store. I have a choice of two routes to get there, like so:

If I take Belmont, I have a five mile drive but if I take Damon, I have an eight mile drive. I then asked her which route I should take.

“Belmont”, she said.

“And that’s exactly the answer that arithmetic will give you”, I said, “because arithmetic can only really tell you that five is less than eight. Math, on the other hand, knows about speed limits, traffic lights,…”

“Rush hour”, said another student.

Yet another student chimed in, “Road repair.”

“Right!”, I said,scribbling the list on the whiteboard, “so if we go back to our example and I tell you that Belmont has a twenty-five mile per hour speed limit and there are five traffic lights between my home and the pet store. Damon, on the other hand, has a forty-five mile-per-hour speed limit and there are only two traffic lights, one at either end of the route, which one would you take?”

“Damon”, she said.

“That’s the difference between math and arithmetic.”

There’s a reason why the phrase “Do the math” actually means “Think it through”.