I ran across a couple of articles that discuss something that I’ve been pondering (and talking about on this blog) for a while now. That is, teaching mathematics without requiring that students do the final calculations by hand.
Here’s the basic idea. Computation (formulating solutions to problems) is more important now than ever. However, since we have calculators, computers and even Web sites to crunch the numbers for us, doing the calculations by hand is out-of-date and should be de-emphasized.
This idea was recently promoted by Conrad Wolfram, the head of Wolfram Research, which produces the software package Mathematica and the math engine Wolfram Alpha. Here’s an interview with Wolfram where he describes his idea in a bit more detail.
I’m not saying this is a bad idea, but I can see that there are any number of ways for someone to take this in a negative way. It takes a while to think this through for those of us who (like me) were raised and educated in the traditional math curriculum.
I teach undergraduate math, so I’m always on the look-out for ways to improve my classroom content. That means that sometimes I use my classroom as a lab for a little empirical research.
For example, this term I’m teaching College Mathematics. This is a 100-level class aimed at non-technical students (we’re a career college) and my students are in a mix of majors like Medical Assisting, Graphic Design and Business Administration. The course description is as follows:
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 it’s essentially a course in functional numeracy. For most of these students, this is the only math class in their program.
I decided to test the theory that the thing most people who claim to hate math actually hate arithmetic. My personal opinion is that arithmetic is unnatural and mechanical (since the learning strategy consists of memorization) and that math places more emphasis on creativity, intuition and critical thinking. With this in mind, on my first day of class I did the following:
- Explain the difference between math and arithmetic.
- Set a policy of ‘no arithmetic by hand, unless it’s absolutely convenient’. (For example, I’m not going to grab a calculator to multiply 9 by 5.)
For each session, I start with a “Math Minute” where I present a short puzzle or thought experiment to get students thinking and discussing some math concept. For the rest of the period I discuss this week’s subject (I can’t change the text or the lesson plan). However, I keep the conversation focussed on concepts rather than calculation. When we work through problems, we spend most of the time thinking through the set-up and then use a calculator (or spreadsheet or Wolfram Alpha) to get the answer. (This is only for problems where the calculation isn’t obvious. See 2 above.)
As you can see, I haven’t made any big changes (evolutionary, not revolutionary). I still have to pay attention to different student learning styles, encourage group participation, share problem-solving tricks and all of the other classroom techniques I’ve been using for years now.
As expected, there was some resistance. I was taking an unusual approach by de-emphasizing those parts of a math class that are traditionally the focus. But overall the response has been positive.
Now I don’t think that all classroom math should be abstracted to machines. In my class, we still use decks of cards and dice to talk about probability, count floor tiles to think about surface area and lots and lots of whiteboard work complete with diagrams. The point is to get students to connect with math and I’m just shifting that connection to the problem set-up process and I’m a fan of whatever works.