What is a Mathematical Circuit?

Have you ever done circuit training at a gym? Then you have an idea what a mathematical circuit is.

The intention is to keep you focused and engaged on practicing the skills you need to acquire, without allowing you to get tired or bored with the routine. In a gym you might do 20 sit-ups, then move to another station and do 20 lunges, then to another station and do 20 jumping jacks. Then you might repeat the circuit, or you may continue to visit other stations and do work with weights and then perhaps ride a stationary bike for 5 or 10 minutes. At first you might “warm up” with some stretches or easier exercises, and hit the peak of your work-out 1/3 to 2/3 of the way through it. A professional trainer would devise a circuit for an athlete (or a weekend warrior) to work on cardio, strength and flexibility (for example).

The mathematical circuits I am crafting (and my colleagues are helping me check), have many of the same elements as circuit training at the gym. Students enter the circuit on an “easy” problem, solve it, and then hunt for their answer to advance in the circuit. [Note: If students can not find their answers, they know they are doing something wrong – this element of self-check in the math classroom is essential.] As students move forward in the circuit, the problems become progressively more difficult, and challenge their previous skills and knowledge. With almost 25 years of high school mathematics teaching experience, I know where students’ common errors and misconceptions are, and so I weave those problems in to the circuit.

Most circuits typically have between 12 and 28 problems to work. However, the students do not feel that they are staring at a blank paper, moving at a snail’s pace through their work. Students get to move around on the page, similar to moving around the gym, which helps keep them engaged. Each problem has a space to work it out. The circuits are great for review, or for weaving two concepts together, or for practicing a specific skill (such as order of operations). Circuits are great for guided practice, independent practice, or even cooperative learning.

I first saw a circuit a few years ago. An AP Calculus colleague of mine, Nancy Stephenson from Houston TX, forwarded a 24-question review circuit she wrote to me. I used it with my AP students for several years. Then, I wrote a two separate review circuits for Algebra I in preparation for the state test. The students reached a whole new level of study independence while they were working on them since thy could easily check their answers and not get bored by just doing a problem, then the one underneath, then the one underneath that, etc.

In the summer of 2013 I began creating focused circuits that did not just skip around in the review, but probe the material at a deeper and deeper level as students advanced in the circuit. So far I have written about 50 circuits on topics which range from elementary math to calculus. My circuits are used by students in our high school, and by students all over the country in high schools and colleges. I have led workshops on circuit writing and one of my university colleagues uses my circuits as part of his professional development training sessions. But the most exciting part about my circuit writing is that I have inspired several of my colleagues to write circuits and theirs are excellent! The upshot is that lots of students are engaging with mathematics on a high level.

Help us spread the great news about the benefits of mathematical circuit training!

I have started posting my mathematical circuits (some for FREE and some for sale) on “Teachers pay Teachers”. Please search “Mathematical Circuit Training” on http://www.teacherspayteachers.com.

Here is the first page of a free four-page algebra review circuit:

Happy training!