I have found my niche for this part of my career – I’m a math teacher and I love to make my students debate. Make no mistake – it takes some time to do a debate in class, it takes preparation, and it takes up a class period that could be used for instruction or assessment or a project or an exploration or a computer lab, which are the things that take place most days in most math classes around the country.

In the (no longer very new) Common Core Standards, Math Practice 3 (MP3) is one of the 8 Standards for Mathematical Practice, which are standards that cut across grade/content levels. MP3 states that students should be able to *“Construct viable arguments and critique the reasoning of others.”* A debate is defined by Oxford Dictionaries as *“A formal discussion on a particular matter in a public meeting or legislative assembly, in which opposing arguments are put forward and which usually ends with a vote.” *It is easy to see how well these can fit together. A student debate about a mathematical proposition is one in which they put forward arguments in favor of or opposition to the proposition. Through this process, they are given opportunities to further develop and synthesize ideas and create examples to support their arguments, which requires them to apply ideas that they can understand (and remember). In sum, it covers all the bands of Bloom’s taxonomy (which has its own controversy, acknowledged, but that’s another conversation).

For these reasons, I have found a debate to be an excellent way to review a unit after it has finished. For example, after covering solutions of linear equations in my Algebra 1 classes, we had a debate in which students argued that either elimination or substitution was the best approach to take in order to solve a linear system. I did not create an experiment that is worthy of peer review, but as a case study, in my two classes, assessment scores increased on average from 2.4 on substitution and 2.1 on elimination to 3.6 on substitution and 3.4 on elimination. The pass rates for substitution increased from 67% to 95%, and on elimination increased from 38% to 90%. (My assessments are SBG assessments scored on a scale from 0 to 4. These results cannot only explained by the debate, as students also got the feedback from their first assessments, and not all students retook their assessments. But it is some nice anecdotal evidence.)

That should be enough of a reason to include debates in math classes, but I’ve skipped over the most important reason. It’s a lot of fun! Students get to collaborate, research, and then they are encouraged to argue, with some extra points (not extra credit of course) on the line. There are a variety of formats that we can use for debates, and they can range from a short “Which One Doesn’t Belong” warm up activity to a formal debate, and everything in between. Students are able to understand the protocols fairly quickly, and get used to preparing for debates because they could come up at any time. In fact they will sometimes ask if we can debate a topic if it isn’t immediately settled in class. (Case in point- a student asked if parallelograms could be defined as a subset of trapezoids. In other words, are trapezoids defined as having at least one pair of parallel sides, or exactly one pair of parallel sides? I realized that I didn’t have a definite answer, and that it isn’t a settled definition, and lo and behold, students begged for a debate, which we did a week later.)

Are you sold on debates yet? For more information, you can take a look at my Google Slides document from my presentation at the NCTM 2017 Annual Conference in San Antonio.

How did the students resolve the parallelogram/trapezoid question?

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I have two geometry classes, so two debates, and both classes had different winning sides. I’d have to go back and look at my notes for those debates to see all the reasons, but there was a really interesting philosophical piece about the importance of inclusion to have a parallelogram be a special type of trapezoid. On the other hand, good arguments were made for distinguishing between a parallelogram and trapezoid for the same reason that we distinguish between a parallelogram and a kite. Creating more distinct groups allows your vocabulary to be more precise, and then people cannot question the meaning of your words and have to focus on the rest of your statements or arguments. All in all, there was a lot of really great discussion on both sides.

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