This week’s Occupy Math is about a teaching technique that increased attendance, raised test scores, and led to security coming about all the noise. Occupy math also can never use this technique again. The biggest single obstacle to the teaching of mathematics at the University Level is the use of large lecture classes. When Occupy math taught two sections of thirty students, he could lavish personal attention on the individual students. Now his ability to bellow to the people half-asleep in the back row is more apparent than his skill at individual instruction. Others at smaller Universities and Colleges, or in high schools, might still be able to use this technique.

**Large lecture classes severely limit the range of instruction techniques.**

The origins of this teaching technique are humble. Occupy Math had ten minutes to plan a lecture and was running a little ahead of the syllabus. He remembered both the game show Jeopardy! and a wonderful category-based current events game that the most excellent eight grade home-room teacher, Marion Wilbur, held every week. She was trying to get us to read the paper and, at least in Occupy Math’s case, it worked. To plan a lecture in ten minutes, five sets of five cards, like the ones pictured above, were quickly penned on index cards. The topic and point value are one one side of the cards and the problems are on the other. Each set of five cards was on a different topic. More points means the problem is harder.

The class was divided into competing teams and volunteers came to the board – one from each team – to work the problems. A correct answer, circled, was needed for victory. This in class exercise was hugely popular, but there were problems with it. Resolving these problems led to the following codification of the technique.

**Browsing these rules, try and imaging what events led to the later rules.**

- Each team supplies a volunteer. If a volunteer does to rise

promptly the instructor will pick one. - The first person to volunteer gains the right to pick the category and point value of the problem.
- The right to choose the category and point value alternates between the teams. Harder problems may be picked before easier one.
- The student that correctly completes a problem and circles their answer first gets the full point value of the problem as their individual score.
- The student that is second gets ten fewer points than the problem was worth, or zero if this is larger for their individual score.
- The winning team gets ten points apiece, fifteen if all the problems are worked. This is in addition to individual scores.
- The audience may help their person at the board by giving helpful suggestions that are not the answer or a logical next step. For example, if the player at the board has added 3+3 and gotten 9, a good step might be to ask “What is 3+3?”.
- Suggestions made must be clearly audible to both players. If they are not the instructor will repeat or compel the audience member to repeat their remarks.
- If an audience member suggests a logical next step or blurts out the answer the instructor cries “foul” and the problem is scored as if the other team has correctly completed the problem.
- Copying the other player’s work or borrowing ideas from it is
*strongly encouraged*. - A player may block the other player’s line of sight with a hand held object no larger than a notebook.
- A single team member may join the active player at the board to block lines of sight. Any speech by this team-mate constitutes a foul.
- Each team must keep any people at the board and their writing strictly on their own side of the board.
- The instructor is permitted to make helpful remarks, particularly if the contestants are stuck. The instructor cannot commit a foul.
- In case of a tie, no team points are awarded.
- No player may come up twice until every player has come up once.

These rules evolved over time and have the following goals. Rule 9, 10, 11, and 12 *increase engagement of the class*. Rule 7 is *critical*; it makes it apparent who the smart players are and help nucleate study groups. Rule 10 engages the very powerful mechanisms in the human brain concerning cheating and getting freebies. Since its horribly unfair, Occupy Math developed the following rationale: You cannot cheat past the other player and get the answer up first, unless you have some idea of you own.

Rules 5 and 6 also increase engagement and make the application of Rule 7 more important. Rules 11 and 12 make people feel better about Rule 10 because they can do something about it. Rules 11 and 12 also make rule 13 very necessary. Rule 14 must be used judiciously; often when one team is way behind. It permits the instructor to adjust team balance. Rule 15 prevents an interesting form of collusion between teams.

**Finally, rule 16, well, we’ve all met the student that caused that rule.**

Once *Sports Day* – a name chosen to suggest and encourage teamwork – became a regular part of Occupy Math’s first and second year courses, it was an item in the grading scheme. For each student 10% of the grade was dependent on earning 100 points in sports day (easy if you show up) and any extra points were transferred to homework; care is needed to scale the homework points to keep this from getting out of hand. What were the effects of sports day?

**Dear God, sports day improved attendance.**

- Sports day was Thursday and the problems were on the material covered in lecture on Monday and Tuesday. On Friday, Occupy Math would work all the problems with comments on best practices and techniques for improving speed.
- There were 20 sections of calculus courses. The two that had sports day as part of their instruction scored 10-15% higher on exams not written by Occupy Math. Apparently showing up to class and working problems improves performance?
- As far as Occupy Math knows, having security respond to noise complaints is not a usual result of holding a math class.
*Joyful*noise is unprecedented. A team managed to both out-score a rival team and, by working the last available problem, increase the team reward to 15 point. Imagine students cheering wildly in a math class where they are working problems at the board. Hard to picture, isn’t it?

The process of picking someone to come to the board is also something you can play with. I would have a student pick a number and count from a starting student (skipping people that had already come up) to find the victim. This has the interesting feature of making the victimization the fault of the student that picked the number. It also sometimes goes humorously wrong. Once a student (who was picking large numbers because that got the count far from him) picked a number so large it wrapped around and he picked himself.

Some caveats and suggestions. Sports day cannot be used effectively in upper level University courses. Reasonable problems in those courses take hours to solve. Avoid being too clever when you write problems – a problem that takes ten minutes to solve breaks the rhythm of the event. It is also critical to appear even-handed when using Rule 14 unless you have a serious underdog. If one side of the room has an advantage, move people.

Occupy Math misses the days of yore when he could teach students as much as he taught classes. If you still have a reasonable sized room full of students and decide to try sports day, please comment or tweet and let us know. There are a number of similar math activities available online, but crafting your own decks lets you tailor the problem to the students and topic at hand. Another reason to comment or tweet is if you found a really interesting house rule.

I hope to see you here again,

Daniel Ashlock,

University of Guelph,

Department of Mathematics and Statistics