Teaching With Group Work On Large Surfaces

These are notes to accompany Eric Hsu's great lost talk from the 2017 Joint Mathematics Meetings, cancelled due to snowstorm.

Class Set-up

• Daily team problem solving on large surfaces
• Online HW, computer graded, symbolic aerobics.
• Supplemental videos by Arek Goetz, but by halfway, no one was watching
• The groups work at large surfaces. Blackboards, and when wall space is available, I use static paper which turns walls into whiteboard space. Lacking wall space, you can use easels or small whiteboards.

Opening Class: Norms and Techniques

• The Worksheets. http://betterfilecabinet.com/f08/226ws.pdf. The videos use Worksheet 1. Sometimes I introduce the problem before giving out the worksheet. https://www.youtube.com/watch?v=-2Ex4rWhSc4
• Groups.
  • I go back and forth between openly random groups (no more than 4) and letting them pick. I don't do any "ability" based algorithms, on purpose. Students are fast and slow, but speed depends on the task.
    https://www.youtube.com/watch?v=Gbdw7rWNSu8
    • Randomizing algorithms: count off modularly to N, count off and divide by N and find your remainder, hand out cards when they arrive, find at least one person you haven't worked with.
• Managing the Group Work
  • Circulate quickly. Don't stay with a group for more than a minute.
  • Scan large surface work in the room to see people's progress. Go prod groups that are either "done" or stuck/far behind.
  • Have in your pocket some scaffolding questions and also extensions.
  • If they think they're done with task, ask "Is this everyone's answer? So everyone can explain this?"
    https://www.youtube.com/watch?v=ApLed2m4-eo
    • Ask a random person (not always the most certain or uncertain looking one) to start the explanation (sometimes I spin the Pen Of Fate and ask whomever it points to)
    • Then ask another person to continue.
    • If time, ask them a follow-up to check their understanding.
    • If anyone seems disconnected from group answer, be sure to ask them to continue or confirm the answer. If they are openly confused/disagreeing, tell the group you'll come back in two minutes and they should convince everybody. Then loop back.
    • If they are really done, tell them to pat themselves on the back, then give them another task. Either continue to the next class-wide task, or give the a bonus problem/extension.
  • If stuck, DON'T GIVE THEM A HINT YET. Ask them what they've tried.
    • If they abandoned a good strategy, tell them that was a good idea and they should go back to that.
    • Praise any interesting strategies, fruitful or not.
    • If they're stuck, try to ask them a key simpler question rather than suggesting a strategy. "Is this a graph of constant hoisting?"
    • Leave the group with a productive next question as soon as possible.
• Whole Class Discussions
  • Don't just reward the bold, quick and loud. You can ask a question and then wait for four hands before letting people talk.
    https://www.youtube.com/watch?v=yNfJNxag6a4
  • I'm not organized enough to use clickers, but I use a thumb poll for easy interactivity. Up, down and in-between.
    https://www.youtube.com/watch?v=PT5LgbNr0CE
  • When someone gives a "crazy" creative answer, you need to give it status. https://www.youtube.com/watch?v=761cw1yitaA
    • Enjoy it publicly and also make people follow up mathematically. Spend class attention on it. In fact, on the first day, you should incite/invite crazy creative answers. People need to know they can use their whole creative minds and that they can do math with their own personality.
  • Choose some key checkpoints that you really want every group to get to. For me, that's usually one or two key steps/ideas per task.
    • If a lot of people are stuck, you can have them stop and look around the room to get ideas.
    • Or have people share a partial result, like "what did people get for the derivative at x=0?", particularly if people disagree. Then just send them back to groups without resolving the disagreement. "Who's right?"
  • There might be 2-3 checkpoints per class session that I want to discuss as a whole class. For those, push along the slower groups until they get at least a partial result. Then give a mini-lecture.
• Decent Group Work Task Qualities
  • Non-routineness. ​It's okay to start off with a warm-up/check-up routine task, but if all questions are routine, the fast students will be bored/over-confident and the slow students will feel depressed.
  • Almost anything that requires interpretation, or deciding something due to a calculation.
  • Anything they could argue about using math. "What the most realistic?"
  • Multiple solution paths. Good for non-boring aerobics.
    • E.g. 6.4. Compute this derivative using product & quotient, and then do this using only constant, sum, diff and power. & 8.5. (x^3)^5 ‘ using chain rule, using power rule. Practice for algebra, exponents, exercises derivative rules, has a built-in check.​
  • Interesting partial results.
  • Almost any word problem.
  • Problems solved with graphs. Tables ok.
  • Routine tasks, prematurely!
    • You can take something you were going to lecture on, and let them try it first. Then if no one gets it, do a mini-lecture. Even if they get it, it’s good to sum it up.
    • I ask them to write a derivative definition from idea of limit of average rates of change. Then you can mini-lecture about it because they’ve been thinking about it.
    • They can try a task from a later chapter.
    • Or it can be a routine task without the scaffolding or context (so they don't know which approach to take).
  • A lot more thoughts on picking and using rich tasks at Hsu, E., Kysh, J., and Resek, D. (2007). Using Rich Problems for Differentiated Instruction. New England Mathematics Journal, 39, 6--13. http://bfc.sfsu.edu/papers/HsuKyshResek-RichProblems.pdf (The Complete Director's Cut)​

Further Resources

• Calculus I With Group Work, Fall 2008 (Materials, worksheets, teaching outline)
• The Better File Cabinet, a database of Treisman workshop calculus and precalculus problems.
• Hauk,S., Speer, N. M., Kung, D., Tsay, J.J., & Hsu, E. (2016). Video cases for college mathematics instructor professional development. Retrieved from http://collegemathvideocases.org.
• Bressoud, D., Mesa, V., Rasmussen, C. (Eds.), Insights and Recommendations from the MAA National Study of College Calculus. Washington, D.C.: Mathematical Association of America. http://www.maa.org/sites/default/files/pdf/cspcc/InsightsandRecommendations.pdf
• Hsu, E., Murphy, T. J., & Treisman, U. (2008). Supporting High Achievement In Introductory Mathematics Courses: What We Have Learned From 30 Years of the Emerging Scholars Program. In M. Carlson, & C. Rasmussen (Eds.), Making the Connection: Research and Teaching in Undergraduate Mathematics. Washington, DC: Mathematical Association of America. Print ISBN: 978-0-88385-183-8. Available at http://bfc.sfsu.edu/papers/Hsu-Murphy-Treisman-final.pdf
• Hsu, E., Kysh, J., and Resek, D. (2007). Using Rich Problems for Differentiated Instruction. New England Mathematics Journal, 39, 6--13. http://bfc.sfsu.edu/papers/HsuKyshResek-RichProblems.pdf (Full Director's Cut)

First posted January 6th, 2017