Hierarchy of Student Needs (sorry Maslow)

1. Base need
- Shelter, health, food.
- To get a good grade
- To have a fair shot to get a good grade
2. Safety
- To be respected in class
- To ask questions honestly
- To have personal boundaries
- To be comfortable*
  - adjustment period to being pushed to be active
- Teacher to be in charge
3. Love and belonging
- To be liked by the teacher
  - At least for the teacher to want them to succeed
- To be liked by peers
- To feel belonging to the college
4. Esteem needs
- To understand
- To get the right answer
- To show off their talents
- Students can show off: quickness, humor, creativity, worldly experience, academic language, drawing/visual skills, independence.
  - want to build on their power and harness it for math power
  - Full brain, not guessing at the answer we want to hear
5. Personal growth

Quality Group Tasks

(look at Worksheets 2, 3, 4). Take general comments.
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.
Don't over-structure. Flag Hoist could have been a step-by-step worksheet: "now estimate the slope at three points", "describe what the hoister is doing at t=0, 2 and 4. You can always ADD hints and structure. Figuring out what to do is part of the adventure and creativity.
Almost anything that requires interpretation, or deciding something due to a calculation.
- Anything they could argue about using math. "What the most realistic?"
Converting between representations.
- Graphs and tables are good because whole groups can look at them together.
- Graphs, tables, verbal, symbolic, kinesthetic
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).
- Almost any word problem they don't have a rote recipe for solving.
Differentiation (pedagogy, not calculus): content, process and product
- Interesting partial results.
  - Sub-cases solved. Solved with simplifying assumptions. Intriguing approaches that dead-ended for interesting reasons.
  - You want people lifting their appropriate weight.
- Admit multiple solution paths.
  - Then in de-brief have multiple approaches presented. Ideally, make connections between them.
  - Also, good for non-boring aerobics. Compare different methods. 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.
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)

Adjustment Period

Students. About four weeks.
- About 25% are really into it right away.
- About 50% go along with it, seeing if you'll stick with it.
- About 25% are suspicious and may take a little longer. They want to see if they can get a good grade in this format. So have an early Big Fun Quiz. Give them praise, build on their connections to classmates...
You. A semester or a lifetime.
- How do you know how hard a problem is, or how rich it is?
- You learn through time and honest observation. I always write a short sentence after the class in my day plan noting how hard the task was and improvements for next time.
- Don't change everything at once. I often have to back off of something too-ambitious after week 3.

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 August 16th, 2017