Chapter 5 reminds teachers that students need to practice in targeted areas at appropriate challenge levels. Students should receive feedback on how that practice goes. Generally frequent feedback is better. Generally rapid feedback is better (but exceptions are given- for instance if debugging a spreadsheet is a task, correcting errors immediately does not allow students to practice the skill). Students also need sufficient practice. Early practice does not make many gains as students may make many errors. Too much practice on the same skill leads to small progress in the later problems. since students may already have mastery (see S-shaped graph on page 135).
I need to remember to remind students of the goals as they attempt problems. I will also ask students more often to tell how they used my feedback in subsequent work to make sure they are reading, or listening and then applying recommendations.
My list of recommendations to myself is repeated once again with the addition in red.
ONCE A SEMESTER, OR INFREQUENTLY
- Math 081 and Math 131: On the second day give a pre-assessment of required skills and start remediation immediately.
DAILY, OR FREQUENTLY
- Write a concept map of my own thinking to see how an expert organizes the information and select tasks that help convey that organization.
- Explicitly overview the lesson plan for a section so that students can see how each part fits in
- Math 081: Use brainstorming more often to see what students know about a topic in the course the first time it is introduced. (The Math 081 curriculum is a lot like a “spiral” where key topics like proportion are revisited several times.)
- Math 081 and Math 131: Explicitly list the pre-requisite topics daily instead of less frequently
- Compare problems that on the surface look the same, but that use different mathematical principles
- Math 131: Introduce several “Rules of Thumb” in the finance chapter so students will know when they are dealing with loans, when annuities, when saving for retirement .
- Ask reflection “What did you learn?” questions on assignments.
- Ask “How did you use prior feedback?” questions on assignments.