To achieve mastery students need to acquire skills, practice with those skills and know when to apply them. The students go from unconscious incompetence to conscious incompetence to conscious competence to unconscious competence. Meaning at first students do not know what they do not know. Eventually they know what they need to do, but have to think about how to do it. Eventually the task becomes automatic.
Some ideas include training in aspects beyond the basic curriculum like how to work in groups and ways to scaffold the work, or isolate certain skills when students are novices.
The chapter also focuses on transfer. One reminder that I will try to implement more often is to make comparisons between problems that show the true underlying principle. For instance two problems in physics may both be about pulleys, but the important principle in one might be gravity while in the other it is friction.
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.