Examine your text for problems that do not emphasize covariational reasoning but nevertheless entails it in a fundamental way.
- Explain how the problem's wording suppresses, diminishes, or ignores covariational reasoning.
- Explain how ideas of covariational reasoning really are central to understanding the problem and deciding what to do to solve it (assuming this is not a problem on which on can go to "automatic pilot").
Interview one student on this problem. Use your interview to understand:
- What your student understands about this problem.
- How his or her understanding of the problem is related to what he or she does in solving it.
Report your interview with these two headings – what your student understood about the problem and how his or her understanding was related to what he or she did.
Locate a problem in a text that you're using this semester that has the potential to promote students' understanding of the function concept and covariational reasoning abilities. Create the following to extend this problem.
1. An in-class activity that promotes the building of a mental structure of the situation and that prompts students to: i) attend to how the quantities in the situation are changing in tandem with each other; ii) reverse the function process; iii) provide meaningful connections across function representations, etc.
2. A lesson plan that describes how you would implement this activity in your classroom.
3. A follow-up homework assignement that reinforces the main ideas and connections of the in-class lesson.
Modify as you like :-)