So should responses to these be a bonus on a quiz, or just part of the quiz?
1 – Algebra is powerful and applicable
2 – Each different representation – graphic, verbal, numberic, and algebraic – has its own strengths and weaknesses
3 – Some algebraic properties appear confusing and unnatural. Why does Algebra have all these rules to understand? Why couldn’t the rules just be simpler?
“Each problem that I solved became a rule which served afterwards to solve other problems.” – Descartes
I think (therefor I am) this will be my standard answer to students when they ask: When will I ever use this? Not only is it a valid response, but it either a) buys me time to think of a more legitimate answer, or b) passes that responsibility to a future maths teacher.
In any case – I’m pretty happy with my students so far. They’ve retained more over the summer than I thought. Or, I planned on them not remembering very much and started too early in the book? Oh well, I’ll get through what I need to, what’s the harm in strengthening an already semi-solid foundation?