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Re: approaches to content



Thanks, Nancy, for the very interesting description of your work. This has been helpful to me as an example of structuring the content. In particular, you wrote

 For
example, instead of starting with linear functions, we tend to work with students on activities that involve varying quantities of amount and rate,
so that when they do encounter the 'degenerate' case of a linear
relationship, it is seen as a simpler case rather than a different
phenomenon. Students don't encounter linear relationships nearly as often as they do more complex ones in life, so it is much easier to draw on their
prior knowledge in supporting their thinking about and mathematizing
relationships when we start with more complexity.

which sounds to me like moving from the general to the particular, that is,
that the kids are acquiring a general concept or method.

Again, as with Peg's work, I'm wondering if the students "model" the general
relation (between amount and rate, etc.) with some sort of special
diagrams, or formulas, or tables, or special algebraic notation, and whether this helps them assimilate the general concept. I'd also be interested if you have methods for *assessing* whether students are actually solving problems by moving from the general to the particular, or just solving each particular problem as a new
case.

That is, how can you assess that:

, it is seen as a simpler case rather than a different
phenomenon.

Peter