Tips for writing the 2-Problem Paper
1. Provide explicit prompts for both problems being compared (college-level
and K-8). Include in the prompt any special circumstances or instructions
that affect the problem (for instance, if you want to constrain respondents
to use a particular type of approach, say concrete models or the traditional
algorithm).
2. Keep in mind that the college-level problem is not to work a single example,
but to *use* one or more examples to describe and explain a general
computational strategy or algorithm. (Details for each option are provided
on the course web page.)
3. Keep in mind that the K-8 problem is not a general concept or procedure but
a specific task with an identifiable prompt.
4. Avoid mismatched comparisons between college-level problems which require
developing or justifying an algorithm and K-8 problems which are simple
applications of known computational approaches. (If you perceive any kind
of contradiction between this and the previous tip, note that K-8 problems
can require students to develop, generalize or justify approaches at a level
higher than a single computation. They can also apply such approaches in
other contexts which cause a primary mathematical idea to emerge.)
5. Be sure your solution to the college-level problem includes an explanation
or justification of the solution, e.g., why does the approach take the form
it does?
6. Separate your personal "story" or experience with the problem from your
explanation of the solution, because the order in which you discovered or
constructed different parts of the solution may not be the best or
clearest way to present them coherently. If you must include aspects of
your personal experience, confine them to a paragraph (or two) clearly
separate from the solution proper.
7. Separate your general explanation of a procedure from any example you give.
State the general procedure in general terms, and only after it's completed
give the example as an application of the procedure you've just described.
8. Your analysis of the ideas contained in the K-8 problem should avoid
discussions of what happened when you used this problem with students, and
focus on properties of the problem itself (although this does include what
possible solution methods may apply).
9. Your paper should read as a coherent, self-contained narrative, eliminating
all references to question numbers and parts (e.g., 1(a)). Use the
questions to which you are responding, to outline or structure your paper,
but make the discussions and examples your own, rather than letting the
paper read as a series of short answers to isolated questions posed by
someone else. Take the ownership necessary to allow you to present your
explanations in the order and form that seem clearest to you.