One way to differentiate in math class is creating open-ended tasks and questions (I talked about several differentiation strategies I use here – Mathematically Speaking).
I think it is useful to clarify the scheme of mathematical problems – below I used Foong Pui’s research paper:
“Problems in this classification scheme have their different roles in mathematics instruction as in teaching for problem solving, teaching about problem solving, or teaching via problem solving.”
1. CLOSED problems are well-structured problems in terms of clearly formulated tasks where the one correct answer can always be determined in some fixed ways from the necessary data given in the problem situation.
A.Routine closed problems – are usually multi-step challenging problems that require the use of a specific procedure to arrive to the correct, unique, answer.
B. Non-routine closed problems – imply the use of heuristics strategies * in order to determine, again, a single correct answer.
*Problem-solving heuristics: work systematically, tabulate the data, try simpler examples, look for a pattern, generalize a rule etc. Read the rest of this entry »