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

**problem solving, or teaching**

*about***problem solving.”**

*via***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 »