...in USA (cont..)

NCTM (National Council of Teachers of Mathematics) - focus on concept development and problem solving.

By learning and acquiring a variety of broad-based ( general ) mathematical problem-solving

strategies (heuristics) students are equip to be a better problem solvers across the topics in mathematics or transferring those skills to a variety of problems. Some of the general problem solving strategies are :

1. Characterize the problem : What is given? What is needed?What is missing? etc

2. Have you seen this before? : or different form ?

3. Look for pattern : eg Gauss recognized a pattern 1+2...+100 = ?

1+100=2+99=...101 (50 pairs)

50 @ 101 = 5050

4. Simplification/reduction : can the problem be broken up into smaller or manageable

sub-problems?

5. Work backwards : when trying to prove a theorem, it may begin from the conclusion and back track logically

6. Modeling/simulation : a mathematical model may be developed that simplify some complicated process/phenomena in the real word (representing/translating into a mathematical forms eg table, diagram, chart, graph, equation, relationship, function, inequalities, matrices, etc)

7. Logical reasoning/arguments - inductive and deductive reasoning,

8. guess and check/improve - develop a sense of estimation

9. make and test conjectures

10. formulate/pose problems from situations within and outside mathematics

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