Problem Solving in Mathematics
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# Problem Solving in Mathematics

Problem Solving skills are essential skills
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## Why Is Problem Solving in Maths Essential?

Inspirational teachers presents challenging tasks to support students to generate and investigate questions,gather relevant information and develop ideas. Problem solving has special value as a vehicle for learning new concepts and skills or the reinforcement of skills already acquired.  Approaching mathematics through problem solving can create a context which simulates real life and therefore justifies the mathematics rather than treating it as an end in itself.

National Council of Teachers of Mathematics (NCTM, 1980 and 1989) recommended that themathematics curriculum should be organized around problem solving, focusing on:

(i)  developing skills and the ability to apply these skills to unfamiliar situations

(ii)  gathering, organising, interpreting and communicating information

(iii)  formulating key questions, analyzing and conceptualizing problems, defining problems and goals, discovering patterns and similarities, seeking out appropriate data, experimenting, transferring skills and strategies to new situations developing
curiosity, confidence and open-mindedness (NCTM, 1980, pp.2-3).

All types of mathematical problems serve a useful purpose in mathematics teaching. The higher the math class, the more types of problems students can engage with if a good foundation has been gained in earlier classes.

CLOSED Problems and Investigations

Problems with a definitive answer usually testing memorization and application of
familiar skills and contexts

OPEN Problems and Investigations

Problems which stimulate higher order mathematical thinking.

WORDED PROBLEMS

Worded problems are possibly the most feared type of problem solving situations in mathematics. They require students to apply logical reasoning and interpretation to show their knowledge of mathematical concepts.  Confidence is built in students through exposure, practice and a systemic problem solving process

SOLVING A PROBLEM – The Systematic Process

In solving any problems, it helps to have a working procedure.

Read Analytically - Process and understand

o read and restate the problem
o Underline clue words
o What is the unknown?

o What data/ facts are you given?

o What is the condition?

Method – Think and decide how you might solve the problem

o Look at the unknown!

o Have you seen a problem like this before?

o Do you know a related problem?

o Define the strategies you think may solve the problem

Have a Go -- After deciding on a plan, you should try it and see what answer you come up with.

o Can you see clearly that the step is correct?

o But can you also prove that the step is correct?

Reflect -- Once you've tried it and found an answer, go back to the problem and see if you've really answered the question. Sometimes it's easy to overlook something. If you missed something check your plan and try the problem again.

o Critically look over the solution

o Did you answer the question?

o Can you check the result?

o Does it seem probable?

o Can you follow the working out?

o Have you used the right symbols, operations and units?

o Can you derive the result differently?

o Can you see it at a glance?

Top ten PROBLEM-SOLVING STRATEGIES

1. Make a table

2. Make an organised list

3. Look for a pattern

4. Guess and check

5. Draw a picture or graph

6. Work backwards

7. Solve a simpler problem

8. Make a model

9. Brainstorm

10. Write an equation/formula

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