Problem Solving Vs Problem Posing

1 PROBLEM SOLVING VERSUS PROBLEM POSING

1.0 PROBLEM SOLVING IN MATHEMATICS 1.1 Problem Solving How to Solve It: A great discovery solves a great problem but there is a grain of discovery in the solution of any problem. Your problem may be modest; but if it challenges your curiosity and brings into play your inventive facilities, and if you solve it by your own means, you may experience the tension and enjoy the triumph of discovery.

a) b) c) d) e) f) g) h)

2 PROBLEM SOLVING VERSUS PROBLEM POSING

1.2 Four Phases in Solving a Problem

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1.3 Problem Solving Approach • • • • • •

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My early problem-solving courses focused on problems amenable to solutions by Polyatype heuristics: draw a diagram, examine special cases or analogies, specialize, generalize, and so on. Over the years the courses evolved to the point where they focused less on heuristics per se and more on introducing students to fundamental ideas: the importance of mathematical reasoning and proof..., for example, and of sustained mathematical investigations (where my problems served as starting points for serious explorations, rather than tasks to be completed). a) c)

3 PROBLEM SOLVING VERSUS PROBLEM POSING

2.0 PROBLEM POSING

2.1 Introduction

2.2 Problem Posing in Mathematics

2.3 Problem Posing phases 1.

2.4 Problem Posing in Mathematics Learning

3.0 WAYS TO CHANGE A PROBLEM

3.1 Change the Numbers

4 PROBLEM SOLVING VERSUS PROBLEM POSING

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Figure 1: A cow tethered to barn aba bttaa < t < bb < t < ab,t > a + b •

• 3.2 Change the Geometry •

shapes

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dimension

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structure of the space

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symmetry

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location

3.3 Change the Operation • •

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3.4 Change the Objects under Study

3.5 Remove a Condition or Add New Conditions

5 PROBLEM SOLVING VERSUS PROBLEM POSING

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3.6 Remove or Add Context • •

• 3.7 Repeat a Process

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4.0 PROBLEM SOLVING AND PROBLEM POSING 4.1 Benefit of Problem and Problem Posing QUEST (Quality Undergraduate Education Simulations and Tools in Biology

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4.2 Relation of Problem Solving and Problem Posing Method think

6 PROBLEM SOLVING VERSUS PROBLEM POSING

4.3 The Process of Posing a Problem

5.0 CONCLUSION

REFERENCES Research in Science Education The art of problem posing Affect and mathematical problem solving Practical and theoretical foundations for implementing creative problem solving strategies for instruction in technology education Journal of Creative Behavior Instructional strategies for technology education