introduction to problem solving pdf

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1.1: Introduction to Problem Solving

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• Page ID 9821

• Michelle Manes
• University of Hawaii

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The Common Core State Standards for Mathematics ( http://www.corestandards.org/Math/Practice ) identify eight “Mathematical Practices” — the kinds of expertise that all teachers should try to foster in their students, but they go far beyond any particular piece of mathematics content. They describe what mathematics is really about, and why it is so valuable for students to master. The very first Mathematical Practice is:

Make sense of problems and persevere in solving them.

Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary.

This chapter will help you develop these very important mathematical skills, so that you will be better prepared to help your future students develop them. Let’s start with solving a problem!

Draw curves connecting A to A, B to B, and C to C. Your curves cannot cross or even touch each other,they cannot cross through any of the lettered boxes, and they cannot go outside the large box or even touch it’s sides.

Think / Pair / Share

After you have worked on the problem on your own for a while, talk through your ideas with a partner (even if you have not solved it).

• What did you try?
• What makes this problem difficult?
• Can you change the problem slightly so that it would be easier to solve?

Problem Solving Strategy 1 (Wishful Thinking).

Do you wish something in the problem was different? Would it then be easier to solve the problem?

For example, what if ABC problem had a picture like this:

Can you solve this case and use it to help you solve the original case? Think about moving the boxes around once the lines are already drawn.

Here is one possible solution.

Introduction to Problem Solving

Cite this chapter.

• Ian David Chivers B.Sc., M.Sc., M.B.C.S. C.Eng. 2 &
• Jane Sleightholme M.Sc. 2  

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The aims are:-

to examine some of the ideas and concepts involved in problem solving;

to introduce the concept of an algorithm;

to introduce two ways of approaching algorithmic problem solving;

to introduce the ideas involved with systems analysis and design, i.e. to show the need for pencil and paper study before using a computer system.

They constructed ladders to reach to the top of the enemy’s wall, and they did this by calculating the height of the wall from the number of layers of bricks at a point which was facing in their direction and had not been plastered. The layers were counted by a lot of people at the same time, and though some were likely to get the figure wrong the majority would get it right... Thus, guessing what the thickness of a single brick was, they calculated how long their ladder would have to be. Thucydides, The Peloponnesian War

‘When I use a word,’ Humpty Dumpty said, in a rather scornful tone, ‘it means just what I choose it to mean — neither more nor less’ The question is,’ said Alice, ‘whether you can make words mean so many different things.’ Lewis Carroll, Through the Looking Glass and What Alice found there .

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Bibliography

Aho A. V., Hopcroft J. E., Ullman J. D., The Design and Analysis of Computer Algorithms , Addison Wesley, 1982.

Google Scholar  

Beckman F. S., Mathematical Foundations of Programming , Addison Wesley, 1981

Bulloff J.J., Holyoke T.C., Hahn S.W., Foundations of Mathematics — Symposium Papers Commemorating the 60 th Birthday of Kurt Godel , Springer Verlag.

Dahl O. J., Dijkstra E. W., Hoare C. A. R., Structured Programming , Academic Press, 1972.

Davis M., Computability and Unsolvability , Dover, 1982.

Davis W. S., Systems Analysis and Design , Addison Wesley, 1983.

Fogelin R. J., Wittgenstein , Routledge and Kegan Paul, 1980.

Godei K., On Formally Undecidable Propositions of Principia Mathematica and Related Systems , Oliver and Boyd.

Hofstader D., The Eternal Golden Braid , Harvester Press.

Hopcroft J. E., Ullman J. D., Introduction to Automata Theory, Languages and Computation , Addison Wesley, 1979.

Kernighan B. W., Plauger P. J., Software Tools , Addison Wesley, 1976.

Knuth D. E., The Art of Computer Programming , Addison Wesley

Millington D., Systems Analysis and Design for Computer Applications , Ellis Horwood, 1981.

Wirth N., Program Development by Stepwise Refinement , Communications of the ACM, April 1971, Volume 14, Number 4, pp. 221–227.

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Ian David Chivers B.Sc., M.Sc., M.B.C.S. C.Eng. & Jane Sleightholme M.Sc.

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© 1995 Springer-Verlag London Limited

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Chivers, I.D., Sleightholme, J. (1995). Introduction to Problem Solving. In: Introducing Fortran 90. Springer, London. https://doi.org/10.1007/978-1-4471-3031-4_5

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An Introduction to Problem Solving

To successfully solve any problem, the most important issue to get actively involved. Levine [Lev94] calls this “The Principle of Intimate Engagement.” Writers on problem solving often use terms like “roll up your sleeves” and “get your hands dirty.” It means actively engaging with the problem, and doing some work to get it done. For easier problems, you will “see” an answer fairly quickly once you actively engage, and the issue then is to work through to completion.

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