Mathematical Problem Solving IVESMarch2011

7/29/2019 Mathematical Problem Solving IVESMarch2011

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New Strategies in Problem Solving:

How to Develop Confident andFlexible Problem Solvers

Incarnate Word AcademyElementary Level

March 4, 2011

Dr. Sarah IvesAssistant Professor of Mathematics

Texas A&M University Corpus Christi


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Outline of Session

Overview of Problem Solving NCTM Problem Solving Standard

What is a problem?

Is there a process?

What are some strategies?

Problem Solving in Action

Planning for Instruction on Problem Solving

Questions and Further Discussions


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NCTM Problem Solving Standard

The National Council of Teachers ofMathematics has included Problem Solvingasone of the process standards:

Instructional programs from pre-kindergarten

through grade 12 should enable all students to Build new mathematical knowledge through

problem solving

Solve problems that arise in mathematics and in

other contexts

Apply and adapt a variety of appropriate strategiesto solve problems

Monitor and reflect on the process of

mathematical problem solving

NCTM (2000). Principles and Standards for School Mathematics. Reston, VA: Key

Curriculum Press.


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What is a Problem?

Charles and Lester (1982) define a mathematicalproblem as a task for which:

1. The person confronting it wants or needsto finda solution;

2. The person has no readily available procedurefor finding the solution; and

3. The person must make an attemptto find asolution.

Charles, R. I., & Lester, F. K., Jr. (1982). Teaching problem solving: What, why, & how.

Palo Alto, CA: Seymore.

Problem solving means engaging in a task for

which the solution method is not known in

advance (NCTM, p 52)


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The Problem-Solving Process

Polyas (1957) 4-step process:

1. Understand the problemProvide time for studentsto identify the goal, what information is needed and what isextraneous, and detect any missing information;

2. Devise a plan to solve the problemStudentswill use various strategies, have them discuss differentways to solve the same problem;

3. Implement a solution planencourage students to

use their own ingenuity to develop a solution plan; and

4. Reflect on the problemhave students look backat the problem; they should be ready to explain and

justify their solutions when asked.

Polya, G. (1957). How to Solve It (2nd

Ed.). New York: Doubleday.


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Problem Solving Strategies

Find a Pattern

Draw a picture

Solve asimplerproblem

Use Table orChart

Consider allPossibilities

LogicalReasoning

WorkBackwards

Changing Pointof View

Guess &

Check

Write OpenSentence

Act out orModel problem


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Problem Solving in Action

Now its your turn!

1.Barnyard animals

2.Euler Squares

3.Pocket change

4.Candy bags

5.Rabbits & hutches

6.Party tables

7.Frogs & Lily pads

Source: http://sci.tamucc.edu/~sives/1350/problem_solving11.html
http://sci.tamucc.edu/~sives/1350/problems_solving.htmlhttp://sci.tamucc.edu/~sives/1350/problem_solving.htmlhttp://sci.tamucc.edu/~sives/1350/problem_solving.htmlhttp://sci.tamucc.edu/~sives/1350/problems_solving.html


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Planning for Instruction onProblem Solving

Several Important Components:

Selecting appropriate tasks and materials,

Identifying sources of problems,

Clarifying the teachers role,

Organizing and implementing instruction, and

Changing the difficulty of problems.


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Teachers Role

Instead of: Focusing on helping

students find an

answer,

Providing solutionstrategies,

Expecting specific

responses,

The teacher: Is prepared to see where the

students observations andquestions may take them.

Encourages multipleapproaches and allows time forcommunication and reflectionabout those strategies.

Is ready to ask questions thatuncover students reasoningbehind the process (Rigelman,2007, p. 312).

Rigelman, N. (2007). Fostering mathematical thinking and problem solving: The

teachers role. Teaching Children Mathematics, 13(6), 308-314.


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Organizing and ImplementingInstruction

Classroom Climate

Open, supportive, encourage children to trydifferent strategies

Grouping Children

Include individual, small-group, and whole-classproblem-solving experiences

Allocating time

Problem solving should be an integral part of

mathematics instruction, not Fridays only Assessing childrens understanding

Ongoing assessment of understanding andproblem-solving skills can be done by having

students discuss and present solutions


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Additional Resources

LINKS TO THE INTERNET Problems of the Week:

http://www.mathforum.org/pow/ Contains several

weekly Problems of the Week as well as a

mechanism to submit solutions electronically. Past

Problems of the Week and solutions are alsoavailable.

Open-ended Math Problems:http://www.fi.edu/school/math2/ Contains open-ended

math problems at several different levels of difficulty

for middle school students. Education Places Brain Teasers:

http://www.eduplace.com/math/brain/ Contains math

puzzles for Grades 3-8 as well as solution hints.

Source: Bezuk, N., Cathcart, W., Pothier, Y., & Vance, J. (2011). Page 59.
http://www.mathforum.org/pow/http://www.fi.edu/school/math2/http://www.eduplace.com/math/brain/http://www.eduplace.com/math/brain/http://www.fi.edu/school/math2/http://www.mathforum.org/pow/


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Additional Resources

RESOURCES FOR TEACHERS Reference Books: Problem Solving

Baroody, A. (1993). Problem Solving, Reasoning,and Communicating: Helping Children ThinkMathematically. New York: Macmillan.

Charles, R., Lester, F., & ODaffer, P. (1987). Howto Evaluate Progress in Problem Solving. Reston,VA: National Council of Teachers of Mathematics.

ODaffer, P. G. (1988). Problem Solving: Tips forTeachers. Reston, VA: National Council ofTeachers of Mathematics.

Reys, B. (1982). Elementary School Mathematics:What Parents Should Know about ProblemSolving. Reston, VA: National Council of Teachersof Mathematics.

Source: Bezuk, N., Cathcart, W., Pothier, Y., & Vance, J. (2011). Page 59.


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Questions, Comments?

Main Source: Bezuk, N., Cathcart, W., Pothier,Y., & Vance, J. (2011). Learning Mathematics inElementary and Middle Schools: A Learner-Centered Approach (5thEd.). Boston, MA:

Pearson. http://sci.tamucc.edu/~sives

[email protected]

(361) 825-2151
http://sci.tamucc.edu/~sivesmailto:[email protected]:[email protected]://sci.tamucc.edu/~sives

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Mathematical Problem Solving IVESMarch2011