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					                            Problem Solving in Mathematics

Category: Mathematics
Grade: 4 to 9

1. What is the purpose of Problem Solving          needed, notes and suggestions, and
in Mathematics?                                    answers.
The purpose of this approach is to emphasise      Laboratory activities: Investigations
the use of problem solving skills in the           involving mathematical applications.
                                                  Teaching mathematical concepts: In
2. With whom can it be used?                       addition to the sections in each book on
The grade level books for grades 4-8 and 9         grade level content topics, there is an in-
are suitable for use with students of all          service guide self-servicing audiotapes for
abilities. Additional problems appropriate for     teachers. The principal can also be
low achievers are contained in the Alternative     provided with an audiotape to acquaint
Problem Solving in Mathematics book. The           him or her with the administrative
activities in the Alternative Problem Solving      responsibilities and support necessary for
in Mathematics book differ from the regular        implementing the program.
books in the level of math computation and
length of time needed for completion. They       4. What teaching procedures should be
are generally appropriate for students in        used with Problem Solving in
grades 4-6.                                      Mathematics?
                                                 Specific procedures used vary according by
3. What is the format of Problem Solving         activity. In general, the program emphasizes
in Mathematics?                                  the direct teaching and use of problem
Each book is centered around grade-              solving strategies. Examples of strategies
appropriate topics, and includes the following   used in the program are the
sections:                                        following:

 Getting Started: Direct instruction of         A. Problem Discovery, Formulation
  problem solving strategies.                     State the problem in your own words
                                                  Clarify the problem through careful
 Drill and Practice: Review activities for          reading and by asking questions
  the beginning of the year.
                                                 B. Seeking Information
 Challenges: Problems of greater                 Collect data needed to solve the problem
  difficulty appropriate for later in the year    Record solution possibilities or attempts
  after experience with problem solving.
                                                 C. Analysing information
 Teacher commentaries: Comments from             Eliminate extraneous information
  teachers on teaching objectives, problem        Make and/or use a systematic list or table
  solving skills pupils might use, materials
                                                 D. Solve-Putting it together
 Synthesis                                      disabilities and students at risk for math
 Make reasonable estimates                      failure.
 Detect and correct errors
E.   Looking back                                1. Cawley, F. & Parmar, R.S. (1992).
    consolidating                                  Arithmetic programming for students with
    Explain how you solved a problem               disabilities: An alternative. Remedial and
    Find another answer when more than one         Special Education, 13, 6-18.
     is possible                                 2. Jitendra, A. & Xin, Y.P. (1997).
                                                    Mathematical word-problem-solving
F. Looking ahead-Formulating new                    instruction for students with mild
   problems                                         disabilities and students at risk for math
                                                    failure: A research synthesis. The Journal
 Create new problems by varying a given
                                                    of Special Education, 30, 412-438.
                                                 3. Lane County Mathematics Project:
                                                    Problem Solving in Mathematics. (1983).
5. In what types of settings is Problem
                                                    Palo Alto, California: Dale Seymour
Solving in Mathematics useful?
This program is meant to be integrated into
                                                 4. Schaaf, O. (1984). Teaching problem-
the regular curriculum. Lessons in the
                                                    solving skills. Mathematics Teacher, 77,
Problem Solving books can be used to replace
regular textbook pages. Also, regular
                                                 5. Schaaf, O. (1979). Introduction to the
textbook pages might be used as practice for
                                                    LCMP Mathematics Problem-Solving
the problems presented in the Problem
                                                    Programs. ERIC Document Reproduction
Solving book.
6. To what extent has research shown
                                                 Reviewed by: Naomi Slonim
Problem Solving in Mathematics to be
Although no carefully controlled longitudinal
studies have been conducted, evaluations by
the authors have demonstrated positive
effects of the program. These include gains
on standardized achievement tests and special
problem-solving skill tests. In addition,
teachers have indicated that problem-solving
strategies taught in the program generalize to
other subjects such as Social Studies,
Language Arts, and Science. The most
significant gains occurred with exclusive use
of the program and use as specified in teacher
commentaries and in-service materials.

In addition to program evaluation by the
authors, research shows positive effects of
mathematical word-problem solving/strategy
instruction for students with learning

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