Problem Solving in 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
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).
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
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