Summary of Szetela & Super (1987)
Running head: SUMMARY OF SZETELA & SUPER (1987)
Analytic Summary of Szetela and Super (1987):
Calculators and Instruction in Problem Solving in Grade 7
Samuel Otten
Michigan State University
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Summary of Szetela & Super (1987)
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Analytic Summary of Szetela and Super (1987):
Calculators and Instruction in Problem Solving in Grade 7
Problem solving is at the core of the discipline of mathematics, yet elementary
and secondary students of mathematics have “a great deal of difficulty” as soon as a
problem requires more than a single application of a mathematical algorithm (p. 215).
Moreover, it is often the case in mathematics classrooms that problem solving only
appears in the form of “story problems” which require a translation of real-world
information into the appropriate mathematical language, which addresses only one type
of problem solving ability. More sophisticated process problems are rarely, if ever, found
in mathematics classrooms. These are problems the solutions of which require multi-steps
and a synthesis of content knowledge.
Student deficiency in problem solving ability is a significant issue in mathematics
education, and the related problem of how to teach problem solving is the primary focus
of the article. There has been contention over this matter in the past. Some researchers
have argued that certain content-independent problem solving strategies can be taught,
whereas other researchers have countered that content-independent strategies are
characteristic of weak problem solvers who are unable to employ the more powerful
content-specific strategies (see p. 215-216). Secondarily, there is debate in the
mathematics education community about the impact of calculators in the hands of
students and the presence or absence of sex-related differences in problem solving ability.
Szetela and Super designed their research so as to speak to these topics as well.
The purpose of the study was to determine the effectiveness of an instructional
program that emphasized certain problem solving strategies. The authors intended to
Summary of Szetela & Super (1987)
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simultaneously gather data regarding the effect of calculators as problem solving tools
and regarding possible sex-related differences in student problem solving performance.
Theoretical Perspective
Szetela and Super did not seem to concern themselves with developing an explicit
theoretical frame for this article, but there were theoretical guidelines present in the
machinery of their study. The introductory pages cited an array of past work, but only to
include their voices in the topics at hand and not to harvest any overarching framework,
as far as I could tell. It was not until reading the method and procedure sections that I was
able to recognize Pólya’s (1957) problem solving model—understand the problem,
devise a plan, carry out the plan, look back—as the primary framework. The theory of
metacognitive processes explicated by Lester and Garofalo (1985) was also employed as
it relates to problem solving.
Research Questions
The research questions were enumerated just prior to the method section. They
were as follows:
1. What differences are there among the three treatment groups on the
following criterion variables?
a. Solving translation problems
b. Solving process problems
c. Solving more complex problems
d. Attitude toward problem solving
e. Computational skills
2. What are the differences between boys and girls in problem-solving
performance?
3. What are the effects on teachers' perceptions of problem solving?
Summary of Szetela & Super (1987)
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Method
Forty-two grade 7 classes participated in the study. They were divided into three
groups: 14 classes with problem solving instruction and calculators (CP Group), 10
classes with problem solving instruction but no calculators (P Group), and 10 classes with
no special problem solving instruction and no calculators (C Group). Teachers of the CP
and P groups were trained for several days throughout the school year in problem solving
instructional strategies and were given problem solving materials to supplement the
classroom text. Tests comprising translation problems, process problems, and complex
problems were administered once in the middle and once at the end of the school year.
Student attitude toward problem solving was also measured near the end of the school
year.
Findings
The P Group scored significantly higher than the C Group on tests of translation
and process problem solving. The CP Group scored significantly higher than the C Group
on the translation tests and significantly higher than both the P and C Groups on the test
of attitude toward problem solving. As for sex-related differences, no significant
differences in performance were found within the treatment groups, but altogether the
boys scored significantly higher than the girls on translation and process tests.
The statistical analysis techniques employed by Szetela and Super seemed
appropriate and were specifically chosen to compare the groups rather than the individual
students within the groups. A separate statistical analysis, one more individually
designed, was implemented with respect to the question of sex-related differences with
regard to problem solving success.
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Conclusions
Szetela and Super conclude that instruction with a focus on problem solving
strategies and supplementary problem solving materials is slightly more effective at
developing successful problem solvers than is traditional instruction. Also, students
taught with calculators exhibited a more positive attitude toward problem solving and
there was no documented loss in “pencil-and-paper skills” (p. 225). The authors suggest
that the resistance to the use of calculators in math classrooms may be misguided in terms
of problem solving.
An obvious question to ask the researchers is this: why didn’t the CP and P
Groups display a more pronounced effect? This question was addressed in the article. It
was reiterated that significant differences were measured, and a few explanations for the
lack of further differences were offered. First, teachers in the experimental groups
reported that they tended to neglect the “looking back” stage of Pólya’s model, and
students in general are not likely to engage in this important stage if not guided to do so
by the teacher (p. 226). Second, teachers in the control group increased their emphasis on
problem solving based on school district recommendations and a possible Hawthorne
effect, implying the distinction between experimental and control was blurred. Third, it
may be that the “knowledge domain dominates the use of general problem-solving
strategies” (p. 226), as suggested by others cited in the introduction. Fourth, the ability to
problem solve is complex and it may take years for instruction to have a large-scale
effect. I would also suggest that this same complexity may make the construct of
“problem solving ability” difficult to capture in three- and four-item tests, as attempted here.
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The article closed with a discussion of teaching implications. The authors posited
that time spent in the classroom on computation and calculation, things that could be
done quickly with a calculator, is time that may be better spent developing problem
solving skills and metacognitive processes in the students. They contend that the teaching
of problem solving could be improved via a reassessment of curriculum priorities and an
alteration of classroom environment.
Overall Remarks
This article made a bold attempt to investigate the effectiveness of instructional
strategies focused on problem solving, and found that after a year’s time there were only
slight improvements in students’ problem solving ability. I was drawn into the article
because of my agreement with the researchers on the importance of problem solving in
mathematics education. I was able to see how the presence or absence of calculators
factored into the issue, but it was not as clear to me why the analysis of sex-related
differences was included in the study. To me this seemed slightly off topic. Perhaps this
was relevant to the “buzz” at the time of publication.
It may be the case that the last paragraph of the article was the most important,
where the authors stated that much more research in this domain is required because
many more questions remain. Are the existing models of problem solving adequate? Are
the existing measures adequate? How can teachers with limited problem solving
experience develop rich problem solving classrooms? Good questions all.
Summary of Szetela & Super (1987)
References
Lester, F. K., Jr., & Garofalo, J. (1985). Metacognition, cognitive monitoring, and
mathematical performance. Journal for Research in Mathematics Education, 16,
163-176.
Pólya, G. (1957). How to solve it (2nd ed.). Princeton, NJ: Princeton University Press.
Szetela, W. & Super, D. (1987). Calculators and instruction in problem solving in grade
7. Journal for Research in Mathematics Education, 18(3), 215-229.
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