Problem Solving: An Assessment of Student Attitudes, Expectations, and Beliefs

Charles F. Yokomoto
Indiana University-Purdue University Indianapolis
Walter W. Buchanan
University of Central Florida
Roger Ware
Indiana University-Purdue University Indianapolis

Abstract:

We will describe a study of student attitudes, expectations, and beliefs about problem solving in the engineering technology classroom as they relate to learning strategies for problem solving based examinations. The authors have developed an assessment instrument which asks students to respond to four kinds of items: (1) their expectations about problem solving, (2) their strategies for preparing for exams, (3) their self-assessment of their problem solving skills, and (4) their appreciation of mathematics, physics, algebra word problems, and puzzles. Student responses were analyzed statistically to determine if there were any significant relationships among the items.

Introduction

Better models of the learner must be developed so that more effective teaching strategies can be developed. Considerable work has been done in developing models of the learner in the engineering classroom from the point of view of learning styles, cognitive styles, and personality type. In this study of the learner, the modeling is done from the point of view of beliefs and attitudes and their relationship to problem solving strategies. Previous efforts were conducted by Rodman, et. al. [1] and Rosati, et. al. [2]. The Rodman study looked at the relationship between problem solving heuristics and personality type using the Myers-Briggs Type Indicator as the personality assessment instrument. The Rosati study took the Rodman study one step further and look at differences in beliefs and attitudes between beginning students (first and second year students) and advanced students (third and fourth year students). It also look at the relationship between personality and beliefs/attitudes, again using the Myers-Briggs Type Indicator as the assessment instrument. Both studies were conducted in the engineering classroom environment.

In this study, the environment was the electrical engineering technology curriculum at the junior year. An inventory, shown in Figure 1, was prepared with items similar to those used in the Rosati and Rodman studies, but they were revised to reflect a shift in emphasis toward problem solving. Additional items were written to assess student reactions to mathematics, physics, puzzles and riddles, and algebra word problems. A final item asked students to self-assess their competencies as problem solvers. The inventory is divided into two basic sets of items, with the first set (items 1-11) assessing student beliefs and attitudes toward problem solving in the learning and testing process. These are listed under the heading, ``Assessment of Cognitive Factors.'' The second set (items 12-16) assessed student appreciation for mathematics, physics, algebra word problems, and puzzles, and it also assessed student self-perception of their competencies as problem solvers. These are listed under the heading, ``Assessment of Personal Factors.'' Cognitive factor items were written as statements such as, ``The instructor or textbook should demonstrate at least one example similar to each homework problem (item 2),'' and ``I try to solve as many drill and end-of-chapter problems as I can when preparing for exams (item 3).'' Personal factor items were written as statements such as, ``I enjoyed my required math courses,'' and ``I would characterize myself as competent in solving homework problems.'' Students could select ``strongly agree,'' ``agree,'' ``disagree,'' or ``strongly disagree'' as their response on each item.

A statistical analysis of the data was performed to identify any significant relationships between the personal factors and the cognitive factors and among the cognitive factors.

The Method

The sixteen-item inventory was administered to 60 electrical engineering technology juniors. Student anonymity was preserved by asking students to use a code number for identification should follow-up instruments be administered in the future. The percentages of each response are shown in Table 1. For example, for the statement ``Solving homework problems on schedule, as they are assigned, is important for high levels of achievement on exams in technical courses in my major,'' 60%selected ``strongly agree,'' 35%selected ``agree,'' 5%selected ``disagree,'' and none selected ``strongly disagree.''

It is interesting to note that 81.7%of the students strongly agree that the instructor or textbook should demonstrate at lease one example similar to each homework problem (item 2). Also of interest is that a little more than 71%of the students agreed or strongly agreed that it is more important to be able to solve exam problems from basic principles (item 4), yet 75%agreed or strongly agreed that they tried to memorize the step-by-step calculations that were used to solve homework problems (item 8) and 93.2%agreed or strongly agreed that they did not of their learning from drill problems, examples, and solutions to homework problems. Understanding the beliefs and attitudes expressed by students can help faculty be more effective in the teaching/learning process.

Relationships Among the Items

To investigate the relationships among the items, a four point scale was used to represent the four allowable choices, with 1 = strongly agree, 2 = agree, 3 = disagree, and 4 = strongly disagree. A statistical t test for the significance between the difference between two means was used to investigate possible relationships that might exist among the items. To simplify the statistical testing, two sub-groups were formed for each item in the set of personal factors (appreciation of math, physics, word problems, and puzzles, and self-assessment as a problem solver). Then the mean scores for each sub-group each item were compared for each of the two groups for each item. The significant results are summarized here.

Concerning Required Physics Courses (Item 15)

Students who answered ``strongly agree'' or ``agree'' that they enjoyed their required physic courses formed one sub-group, and those who answered ``disagree'' or ``strongly disagree'' formed a second sub-group, forming bipolar groupings. When the t test for the significance of the difference between the mean scores for the two sub-groups was run on each item, the following were significant:

  1. Those who said that they enjoyed their required physics courses were more likely to characterize themselves as competent problem solvers (mean score = 1.6) than those who did not say the same (mean score = 2.0), p < .05.

  2. Those who said they enjoyed their required physics courses were more likely to say that they enjoy solving puzzles and riddles (mean score = 2.0) than those who not say the same (mean = 2.9), p < .02.

  3. Those who said they enjoyed their required physics courses were more likely to say that they enjoyed their required math courses (mean score = 2.0) than those who did not say the same (mean score = 2.7), p < .05.

The first of the three items appears to be the most meaningful for engineering technology education. Since problem solving plays a significant role in the educational process of the electrical engineering technology major and in being a practicing technologist, models for understanding competencies in problem solving may be developed by looking at the kind of learning that takes place in physics courses taken by technology majors and understanding what it is about them that helps students develop confidence in their problem solving competencies. The second item confirms what we know about physics-that physics problems are difficult, i.e., they are like puzzles. The mental processes that are needed to solve puzzles, such as insight, brainstorming, withholding judgment, and going outside the box, may give clues on how to help students appreciate physics. The third item confirms what many would already guess-that there is a relationship between liking physics and liking math.

Concerning Algebra Word Problems (Item 12)

In a similar manner to the analysis of the data regarding physics courses, students were divided into two bipolar, sub-groups based on their attitude toward their required math courses. Here are the significant items.

  1. Those who said they enjoyed solving algebra word problems were less likely to say that they did most of their learning from drill problems, examples, and solutions to homework problems (mean score = 1.9) than those who did not say the same (mean score = 1.5), p < .05.

  2. Those who said they enjoyed solving algebra word problems were more likely to say that they enjoyed their required math courses (mean score = 1.9) than those who did not say the same (mean score = 2.6), p < .025.

The first item in this group appears to conform to common sense. Solving algebra word problems requires deeper thinking than executing calculations and using formulas. It seems reasonable that students who enjoyed solving word problems would be less likely to spend a considerable amount of time with drill problems and examples and more time learning the concepts and principles. This item suggests that writing homework problems in a way similar to algebra word problems can be used as a training tool to help students develop higher level learning skills. The second item simply confirms a common sense intuition that there would be a relationship between liking math and enjoying word problems.

Concerning Student Self-Assessment As Problem Solvers (Item 16)

Because of the small number of students who selected ``disagree'' or ``strongly disagree'' on their competency as a problem solver (item (16), the two sub-groups used in the t test were formed differently than previously. Those who selected ``strongly agree'' formed one group, and those who selected ``agree,'' ``disagree,'' and ``strongly disagree'' formed the second group, and thus the two groups are not bipolar. Using this pairing, the significant items are the following.

  1. Those who strongly agreed that they were competent as problem solvers were less likely to say that they prepared for exams by memorizing the step-by-step calculations used to solve the homework problems (mean score = 2.5) than those who did not strongly agree (mean score = 1.8), p < .01.

  2. Those who strongly agreed that they were competent as problem solvers were more likely to say that they tried to solve as many drill and end-of-chapter problems as possible (mean score = 1.5) than those who did not strongly agree (mean score = 2.1), p < .01.

The first item indicates that the most competent problem solvers, by self-assessment, did not memorize step-by-step calculations as much as those who did not strongly agree. This suggests that those less competent may be doing more memorizing more than learning. The second item suggests that competency in solving problems is related to working extra drill problems and extra end-of-chapter problems. These items gives us clues on ways to coach students to become more confident in their problem solving capabilities.

Other Factors

There were no additional significant results concerning the enjoyment of mathematics other than physics-math relationship discussed previously, and relationships among the cognitive factors were not investigated at this time. We focused on for looking for significant items on the basis personal factors at this time because it would be easier to make inferences about physics, math, word problems, puzzles, and self-assessed competencies.

Concluding Remarks

This is a pilot project that focuses on the study of personal factors and how they affect problem solving attitudes and beliefs in electrical engineering technology students. The purpose of the study is to learn more about the learner as a first step in developing coaching and teaching schemes to improve problem solving and self-assessment as a problem solver. Initial results indicate that we can learn about the problem solver and his/her strategies and attitudes through an understanding of more basic learning experiences in subjects such as physics and mathematics and on activities such as solving word problems and puzzles.

References

  1. Rodman, S.M., Dean, R.K., and Rosati, P.A., Self-perception of engineering students' preferred learning style related to MBTI type, Proceedings of the ASEE Annual Conference, 1986, pp. 1303-1313.

  2. Rosati, P. and Yokomoto, C.F., Student Attitudes Towards Learning: By Seniority and By Type, Proceedings of the ASEE Annual Conference, June 1993, Urbana-Champaign, pp. 2038-2042





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Fri Oct 6 16:19:59 PDT 1995