Charles F. Yokomoto
Indiana University-Purdue University Indianapolis
Walter W. Buchanan
University of Central Florida
Indiana University-Purdue University Indianapolis
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.  and Rosati, et. al. . 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 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.
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.
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:
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.
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.
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.
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.
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.
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.
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.