Effects Of Variable Mix On Student Mathematics Performance

Engineering and Engineering Technology students encounter a wide variety of variables in their coursework. To prepare for courses in their specific majors, these students usually take a common core of mathematics classes, which are typically taught using x and y. The authors wished to determine whether students’ mathematical performance using other variables was on a par with their ability to manipulate x and y. A ten problem quiz was designed in two versions: one using only x and y, the other using a wider range of variables. The problems were identical in all other respects. Since the population to be tested included first-year students, none of the problems was calculus-based. One of the questions did not use any variable at all. This was included as a control question. The quiz was given to one hundred twenty-four students in first, second, and third year courses at Georgia Southern University. The sample population is a mix of Engineering and Engineering Technology majors, including native and transfer students. Students in several classes were given the quiz with the two versions randomly distributed within each class. Students taking the xy version of the quiz scored significantly higher than students taking the mixed-variable quiz. Students with higher class rankings (juniors and seniors) showed a lower difference between the quiz versions than did students classified as freshmen / sophomores. Classification of students’ rankings was based on individual mathematics course histories as reported by the students. This paper presents the detailed results of the study, along with suggestions for further research into this topic. These results may be useful in indicating areas where review is needed. Introduction On presenting a set of technology-based problems for teaching mathematics to engineering students, Klebanoff and Winkell 1 noted the compartmentalization that exists in which students see little substantive relationship between math, science and engineering. Although they speculated that the type of symbolic manipulations that students are asked to perform in mathematics classes does not prepare them for applying mathematical concepts in science or engineering contexts, they did not further explore the lack of perceived relationship. In a study of the knowledge and application of College Algebra, Conway Link 2 asked students to solve for the radius of a sphere using the sphere’s volume formula. He found that only 34.6% of the surveyed students were able to produce a correct answer, but that the number of mathematics courses taken after College Algebra seemed to increase the likelihood of a correct answer. He ascribed this to students’ encountering an increasing number of examples and problems with “non-traditional” variables and formulas as they progress through their coursework. On discussing the problems encountered in teaching mathematics to engineering students, Sazhin 3 noted that changing the basic equation “Proceedings of the 2004 American Society for Engineering Education Annual Conference & Exposition Copyright ø 2004, American Society for Engineering Education” P ge 913.1 x = b/a to the slightly more complex prevented most students from solving it for x. He ascribed this to students’ tendency to memorize equations and their manipulation in a particular notation. The disconnect between mathematics teaching with x and y as preferred variables and the use of more varied and descriptive names in engineering and technology courses may explain why students find it difficult to solve mathematically simple problems in an engineering application. This disconnect has apparently not been investigated before this study. A survey was conducted to determine whether the variables used in solving problems affected students’ mathematical performance. Students enrolled in sophomore and junior level engineering and engineering technology courses at Georgia Southern University were given a ten-problem survey. The students were enrolled in (A) Mechanism Design, a junior level course in Mechanical Engineering Technology, (B) Statics, a sophomore level course for Civil, Electrical, and Mechanical Engineering Technology majors, (C) Statics and Dynamics, a sophomore level course for engineering majors, and (D) Electrical Devices and Measurements, a sophomore level course for Electrical and Mechanical Engineering Technology majors. The survey included two sections. The first section collected information about the students’ mathematics background. Questions in this section addressed which courses had been completed, what grades had been achieved, and the amount of time elapsed since each course was completed. The students’ names and the course in which they were enrolled were also collected. (See Fig. 1) The second section of the survey was a set of ten problems. Six problems involved algebraic solution, two problems involved trigonometry, and one problem involved graphical analysis. A tenth question, not involving any variables, was included as a control question. The survey instrument was prepared in two versions, one using the variables x and y, the other version using the variables g, h, m, n, p, Q, q, r, s, t, and r. The questions on the two versions were identical except for the variables used. (See Figures 2 and 3) The survey was conducted on an unannounced basis. Calculators were allowed. The grade history was completed first, after which fifteen minutes were given for the problem-solving portion. “Proceedings of the 2004 American Society for Engineering Education Annual Conference & Exposition Copyright ø 2004, American Society for Engineering Education” One hundred twenty five survey forms were completed; of these, four were multiple responses from the same individuals, due to enrollment in more than one of the courses surveyed. These multiple responses are not included in the analysis which follows. P ge 913.2