The Usefulness Of Mathematics As Seen By Engineering Seniors

During the academic years of 2001-2003 Rose-Hulman Institute of Technology participated in a NSF sponsored project to determine The Impact of Calculus Reform on Long-term Student Performance. One component of this project was a questionnaire which asked senior engineers about their view on mathematics. A second component of the study was a series of interviews held with graduating seniors. We obtained their responses to their calculus and engineering education. This report will focus on the responses made by senior engineering students concerning the usefulness of mathematics. All responses are from students who attended Rose-Hulman Institute of Technology. Both questionnaire and interview responses will be presented in this the paper. Section I Survey Data Background In the spring of 2002 senior engineering students, who took calculus I in the fall of 1998, were asked to complete the forty-nine question survey. The invitation was e-mailed to the students. To complete the survey students logged on to a website at Duke University. 134 (107 male and 27 female) Rose-Hulman seniors were asked to participate in the survey. A total of 54 students (38 men and 16 women) responded. While a greater percentage of women responded to the questionnaire than were in our original sample this does not seem to significantly influence our results. In no question was there a significant difference between the responses of the male students and the female students. The first four responses were background questions. The remaining 45 questions (5-49) were used to measure the each student’s attitude towards mathematics. There were six major categories of questions: b = Beliefs about Mathematics m = Effective Motivation in Mathematics t = Using Technology to Learn Mathematics o = Learning with Others P ge 10338.1 2 c = Confidence in Learning Mathematics u = Mathematics Usefulness The responses to the questions were marked as strongly agree (SA), agree (A), neutral (N), disagree (D), and strongly disagree (SD). For statistical purposes strongly agree was equivalent to a 1 and strongly disagree was equivalent to a 5. About half of the questions were asked in a negative manner. These questions are referred to with an “a” after the question number. For example u14a means than question seven was asked about “usefulness of mathematics” and was worded in a negative way. Note that all 54 students answered every question. Results Below are the results of the survey relating to the usefulness of mathematics in the undergraduate education of students attending Rose-Hulman Institute of Technology. Question Quest %SA %A %N %D %SD mean s.d. I’ll need a firm mastery of mathematics for my future work. u5 33.3 44.4 18.5 3.7 0 1.93 .82 Mathematics has no relevance to my life. u14a 0 5.6 7.4 29.6 57.4 4.39 .86 I see mathematics as a subject I will rarely use in my daily life after college. u20a 1.9 13.0 9.3 38.9 37.0 3.96 1.08 Mathematics is a worthwhile and necessary subject. u29 55.6 40.7 3.7 0 0 1.48 .57 I will use mathematics in many ways in my life. u33 37.0 51.9 9.3 1.9 0 1.76 .70 Mathematics will not be important in my life’s work. u37a 1.9 5.6 16.7 42.6 31.5 3.98 .95 Knowing mathematics will help me earn a living u43 25.9 53.7 11.1 9.3 0 2.04 .87 I expect to have little use for mathematics which I get out of college. u48a 0 5.6 16.7 40.7 37.0 4.09 .87 It was interesting to note that on fifteen, of the forty-five, questions the students seemed to have strong agreement, with an average response under 2. Three of these questions dealt directly with the usefulness of mathematics. Question Quest %SA %A %N %D %S D mean s.d. I’ll need a firm mastery of mathematics for my future work. u5 33.3 44.4 18.5 3.7 0 1.93 .82 Mathematics is a worthwhile and necessary subject. u29 55.6 40.7 3.7 0 0 1.48 .57 I will use mathematics in many ways in my life. u33 37.0 51.9 9.3 1.9 0 1.76 .70 P ge 10338.2 3 Of the forty-five questions asked, the two questions that the students agreed with most were question 47 (47t) “Learning to use technology was a valuable part of my educational experience in college.”, with an average of 1.44; and question 29 (u29) “Mathematics is a worthwhile and necessary subject.”, with an average of 1.48. Of the forty-five questions asked, there were five questions which students most strongly disagreed with, with an average response over 4. Two of these questions dealt directly with the usefulness of mathematics Question Quest %SA %A %N %D %S D N mean s.d. Mathematics has no relevance to my life. u14a 0 5.6 7.4 29.6 57.4 54 4.39 .86 I expect to have little use for mathematics when I get out of college. u48a 0 5.6 16.7 40.7 37.0 54 4.09 .87 The two questions the students most strongly disagreed with were question 32 (t32a) “Learning to use mathematics software or graphics calculators is a waste of time.”, with an average of 4.48, and question 14 (u14a) “Mathematics has not relevance to my life”, with an average of 4.39. Bar Charts and Correlations Below are the bar charts for each of the 8 questions dealing with the usefulness of mathematics. Questions u5, u14a, u20, u29, u33, u37a, u43, and u48a dealt with the students’ beliefs on “Mathematics Usefulness”. Since all the questions were highly correlated there was no reason to cluster the answers. Question 5: I’ll need a firm mastery of mathematics for my future work. Question 14: Mathematics has no relevance to my life. Question 20: I see mathematics as a subject I will rarely use in my daily life after college. Question 29: Mathematics is a worthwhile and necessary subject. Question 33: I will use mathematics in many ways in my life. Question 37: Mathematics will not be important in my life’s work. Question 43: Knowing mathematics will help me earn a living. Question 48: I expect to have little use for mathematics which I get out of college. Heading %SA %A %N %D %SA NR mean s.d Question5 ut5 33.3 44.4 18.5 3.7 0 54 1.93 .82 Question14 u14a 0 5.6 7.4 29.6 57.4 54 4.39 .86 P ge 10338.3 4 Question20 u20 1.9 13.0 9.3 38.9 37.0 54 3.96 1.08 Question29 u29 55.6 40.7 3.7 0 0 54 1.48 .57 Question33 u33 37.0 51.9 9.3 1.9 0 54 1.76 .70 Question37 u37a 1.9 5.6 16.7 42.6 31.5 53 3.98 .95 Question43 u43 25.9 53.7 11.1 9.3 0 54 2.04 .87 Question48 u48a 0 5.6 16.7 40.7 37.0 54 4.09 .87 Below are the bar graphs showing the results of questions 5, 14, 20, 29, 33, 37, 43, and 48. Remember that the following numerical scale was used: 1 = Strongly Agree 2 = Agree 3 = Neutral 4 = Disagree 5 = Strongly Disagree In looking at the bar graphs one should note the following: On question 5, 77.7% of the students agreed or strongly agreed with only 3.7% disagreed. On question 14, 5.6% agreed while 87% either disagreed or strongly disagreed. On question 20, 14.9% agreed while 75.9% either disagreed or strongly disagreed. On question 29, 96.3% agreed or strongly agreed while nobody disagreed. On question 33, 88.9 % agreed or strongly agreed while 1.9% disagreed. On question 37, 7.5% agreed or strongly agreed while 74.1% disagreed or strongly disagreed. On question 43 79.6% agreed while 9.3% disagreed. On question 38, 5.6% agreed while 87.7% disagreed or strongly disagreed.