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1 This article was downloaded by: On: 6 January 2010 Access details: Access Details: Free Access Publisher Taylor & Francis Informa Ltd Registered in England and Wales Registered Number: Registered office: Mortimer House, Mortimer Street, London W1T 3JH, UK International Journal of Mathematical Education in Science and Technology Publication details, including instructions for authors and subscription information: The effect of an interdisciplinary algebra/science course on students' problem solving skills, critical thinking skills and attitudes towards mathematics Brett Elliott; Karla Oty; John McArthur; Bryon Clark To cite this Article Elliott, Brett, Oty, Karla, McArthur, John and Clark, Bryon(2001) 'The effect of an interdisciplinary algebra/science course on students' problem solving skills, critical thinking skills and attitudes towards mathematics', International Journal of Mathematical Education in Science and Technology, 32: 6, To link to this Article: DOI: / URL: PLEASE SCROLL DOWN FOR ARTICLE Full terms and conditions of use: This article may be used for research, teaching and private study purposes. Any substantial or systematic reproduction, redistribution, reselling, loan or sublicensing, systematic supply or distribution in any form to anyone is expressly forbidden. The publisher does not give any warranty express or implied or make any representation that the contents will be complete or accurate or up to date. The accuracy of any instructions, formulae and drug doses should be independently verified with primary sources. The publisher shall not be liable for any loss, actions, claims, proceedings, demand or costs or damages whatsoever or howsoever caused arising directly or indirectly in connection with or arising out of the use of this material.
2 int. j. math. educ. sci. technol., 2001, vol. 32, no. 6, 811±816 The e ect of an interdisciplinary algebra/science course on students problem solving skills, critical thinking skills and attitudes towards mathematics BRETT ELLIOTT*, KARLA OTY*, JOHN MCARTHUR** and BRYON CLARK*** * Department of Mathematics, ** Department of Computer Science and Technology and *** Department of Biological Sciences, Southeastern Oklahoma State University, Durant, OK 74701, USA; (Received 20 April 2000) This paper brie y describes a newly designed interdisciplinary course called `Algebra for the Sciences that is currently taught at Southeastern Oklahoma State University. The e ects that the course had on students critical thinking skills, problemsolving skills, and attitudes towards mathematics were studied. The traditional college algebra course was used as a control group. The rst semester that the new course was taught, students were randomly placed into one of Algebra for the Sciences or College Algebra. The study lasted for two semesters and a total of eight course sections were usedðfour sections of the experimental course and four sections of the college algebra course. No signi cant di erence was found in problemsolving skills between students in the interdisciplinary course and students in the college algebra course. Students in the interdisciplinary course had slightly larger gains in critical thinking and signi cantly more positive attitudes at the end of the course than the students in college algebra. 1. Introduction Interdisciplinary studies have generated much interest in recent years. In the past, di erent subjects were usually taught as though they were isolated from one another and had nothing in common. Now two or more subjects are often combined into a single interdisciplinary course. For example, Ashland University has a course called Science as a Cultural Force [1] that can be taken for chemistry or philosophy credit. Some universities even o er degrees in interdisciplinary studies [2, 3]. Because of its usefulness as a tool, mathematics has been paired with many di erent disciplines including art, business, physics, chemistry, biology, and environmental engineering [4]. In Interdisciplinary Teaching: Why & How [5, p. 1] Gordon Vars says that in recent years `interest in interdisciplinary teaching and curriculum has increased exponentially. With all of this interest in interdisciplinary courses, it is natural to ask what e ect these courses have on students. This study focuses on an interdisciplinary course called `Algebra for the Sciences that was developed at Southeastern Oklahoma State University. Of particular interest is the e ect that this course has on students critical thinking skills, problemsolving skills, and attitudes towards mathematics. A traditional college algebra course was used as a control group. International Journal of Mathematical Education in Science and Technology ISSN 0020±739X print/issn 1464±5211 online # 2001 Taylor & Francis Ltd DOI: /
3 812 B. Elliott et al. This new interdisciplinary course is di erent from college algebra in that science topics lead to corresponding mathematics topics and modelling is frequently used. The science topics may be introduced by way of an experiment or by faculty from various scienti c disciplines appearing as guest lecturers. For instance, a session on logarithms begins with a physicist leading a discussion on sound. Then the students participate in an experiment where di erent numbers of doorbells are rung and the decibels are recorded. These points (number of doorbells rung vs. total decibels) are then plotted and an attempt is made to nd a model that describes the data. The students soon discover that none of the previous models covered (linear, quadratic, exponential) are appropriate in this situation and that a new type of equation is needed. This leads to a discussion of logarithms by the mathematician. The other topics in the course are introduced in a similar manner. At the conclusion of each topic, each student is assigned an interdisciplinary project. For more information about the particulars of the course see [6]. 2. Methodology 2.1. Subjects This study was conducted at the university in the spring and fall semesters of A total of eight classes were usedðfour classes of the interdisciplinary course and four classes of the traditional college algebra. All classes were taught by the rst two authors of this paper with guest lectures by the other two authors. In the course schedule in the spring of 1998 there were two sections listed as College Algebra. Approximately fty students were allowed into each of these courses. On the rst day of class, half of the students from each section were chosen at random (using a random number generator) to participate in the new Algebra for the Sciences course. They were not told that the course was di erent from the traditional college algebra course and the two instructors were careful to continue referring to the course as College Algebra. In the course schedule in the fall of 1998 there were two sections of College Algebra and two sections of Algebra for the Sciences listed. This time students were able to choose which course they wanted to take. Altogether, this process resulted in a total beginning sample size of 211 students (118 in College Algebra, 93 in Algebra for the Sciences). Because of the high dropout rate in freshmanlevel mathematics classes the ending sample size was only 143 (75 in College Algebra and 68 in Algebra for the Sciences). Of the 211 students at the beginning of the semester, 125 were female and 86 were male. There were 32 di erent majors represented with some of the more common being Undecided (42), Elementary Education (29), Biology (21), Management (14), Conservation (11), Computer Science (10), Music (8), Electronics (6), Health and Physical Education (6), Safety (6), Psychology (6), Sociology (5) and Prepharmacy (5). The ethnic breakdown of the sample was 82% Caucasian, 11% Native American, 4% AfricanAmerican, 2% Hispanic and 1% Asian; total minority percentage was 18%. The mean age of the students in the sample was 21.4 and the median was The mean Composite ACT score of the sample was This is slightly lower than the national mean of 21.0 [7]. The mean Math ACT score of the sample was 17.9, considerably lower than the national mean of 20.8 for
4 E ects on students of an interdisciplinary algebra/science course 813 all beginning freshmen [7] but probably about average for freshmen whose rst math course for credit is an algebra course Instruments To measure problemsolving skills, the two instructors asked common questions on the nals given in College Algebra and Algebra for the Sciences. These questions were categorized and the percentage of students that answered the questions completely correct or `almost completely correct was calculated. A problem was graded as `almost completely correct if the student used an appropriate procedure but made a careless mistake at some point in the problem, such as an arithmetic mistake or a transcription error from one step to the next. Comparisons using a ttest for proportions were made between students in the two courses. The categories and subcategories were graphing (lines, quadratics, exponentials and logarithms) and solving equations (linear, quadratic, exponential, logarithmic and systems). The instrument used for measuring critical thinking skills was the Watson± Glaser Critical Thinking Appraisal (WGCTA). The WGCTA consists of 80 mutliple choice questions and takes 40 to 50 minutes to complete. It is divided into ve subareas: Inference, Recognition of Assumptions, Deduction, Interpretation and Evaluation of Arguments. Each subarea contains 16 questions. The WGCTA was chosen because of its consistency and reliability and because it is considered the `bench mark against which others must be compared [8]. Independent ttests were used to test for di erences in the critical thinking skills between the students in the two courses. To measure students attitudes towards mathematics, statements were used from student evaluations given at the end of the semester in each course. Percentages of students strongly agreeing, agreeing, undecided, disagreeing or strongly disagreeing were calculated for each of ve statements. A Chisquare test for independence was performed on each statement to test for di erences between students in the two courses. The statements used were:. This course has improved my attitude towards math.. Math is important in life.. I plan to take more math courses.. The materials in this course are related to practical situations.. I found this class to be interesting. 3. Results No signi cant di erences were found between students that had been randomly placed into the two courses in the spring of 1998 and those that selfselected in the fall of All other analyses were performed on the aggregate Problemsolving skills Table 1 gives the percentage of students in each course that were completely correct or `almost completely correct on the common problems placed on the nals. As can be seen from table 1, the problemsolving skills of the two groups of students were very similar. In fact, if the 0.05 level is used, no statistically signi cant di erences exist between the two groups in any of the categories. However, two of the di erences were signi cant at the 0.10 level. The College
5 814 B. Elliott et al. Algebra for Sciences College Algebra Graphing Lines Quadratics Exponentials Logarithms Solving equations Linear Quadratic Exponential Logarithmic Linear Systems Table 1. Percentage of students correct or almost correct. Algebra students did better at solving exponential equations p ˆ 0:0752 and the Algebra for the Sciences students did better at solving logarithmic equations p ˆ 0:0883. The other di erence was solving logarithmic equations p ˆ 0:0883 in which the Algebra for the Sciences students did better. Since these two di erences were in opposite directions, and because of the large number of t tests performed, the tendency towards a Type I error is su ciently large that little signi cance should be attributed to these di erences. There were other areas of problemsolving that were not compared because they were not covered in both of the courses. For instance, in the Algebra for the Sciences course, estimation, geometry and regression were covered but those topics were not discussed in College Algebra. Likewise, sequences and series were covered in some sections of College Algebra but not in Algebra for the Sciences Critical thinking skills Table 2 gives the average overall critical thinking score of the students in each course as well as the average scores for each subarea as measured at the end of the semester. The overall scores ranged from 32 to 71 (with 80 possible) and the subarea scores ranged from 1 to 16 (with 16 possible). As can be seen from table 2, the students in Algebra for the Sciences had higher critical thinking scores than the students in College Algebra for the overall score and for each of the subscores. However, a statistically signi cant di erence (at the 0.05 level) was found only on the Inference subscore p ˆ 0:0492. The di erences Algebra for Sciences College Algebra Overall score Inference Recognition of Assumptions Deduction Interpretation Evaluation of Arguments Table 2. Critical thinking scores.
6 E ects on students of an interdisciplinary algebra/science course 815 Algebra for Sciences College Algebra SA A U D SD SA A U D SD 1. This course has improved my attitude towards math 2. Math is important in life I plan to take more math courses The materials in this course are related to practical situations 5. I found this class to be interesting Note: Percentages may not add to 100 due to rounding Table 3. Percentage of agreement by course. in the Overall score p ˆ 0:0687 and the Deduction subscore p ˆ 0:0995 are statistically signi cant at the 0.10 level Attitudes Table 3 gives the percentage of students in each course that strongly agreed (SA), agreed (A), were undecided (U), disagreed (D) or strongly disagreed (SD) to the statements placed on the student evaluations at the end of each course. As can be seen from table 3, the students in Algebra for the Sciences had signi cantly more positive attitudes at the end of the semester than the students in College Algebra. Overall, students in the Algebra for the Sciences course thought their course was more interesting p < 0:005 and practical p < 0:005 than did students in the College Algebra course. They also had better attitudes towards math p < 0:05 at the end of the semester than students in the traditional course. Although statistically nonsigni cant, a greater proportion of students in Algebra for the Sciences thought that math was important in life. 4. Summary Previous studies have shown a positive relationship between students attitudes towards mathematics and their performance in mathematics [9, 10]. Thus, one way that we can attempt to improve a student s performance is to improve their attitude. Furthermore, we would like to improve their attitude as early in their mathematics career as possible. College Algebra, the rst mathematics course in college for many students, has not been successful in doing this. This study has shown that an interdisciplinary course such as Algebra for the Sciences may be more successful in achieving that goal. By doing interdisciplinary projects, students begin to believe that mathematics is useful, important and even interesting. This increased interest may be `more important than their perceived math ability in determining whether they study more mathematics [11]. At the same time, their problemsolving skills and critical thinking skills are not compromised. This study is ongoing in that the students from the two courses will now be tracked through their later mathematics courses. Of interest will be whether the improved attitudes of students from Algebra for the Sciences translates into them enrolling in more subsequent mathematics courses than their counterparts from
7 816 E ects on students of an interdisciplinary algebra/science course College Algebra. The performance of the two groups in these subsequent mathematics classes will also be compared. Acknowledgements The work described in this article was supported by grant #DUE from the Division of Undergraduate Education of the National Science Foundation for the Course and Curriculum Development Program. However, the views expressed are not necessarily those of either the Foundation or the Project. References [1] Ashland University, Chemistry courses and descriptions. Available online at #courses. [2] University of California at Berkeley, Division of undergraduate and interdisciplinary studies. Available online at [3] University of South Florida, Interdisciplinary studies department (IDS). Available online at [4] American Mathematical Society, 1999, Abstracts of papers presented to the American Mathematical Society (Providence, RI: AMS), pp. 213±218. [5] Vars, G. F., 1993, Interdisciplinary Teaching: Why & How (Columbus, OH: National Middle School Association), p. 1. [6] Oty, K., Elliott, B., McArthur, J., and Clark, B., 2000, Primus, 10, 29±41. [7] ACT (American College Testing Corporation), 1998, ACT: Reports: 1998 ACT High School Pro le Report. Available online at t1.html [8] Norris, S. P., and Ennis, R. H., 1989, Evaluating Critical Thinking (Paci c Grove, CA: Midwest). [9] Hensel, L. T., and Stephens, L. J., 1997, Int. J. Math. Educ. Sci. Technol., 28, 25±29. [10] Shaw, C. T., and Shaw, V. F., 1997, Int. J. Math. Educ. Sci. Technol., 28, 289±301. [11] Wallace, D. I., 2000, Focus, 3, 6±7.
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