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The effect of aninterdisciplinary algebra/science course on students'problem solving skills,critical thinking skillsand attitudes towardsmathematicsBrett Elliott , Karla Oty , John McArthur & BryonClarkPublished online: 11 Nov 2010.

To cite this article: Brett Elliott , Karla Oty , John McArthur & Bryon Clark(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, 32:6,811-816, DOI: 10.1080/00207390110053784

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The e� ect of an interdisciplinary algebra/science course onstudents’ problem solving skills, critical thinking skills and

attitudes towards mathematics

BRETT ELLIOTT*, KARLA OTY*, JOHN MCARTHUR** and BRYONCLARK***

* Department of Mathematics, ** Department of Computer Science and Technology and*** Department of Biological Sciences, Southeastern Oklahoma State University, Durant,

OK 74701, USA; e-mail: belliott@sosu.edu

(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 OklahomaState University. The e� ects that the course had on students’ critical thinkingskills, problem-solving skills, and attitudes towards mathematics were studied.The traditional college algebra course was used as a control group. The ®rstsemester that the new course was taught, students were randomly placed intoone of Algebra for the Sciences or College Algebra. The study lasted for twosemesters and a total of eight course sections were usedÐfour sections of theexperimental course and four sections of the college algebra course. Nosigni®cant di� erence was found in problem-solving skills between students inthe interdisciplinary course and students in the college algebra course. Studentsin the interdisciplinary course had slightly larger gains in critical thinking andsigni®cantly more positive attitudes at the end of the course than the students incollege algebra.

1. IntroductionInterdisciplinary studies have generated much interest in recent years. In the

past, di� erent subjects were usually taught as though they were isolated from oneanother and had nothing in common. Now two or more subjects are oftencombined into a single interdisciplinary course. For example, Ashland Universityhas a course called Science as a Cultural Force [1] that can be taken for chemistry orphilosophy credit. Some universities even o� er degrees in interdisciplinary studies[2, 3]. Because of its usefulness as a tool, mathematics has been paired with manydi� erent disciplines including art, business, physics, chemistry, biology, andenvironmental engineering [4]. In Interdisciplinary Teaching: Why & How [5,p. 1] Gordon Vars says that in recent years `interest in interdisciplinary teachingand curriculum has increased exponentially’. With all of this interest in inter-disciplinary courses, it is natural to ask what e� ect these courses have on students.

This study focuses on an interdisciplinary course called `Algebra for theSciences’ that was developed at Southeastern Oklahoma State University. Ofparticular interest is the e� ect that this course has on students’ critical thinkingskills, problem-solving skills, and attitudes towards mathematics. A traditionalcollege algebra course was used as a control group.

int. j. math. educ. sci. technol., 2001, vol. 32, no. 6, 811±816

International Journal of Mathematical Education in Science and TechnologyISSN 0020±739X print/ISSN 1464±5211 online # 2001 Taylor & Francis Ltd

http://www.tandf.co.uk/journalsDOI: 10.1080/00207390110053784

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This new interdisciplinary course is di� erent from college algebra in thatscience topics lead to corresponding mathematics topics and modelling is fre-quently used. The science topics may be introduced by way of an experiment or byfaculty from various scienti®c disciplines appearing as guest lecturers. Forinstance, a session on logarithms begins with a physicist leading a discussion onsound. Then the students participate in an experiment where di� erent numbers ofdoorbells are rung and the decibels are recorded. These points (number ofdoorbells rung vs. total decibels) are then plotted and an attempt is made to ®nda model that describes the data. The students soon discover that none of theprevious models covered (linear, quadratic, exponential) are appropriate in thissituation and that a new type of equation is needed. This leads to a discussion oflogarithms by the mathematician. The other topics in the course are introduced ina similar manner. At the conclusion of each topic, each student is assigned aninterdisciplinary project. For more information about the particulars of the coursesee [6].

2. Methodology

2.1. SubjectsThis study was conducted at the university in the spring and fall semesters of

1998. A total of eight classes were usedÐfour classes of the interdisciplinary courseand 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 asCollege Algebra. Approximately ®fty students were allowed into each of thesecourses. On the ®rst day of class, half of the students from each section werechosen at random (using a random number generator) to participate in the newAlgebra for the Sciences course. They were not told that the course was di� erentfrom the traditional college algebra course and the two instructors were careful tocontinue referring to the course as College Algebra. In the course schedule in thefall of 1998 there were two sections of College Algebra and two sections of Algebrafor the Sciences listed. This time students were able to choose which course theywanted to take.

Altogether, this process resulted in a total beginning sample size of 211students (118 in College Algebra, 93 in Algebra for the Sciences). Because ofthe high dropout rate in freshman-level mathematics classes the ending sample sizewas 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 86were male. There were 32 di� erent majors represented with some of the morecommon being Undecided (42), Elementary Education (29), Biology (21), Man-agement (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% African-American, 2% Hispanic and 1% Asian; totalminority percentage was 18%. The mean age of the students in the sample was 21.4and the median was 19.0. The mean Composite ACT score of the sample was 20.0.This is slightly lower than the national mean of 21.0 [7]. The mean Math ACTscore of the sample was 17.9, considerably lower than the national mean of 20.8 for

812 B. Elliott et al.

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all beginning freshmen [7] but probably about average for freshmen whose ®rstmath course for credit is an algebra course.

2.2. InstrumentsTo measure problem-solving skills, the two instructors asked common ques-

tions on the ®nals given in College Algebra and Algebra for the Sciences. Thesequestions were categorized and the percentage of students that answered thequestions completely correct or `almost completely correct’ was calculated. Aproblem was graded as `almost completely correct’ if the student used anappropriate 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 t-test for proportions were made between students in the twocourses. 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 80mutliple choice questions and takes 40 to 50 minutes to complete. It is dividedinto ®ve subareas: Inference, Recognition of Assumptions, Deduction, Interpret-ation and Evaluation of Arguments. Each subarea contains 16 questions. TheWGCTA was chosen because of its consistency and reliability and because it isconsidered the `bench mark against which others must be compared’ [8]. Inde-pendent t-tests were used to test for di� erences in the critical thinking skillsbetween the students in the two courses.

To measure students’ attitudes towards mathematics, statements were usedfrom student evaluations given at the end of the semester in each course.Percentages of students strongly agreeing, agreeing, undecided, disagreeing orstrongly disagreeing were calculated for each of ®ve statements. A Chi-square testfor independence was performed on each statement to test for di� erences betweenstudents 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. ResultsNo signi®cant di� erences were found between students that had been ran-

domly placed into the two courses in the spring of 1998 and those that self-selectedin the fall of 1998. All other analyses were performed on the aggregate.

3.1. Problem-solving skillsTable 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 problem-solving skills of the two groups ofstudents were very similar. In fact, if the 0.05 level is used, no statisticallysigni®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

E� ects on students of an interdisciplinary algebra/science course 813

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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 problem-solving 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 thosetopics 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.

3.2. Critical thinking skillsTable 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 the0.05 level) was found only on the Inference subscore … p ˆ 0:0492†. The di� erences

814 B. Elliott et al.

Algebra for Sciences College Algebra

GraphingLines 68 66Quadratics 60 56Exponentials 56 61Logarithms 56 60

Solving equationsLinear 88 91Quadratic 61 71Exponential 35 49Logarithmic 48 32Linear Systems 80 78

Table 1. Percentage of students correct or almost correct.

Algebra for Sciences College Algebra

Overall score 52.3 49.8Inference 8.4 7.7Recognition of Assumptions 10.7 10.4Deduction 10.2 9.5Interpretation 11.4 11.1Evaluation of Arguments 11.6 11.2

Table 2. Critical thinking scores.

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in the Overall score … p ˆ 0:0687† and the Deduction subscore … p ˆ 0:0995† arestatistically signi®cant at the 0.10 level.

3.3. AttitudesTable 3 gives the percentage of students in each course that strongly agreed

(SA), agreed (A), were undecided (U), disagreed (D) or strongly disagreed (SD) tothe 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 hadsigni®cantly more positive attitudes at the end of the semester than the students inCollege Algebra. Overall, students in the Algebra for the Sciences course thoughttheir course was more interesting … p < 0:005† and practical … p < 0:005† than didstudents in the College Algebra course. They also had better attitudes towardsmath … 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 Algebrafor the Sciences thought that math was important in life.

4. SummaryPrevious studies have shown a positive relationship between students’ attitudes

towards mathematics and their performance in mathematics [9, 10]. Thus, one waythat we can attempt to improve a student’s performance is to improve theirattitude. Furthermore, we would like to improve their attitude as early in theirmathematics career as possible. College Algebra, the ®rst mathematics course incollege for many students, has not been successful in doing this. This study hasshown that an interdisciplinary course such as Algebra for the Sciences may bemore successful in achieving that goal. By doing interdisciplinary projects,students begin to believe that mathematics is useful, important and even interest-ing. This increased interest may be `more important than their perceived mathability in determining whether they study more mathematics’ [11]. At the sametime, their problem-solving skills and critical thinking skills are not compromised.

This study is ongoing in that the students from the two courses will now betracked through their later mathematics courses. Of interest will be whether theimproved attitudes of students from Algebra for the Sciences translates into themenrolling in more subsequent mathematics courses than their counterparts from

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 48 25 20 5 2 26 37 19 12 7attitude towards math

2. Math is important in life 64 18 12 3 3 44 18 20 10 83. I plan to take more math courses 38 25 11 19 7 35 12 18 24 114. The materials in this course are 68 22 8 1 1 24 29 31 10 5

related to practical situations5. I found this class to be 62 22 9 5 2 20 22 35 12 11

interesting

Note: Percentages may not add to 100 due to rounding

Table 3. Percentage of agreement by course.

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College Algebra. The performance of the two groups in these subsequent math-ematics classes will also be compared.

Acknowledgements

The work described in this article was supported by grant #DUE-9652867from the Division of Undergraduate Education of the National Science Founda-tion for the Course and Curriculum Development Program. However, the viewsexpressed are not necessarily those of either the Foundation or the Project.

References[1] Ashland University, Chemistry courses and descriptions. Available online at http://

www.ashland.edu/colleges/CatChem.html #courses.[2] University of California at Berkeley, Division of undergraduate and interdisciplinary

studies. Available online at http://www-learning.berkeley.edu/ugis.html.[3] University of South Florida, Interdisciplinary studies department (IDS). Available

online at http://www.cas.usf.edu/bis/index.html.[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 http://www.act.org/news/data/98/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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