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## International Journal of Mathematical Education in Science and Technology

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## 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

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### 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, 811 — 816

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**The eect 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; 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 Oklahoma State University. The eects that the course had on students’ critical thinking skills, problem-solving 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 dierence was found in problem-solving 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, dierent 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 oer degrees in interdisciplinary studies
[2, 3]. Because of its usefulness as a tool, mathematics has been paired with many
dierent 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 inter-
disciplinary courses, it is natural to ask what eect 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 eect that this course has on students’ critical thinking skills, problem-solving 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

http://www.tandf.co.uk/journals DOI: 10.1080/00207390110053784

Downloaded At: 22:28 6 January 2010

This new interdisciplinary course is dierent from college algebra in that science topics lead to corresponding mathematics topics and modelling is fre- quently 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 dierent 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 1998. 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 dierent 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 freshman-level 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 dierent majors represented with some of the more common 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; total minority percentage was 18%. The mean age of the students in the sample was 21.4 and 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 ACT score 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 ®rst math course for credit is an algebra course.

*2.2. Instruments*

To measure problem-solving skills, the two instructors asked common ques- tions 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 t-test 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, Interpret-
ation 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]. Inde-
*pendent t-tests were used to test for dierences 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 Chi-square test for independence was performed on each statement to test for dierences 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 dierences were found between students that had been ran- domly placed into the two courses in the spring of 1998 and those that self-selected in the fall of 1998. All other analyses were performed on the aggregate.

*3.1. Problem-solving 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 problem-solving skills of the two groups of students were very similar. In fact, if the 0.05 level is used, no statistically signi®cant dierences exist between the two groups in any of the categories.

However, two of the dierences were signi®cant at the 0.10 level. The College

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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 dierence was solving logarithmic equations … p ˆ 0:0883†*

in which the Algebra for the Sciences students did better. Since these two
*dierences were in opposite directions, and because of the large number of t-*
tests performed, the tendency towards a Type I error is suciently large that little
signi®cance should be attributed to these dierences.

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 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.

*3.2. 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 dierence (at the
0.05 level) was found only on the Inference subscore*… p ˆ 0:0492†. The dierences*

814 *B. Elliott et al.*

Algebra for Sciences College Algebra
*Graphing*

Lines 68 66

Quadratics 60 56

Exponentials 56 61

Logarithms 56 60

*Solving equations*

Linear 88 91

Quadratic 61 71

Exponential 35 49

Logarithmic 48 32

Linear Systems 80 78

Table 1. Percentage of students correct or almost correct.

Algebra for Sciences College Algebra

Overall score 52.3 49.8

Inference 8.4 7.7

Recognition of Assumptions 10.7 10.4

Deduction 10.2 9.5

Interpretation 11.4 11.1

Evaluation 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† are*
statistically signi®cant at the 0.10 level.

*3.3. 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 interest- ing. 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 problem-solving 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

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 7 attitude towards math

2. Math is important in life 64 18 12 3 3 44 18 20 10 8

3. I plan to take more math courses 38 25 11 19 7 35 12 18 24 11 4. The materials in this course are 68 22 8 1 1 24 29 31 10 5

related to practical situations

5. 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-9652867 from the Division of Undergraduate Education of the National Science Founda- tion 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 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.**

816 *Eects on students of an interdisciplinary algebra/science course*

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