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«Running Head: EXPLORING TEACHING FINITE MATHEMATICS EXPLORING THE EFFECTIVENESS OF DIFFERENT APPROACHES TO TEACHING FINITE MATHEMATICS Alabama State ...»

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EXPLORING TEACHING FINITE MATHEMATICS 118

Running Head: EXPLORING TEACHING FINITE MATHEMATICS

EXPLORING THE EFFECTIVENESS OF DIFFERENT APPROACHES TO TEACHING

FINITE MATHEMATICS

Alabama State University

University College Department of Mathematics and Science

Science Building Room 302

915 S. Jackson St.

Montgomery, AL 36101 Dr. Mary Alice Smeal msmeal@alasu.edu Dr. Sandra Walker swalker@alasu.edu Dr. Jamye Carter jcarter@alasu.edu Dr. Carolyn Simmons-Johnson csimmons@alasu.edu Dr. Lisa James ljames@alasu.edu Dr. Esenc Balam ebalam@alasu.edu

EXPLORING TEACHING FINITE MATHEMATICS 119

Abstract Traditionally, mathematics has been taught using a very direct approach where the teacher explains the procedure to solve a problem and the students use pencil and paper to solve the problem. However, a variety of approaches to mathematics have surfaced from a number of different directions. The purpose of the study was to examine the effectiveness of three teaching methods on student achievement in undergraduate Finite Mathematics classes at Alabama State University. The three teaching methods stressed traditional teaching methods, the incorporation of graphing calculators, and online learning, respectively. Three hundred sixty-one students formed the control group and were taught by the traditional lecture method, 202 students formed one of the experimental groups which used calculator enhanced instruction, and twenty students formed the other experimental group that utilized online distance learning. The research project examined each teacher's style and compared achievement outcomes. To investigate the performance of the students, a pretest was given to each student at the beginning of the semester before instruction and a posttest was given at the end of each semester after instruction. The results presented a significant improvement (p.001) between the pre-tests and post-tests within each group. The students in the calculator-enhanced group scored significantly higher (p.001) on the post-test than the students in the traditional group.

Keywords: Finite, Mathematics, Undergraduate, Technology EXPLORING TEACHING FINIT

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Traditionally, mathematics has been taught using a very direct approach where the teacher explains the procedure to solve a problem and the students use pencil and paper to solve the problem. However, a variety of approaches to mathematics have surfaced from a number of different directions. The National Council of Teachers of Mathematics (2000) encouraged teachers to incorporate a more student-centered approach as well as utilize technology. The American Mathematical Association of Two-Year Colleges (1996) standards also suggested that technology is an essential part of reform curricula, specifically software and graphing calculators. In attempts to include more students at the university level, many universities are offering distance learning courses as an option (Perez & Foshay, 2002). Another consideration of distance learning is that an estimated 50-75 percent of corporate education uses online technology (Bourne, Harris, & Mayadas, 2005), so familiarity with online education increases a students’ job marketability.

The purpose of the study was to examine the effectiveness of three teaching methods on student achievement in undergraduate finite mathematics classes at Alabama State University.

The three teaching methods stressed traditional teaching methods, the incorporation of graphing calculators, and distance learning, respectively. The research project examined each teacher's style and compared achievement outcomes.

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basic mathematics and science courses at the university level. Alternative approaches to teaching mathematics included distance learning (Perez & Foshay, 2002; Su, 2008), computer-assisted curriculum (Taylor, 2008), and graphing calculators (McCoy, 1996).

In a comparison of achievement using graphing calculators and traditional approaches, the results were mixed. In McCoy’s study (1996) using computer-based mathematics learning, she reported that technology-related tools improved conceptual learning, but computation skills were no different. The Mathematics Department at Columbia College in South Carolina revamped the college algebra curriculum by featuring graphing calculators (Hopkins & Kinard). The new program of study focused on using graphing calculators to help students to learn conceptually and incorporating students’ intuitive understanding about mathematics. Hopkins and Kinard (1998) conducted a study that compared students taught by traditional methods with students involved in the new program that concentrated on graphing calculators. Students in the graphing calculator program performed better on the final exam and had better attitudes toward mathematics at the end of the course. Two studies reported that achievement on final examinations of students using graphing calculators were higher than students who were not using graphing calculators (Quesada & Maxwell, 1994; Stiff, McCollum, & Johnson, 1992).

Wynegar and Fenster (2009) researched achievement of students in college algebra. Each section used a different instructional methodology. The methodologies included computer-aided instruction, traditional lecture, and online teaching in a college algebra course. The final course grade was used to compare the various teaching approaches. Wynegar and Fenster (2009) reported that students in traditional lecture classes performed better than all of the other courses using other methodologies. The conflicting implications from the discussed research studies

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Given the conflicting research found in prior studies between types of instruction in basic

college mathematics courses, the following hypothesis is given:

H1: The performance of students in finite mathematics differs with type of instruction.

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All of the instructors of finite mathematics participated in the study to explore the effectiveness of three methods of instruction to teaching finite mathematics – traditional lecture, calculator-enhanced, and online distance learning. Quantitative research was chosen as the methodology for this study (Hopkins, 2000).

Participants The participants in this study were 584 students enrolled in a freshman-year course in finite mathematics during the Fall Semester 2008, Spring Semester 2009, and Fall Semester 2009 at Alabama State University – a regional, comprehensive, historically black state-supported university. Three hundred sixty-one of these students formed the control group and were taught by the traditional lecture method, 202 students formed one of the experimental groups which used calculator enhanced instruction, and twenty students formed the other experimental group that utilized online distance learning. All classes were capped at twenty-five students, so the student-to-teacher ratio was comparable in all classrooms. Students registered randomly without prior knowledge of the method of instruction utilized by the instructor, with the exception of the online distance learning course. Students enrolled in the distance class had prior knowledge that all lectures, assignments, quizzes and tests would be administered via the computer. The honors

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Instruments The instruments used in this experimental study were a pretest and posttest that had identical questions (See Appendix). The tests measured the students’ level of comprehension of the seven Finite Mathematics course objectives. The testing instrument consisted of 28 questions – 4 on linear functions; 4 on solving systems of linear equations; 4 on the operations of matrices;

4 on sets; 4 on probability; 4 on counting principles; and 4 on statistics. The tests were developed by the mathematics department faculty using the test bank from MyMathLab software program, a personalized interactive multimedia resource.

Research Procedure The Finite Mathematics course consisted of a three-hour credit for one semester. The pretest was administered on the first day of class and all students were allowed to use calculators.

Students in the control group were instructed using the traditional method of lecture and classroom discussions in which students develop into a community of mathematicians as observed by St. Clair, Carter and St. Clair (2009). Students in the calculator-enhanced experimental group used the TI-83 graphing calculator as an integral part of instruction and testing. Ellington (2003) found that students’ operational and problem-solving skills improved when calculators were an integral part of testing and instruction. The online distance experimental group used the computer to receive course content, assignments, and evaluations.

This method allowed students to learn at their own pace and at any place where there is access to the computer. In addition, the two experimental groups incorporated the technology from the MyMathLab software program. The posttest was administered on the last day of class to the students that remained in the course. Only the students who took both the pretest and the posttest

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Analysis of Data The analysis on the lecture, calculator-enhanced, or online distance instruction in finite

mathematics was conducted using the Statistical Package for the Social Sciences (SPSS:

Shannon & Davenport, 2001). The results from the pretest and posttest were used in the analysis.

A 3 X 2 mixed between/within ANOVA was conducted to assess the between-subject and within-subject performance differences. The between-subject factor was the instructional method (traditional, calculator-enhanced, or online distance), while the within-subject factor was time – the time between pre instruction and post instruction.

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In this section, the results from the quantitative analyses will be described. First, the descriptive statistics will be given for each teaching approach. Following that will be a comparison of the means of the three groups. The last two analyses will include a discussion of the results of the tests of within subject effects and multiple comparisons.

Descriptive statistics include the means and standard deviations of the pretest and the posttest for each approach to teaching (see Table 1 on p.8). The descriptive statistical table shows that 583 students participated in the study. There were 361 students who were taught using the traditional method; 202 students who were taught using the calculator-enhanced method; and 20

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Figure 1 (p. 9) compares the means of the pretest and the posttest for the traditional, calculator-enhanced, and online distance groups. The graph shows the growth in achievement within each group. The calculator-enhanced group, with the lowest mean score of 9.04 on the pretest, has the highest mean score of 20.68 on the posttest. The traditional group, with a mean score of 10.01 on the pretest, has the lowest mean score of 15.40 on the posttest. The online distance class, with a mean score of 9.15 on the pretest, has a mean score of 17.40 on the

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A statistical analysis was run within subjects to investigate the significance of the achievement gain within subjects from the pretest to the posttest. Table 2 (below) shows the within-subject effect. At F (2, 580) = 139.04, p.001, η2=.32, a statistically significant withinin subject interaction occurred.

Table 2 Results of the Tests of Within-Subject Effects

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Follow-up univariate analyses from Table 3 (see p. 11) reported that at α =.05, p.01, participants in the traditional group (M=10.01, SD=3.240) achieved statistically significantly higher scores than participants in the calculator group (M= 9.04, SD=3.042) in the pretest.

Despite the statistical significance, no practical significance was indicated due to the small effect size (η2 =.021). At α =.05, p =.653, no statistically significant difference between the online

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statistically significant difference between the online distance group and the calculator-enhanced group was reported.

In the posttest, on the other hand, follow-up univariate analyses indicated that at α =.05, p.001, the traditional group (M= 15.02, SD=3.521) achieved statistically significantly lower scores than the calculator group (M= 20.38, SD=4.244). At α=.05, p.05, the online group (M = 17.40, SD = 4.695) achieved statistically significantly lower scores than the calculator group. At α=.05, p =.205 no statistical significant difference between the online distance group and the traditional group was reported when using multiple comparisons.

However, when a t-test was run between the traditional and online distance group, the traditional scores were statistically significantly lower than the online distance group (α=.05, p.05). At F (2, 580) = 116.81, p.001, η2=.287, a statistically significant between-subjects interaction occurred.

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The use of instructional technology within mathematics classrooms has increased significantly over the past two decades. With the improvement and expansion of graphing calculators and the increased demand for online distance education, educational institutions around the world have incorporated these instructional tools within their mathematics classrooms.

This research conducted a comparison of the effectiveness of three methods of instruction within finite mathematics at Alabama State University--the traditional lecture, calculator

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analyzed the results of identical pretests and posttests for 583 finite mathematics students during the fall 2008, spring 2009, and fall 2009 semesters.



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