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Student attitudes toward integrated mathematics.

Abstract

In these days of national and state standards, accountability and high-stakes testing, one middle school in South Texas attempted an alternative mathematics program aimed at improving students' attitudes towards mathematics with much success.

Introduction

One main message emerged from the results of the Third International Mathematics and Science Study (U.S. Department of Education, 1998). U.S. students do not start out behind; they fall behind. The United States is the only TIMSS nation that went from above average in mathematics in fourth grade to below average in eighth grade (U.S. Department of Education, 1998). It would appear that U.S. students either lose interest, lack motivation, or may be negatively influenced in the mathematics classes they are attending during their middle school and high school grades. Students move from the elementary grades to middle school and eventually into high school without the knowledge, direction, and self-confidence they need (Mizell, 1999). The creation of middle schools was motivated by research showing that young adolescents have distinct developmental needs. They are no longer dependent on the structures that characterize elementary education but they are also not yet ready for the independence of high school. Middle school students demand something different--something that recognizes and builds on their distinctive strengths (The Edna McConnell Clark Foundation, 1997). Advocates for middle schools have insisted on school structures that foster a sense of belonging, confidence, and self esteem in young adolescents, and that support multifaceted learning, meaningful participation in school life, and positive social interaction with adults and peers (Wheelock, 1995). Through these difficult and awkward years, the middle school student needs the understanding and support of schools in order to achieve maximum potential. The National Middle School Association (1999) recognized five key components of exemplary middle schools. The components included (1) interdisciplinary teaming; (2) advisory programs; (3) varied instruction; (4) exploratory programs; and (5) transition programs.

There clearly needs to be a dramatic, rapid, and fundamental improvement in mathematics and science education, particularly in our middle schools and high schools (U.S. Department of Education, 1998). During this period, middle school students form conceptions about themselves as mathematical learners including interest, competence, attitude, and motivation. These conceptions influence how they approach mathematics in high school, which may ultimately influence their life opportunities. In these days of national and state standards, accountability and high-stakes testing, and the charge of leaving no child behind, one middle school in South Texas attempted an alternative practice with much success. "Intelligent Integration" was a program in the urban school's sixth grade utilizing mathematics and science integration along with other pedagogical practices. The program was implemented in six of twelve mathematics classes. The "Intelligent Integration" classes utilized the following educational practices:

* Mathematics and science skills integration,

* Implementation of Howard Gardner's (1991) Eight Multiple Intelligences into activities and/or assessments,

* Cooperative/Collaborative learning, and

* Incorporation of technology (computers and calculators).

Purpose

The purpose of this study was to examine whether or not an interdisciplinary mathematics/science curriculum and pedagogy was superior to a traditional block-scheduling mathematics curriculum as measured by student attitudes. A causal-comparative ex post facto research design was used. Measurement of student attitudes was based on the results of the Integrated Mathematics Attitudinal Survey (IMAS), created by the researcher for this study. The IMAS included two scales: (a) anxiety toward mathematics, and (b) value of mathematics in society. In order to determine the internal consistency of the IMAS, an alpha coefficient was calculated. The research questions included:

1. Does integrating the mathematics curriculum with the science curriculum improve sixth grade students' overall attitudes toward mathematics, based on the mean scores of the IMAS?

2. Does integrating the mathematics curriculum with the science curriculum improve sixth grade students' mean scores of anxiety towards mathematics as measured by the IMAS?

3. Does integrating the mathematics curriculum with the science curriculum improve sixth grade students' mean scores of the value of mathematics in society as measured by the IMAS?

Sample Population

The target population included Grade 6 students in South Texas. The accessible population included Grade 6 mathematics students in a large urban school district in South Texas. The sample included Grade 6 mathematics students attending one middle school involved in a pilot program utilizing integrated mathematics/science curriculum and pedagogy in the urban school district. The middle school had a total sixth grade population of 349 students; however only 207 participated in the IMAS. Students were required to return a parent consent form allowing each student to participate. Without parental consent, students were not able to participate in the survey. Forty-eight and three-tenths percent of the students were male, 51.7% were female, 46.4% were Hispanic, 45.4% were white, and 8.2% of the students were of other ethnic backgrounds. All sixth grade students were first placed into Mathematics 6 or Algebra-Prep categories based on their scores on the state-mandated 2001 Mathematics portion of TAAS (Texas Assessment of Academic Skills). Students were randomly assigned by computer into either the traditional sixth grade Mathematics 6 and Algebra-Prep classrooms or the integrated mathematics/science Mathematics 6 and Algebra-Prep classrooms. There were a total of twelve mathematics classes involved in the study. The twelve classes were as follows: three traditional Mathematics 6 classes, three traditional Algebra-Prep classes, three integrated Mathematics 6/Science classes, and three integrated Algebra-Prep/Science classes.

Those students selected through computer assignment for the traditional sixth grade classes were placed into a 90-minute class of Grade 6 or Algebra-Prep mathematics. A separate, certified teacher who would follow the appropriate Grade 6 science curriculum instructed the science classes for these students. Those students selected through computer assignment for the integrated mathematics/science classrooms were placed into a 135-minute class incorporating the Grade 6 or Algebra-Prep mathematics curriculum and the Grade 6 science curriculum. The instruction would follow the approved mathematics and science curriculum. The same certified teacher taught both subjects for these students. Five teachers, A, 13, C, D, and E taught the twelve mathematics classes involved in the study. Teachers A and B taught the six traditional 90-minute block isolated mathematics classes. Teachers C, D, and E taught the six 135-minute integrated Mathematics/Science classes.

The mathematics/science curriculum and instruction integration was a combination of theme-based integration and skill-based integration. The theme-based integration for the mathematics/science classes was based on six global themes. The students placed in the integrated mathematics/science classes were also placed into integrated language arts and social studies classes. At the beginning of the year, the mathematics/science teachers and the language arts/social studies teachers determined six global themes based on a study of six countries around the world, one for each of the six-week grading periods. At that point, the science curriculum timeline was determined for each six weeks based on physical features of the chosen country or perhaps certain events in history that took place in that particular country. The skill-based integration incorporated the mathematics curriculum with the scientific method of investigation, the scientific process skills, and the science curriculum whenever possible. Incorporating the mathematics and the science curriculum enhanced the opportunity for the students to experience real-world applications and hands-on activities. The goal of the integrated mathematics/science program was for both subjects to be addressed during the 135-minute class period and rarely addressed separately.

Attitudinal Instrument

The IMAS was an instrument created by the researcher for the basis of this study only. The purpose of the attitudinal survey was to collect data concerning the attitudes of students towards mathematics in both the traditional and integrated mathematics groups. The attitudinal survey used for this study was an instrument that was developed by utilizing components of other attitudinal surveys: the Learning Environment Inventory (Anderson and Walberg, 1976), the Classroom Environment Scales (Moos and Trickett, 1974), the Inventory of Affective Aspects of Schooling (Haladyna, Shaughnessy, and Shaughnessy, 1983), the Mathematics Attitude Inventory (Sandman, 1974), The Math Anxiety Questionnaire (Hsiu-Zu Ho et al., 2000), and a questionnaire created by Schoenfeld (1989). The IMAS was composed of two scales: (a) anxiety toward mathematics, and (b) value of mathematics in society. Exploring the surveys mentioned above aided in the development of the two scales. The IMAS used a four-point Likert type of scale-response format with four possible responses: strongly agree, agree, disagree, and strongly disagree as the possible choices. The survey also asked the students to indicate their gender and ethnicity. In order to determine the internal consistency of the IMAS, an alpha coefficient was calculated. This coefficient is a general form in calculating the reliability of items that are not scored right versus wrong (Fraenkel and Wallen, 2000). The greater the consistency in responses among items, the closer the coefficient alpha will be to 1 (Green, Salkind, and Akey, 2000). The alpha coefficient was .5618.

Analysis of the Data

The IMAS was given to students by the researcher during the week of May 13-17, 2002. An independent samples t-test was used to analyze the data collected based on the IMAS. The independent variables were the curriculum and pedagogy presented in the traditional block-scheduling mathematics curriculum classrooms and the integrated mathematics/science classrooms. The dependent variable was students' attitude towards mathematics. The null hypothesis was accepted or rejected at the .05 level of confidence.

Research Question 1 Does integrating the mathematics curriculum with the science curriculum improve sixth grade students' overall attitudes toward mathematics, based on the IMAS? An independent samples t-test was conducted to determine whether a significant difference did exist and the results are as follows. The null hypothesis was rejected. Levene's Test for Equality of Variance indicated that the groups were not equal; the F value (1, 205) equaled 10.334, therefore the p value was .002. The t value (205) of 2.459 was used indicating a p value of .015; eta squared was - .1787. A significant difference did exist between the two groups. A score of 120 was possible on the total attitudinal score of the IMAS. The integrated mathematics/science classroom students had an attitudinal mean score of 93.40, while the traditional mathematics classroom students had an attitudinal mean score of 89.41, a mean difference of 3.99. Therefore, integrating mathematics curriculum with science curriculum did improve sixth grade students' overall attitudes towards mathematics.

Research Question 2 Does integrating the mathematics curriculum with the science curriculum improve sixth grade students' mean scores of anxiety towards mathematics as measured by the IMAS? An independent samples t-test was conducted to determine whether a significant difference did exist and the results are as follows. Although a difference did exist between the two groups, the null hypothesis was accepted at the .05 level of confidence. Levene's test for Equality of Variance between the two groups was not assumed; the F value (1, 205) equaled 6.625, therefore, the p value was .011. The t value (205) of 1.917 was used indicating a p value of .057; eta squared was -.1304. The mean anxiety score of the students in the integrated mathematics/science classroom was 53.98, while the mean anxiety score of the students in the traditional classroom was 51.77. The mean difference between the two groups was 2.21. Although the integrated mathematics/science classroom students had a better sample mean anxiety score, the results of the independent samples t-test indicated that a significant difference did not exist.

Research Question 3 Does integrating the mathematics curriculum with the science curriculum improve sixth grade students' mean scores of the value of mathematics in society as measured by IMAS? An independent samples t-test was conducted to determine whether a significant difference did exist and the results are as follows. The null hypothesis was rejected. Levene's test for Equality of Variance between the two groups was not assumed, the F value (1, 205) equaled 7.824; therefore, the p value was .006. The t value (205) of 2.881 was used indicating a p value of .005; eta squared was -.2114. The mean value score of the students in the integrated mathematics/science classroom was 39.41, while the mean value score of the students in the traditional classroom was 37.64. The mean difference between the two groups was 1.77. The results of the independent samples t-test indicated that a significant difference did exist. Therefore, integrating mathematics curriculum with science curriculum does improve sixth grade students' value of mathematics in society.

Conclusion

A total score of 44 was possible on the value of mathematics in society scale of the IMAS. Survey statements that addressed the value of mathematics in society included the following: a) Math is important; b) Math will help me be successful in the future; c) Math will be important ifl choose to go to college; d) I will need math in the career or job I choose; and e) I will use my math skills in real life situations. The mean value score for the integrated mathematics/science classroom students was 39.42, while the mean value score for the traditional mathematics classroom students was 37.73. Female students enrolled in the integrated mathematics/science classroom students demonstrated the highest value for mathematics in society among gender groups (mean of 39.77); while females in the traditional mathematics classroom demonstrated the least amount of value for mathematics (mean of 37.06). The white students enrolled in the integrated mathematics/science classroom students demonstrated the highest value for mathematics in society among ethnicity groups (mean of 39.70); while the Hispanic population enrolled in the traditional mathematics classroom demonstrated the lowest value for mathematics in society (mean of 36.68).

A total score of 76 was possible on the anxiety scale of the IMAS. Survey statements that addressed the anxieties of mathematics included the following: a) When I am in math class, I usually feel relaxed and at ease; b) Taking math tests scare me; c) I dreaded going to math class this year; and d) I had to do a lot of memorizing in math class. The mean anxiety score for the integrated mathematics/science classroom students was 53.96, while the mean anxiety score for the traditional mathematics classroom students was 51.80. Male students enrolled in the integrated mathematics/science classroom students felt the least anxious about mathematics among gender groups (mean of 54.78). Females enrolled in the traditional mathematics classroom felt the highest degree of anxiety (mean of 51.60.) The Hispanic students enrolled in the integrated mathematics/science classroom students felt the least amount of anxiety when compared to other ethnic groups' attitudes towards mathematics (mean of 53.93); while the Hispanic students enrolled in the traditional mathematics classroom felt the highest degree of anxiety (mean of 51.16).

In summary, this research has provided vital quantifiable analyses that indicate integrating mathematics and science curriculum does improve student attitudes towards mathematics. The data clearly indicated that integrating the mathematics curriculum with the science curriculum did significantly improve sixth grade students' overall attitude concerning mathematics, and students' value of mathematics in society. Integrating mathematics with the science curriculum gave students the opportunity to use mathematics skills outside of isolated mathematics lessons; thus improving their awareness of the value of mathematics in society. Based on this research, it is recommended that mathematics and science curriculums utilize theme-based integration and skill-based integration as often as possible in Grade 6. It is further recommended that the Grade 6 integrated mathematics/science classes be scheduled during a subsequent time period utilizing one teacher for both subjects allowing for easier implementation of the integration of the mathematics and science standards-based curriculum.

References

Anderson, G. and Walberg, H. (1968). Learning environment inventory. (Report No. SE020514). East Lansing, MI: National Center for Research on Teacher Learning. (ERIC Document Reproduction Service No. ED 131997).

Edna McConnell Clark Foundation. (1997). Working together: Harnessing community resources to improve middle schools. New York, N-Y: Mackinnon, Anne.

Fraenkel, Jack R. & Wallen, Norman E. (2000). How to design and evaluate research in education (4th ed.). Boston, MA: McGraw-Hill Companies, Inc. Gardner, Howard. (1901). Frames of Mind: The Theory of Multiple Intelligences. New York, New York: Basic Books.

Green, S.B.; Salkind, N.J.; & Akey, T.M. (2000). Using SPSS for windows: Analyzing and understanding data. (2nd edition). Saddle River, New Jersey: Prentice Hall.

Haladyna, T., Shaughnessy, J. & Shaughnessy, J.M. (1983). A causal analysis of attitude toward mathematics. Journal for Research in Mathematics Education, 14(1), 19-29.

Hsiu-Zo, Senturk, D. Lam., A., Zimmer, J.M., Hong, S. Okamoto, Y., Chiu, S., Nakazawa, Y., & Wang, C. (2000). The affective and cognitive dimensions of math anxiety: a cross-national study. Journal for Research in Mathematics Education, 31(3), 362-379.

Mizell, H. (1999). More quotes about the whys of urban middle school reform. (Online).Available: http://www.middleweb.com/Thewhysof.html

Moos, Rudolph H., Trickett, Edison J.; (1973). Social environment of junior high and high school classrooms. Journal of Educational Psychology, 65(1), 93-102.

National Council of Teachers of Mathematics. (1999). Curriculum and evaluations standards for school mathematics. In Principles & standards for school mathematics. Retrieved January 2000, from http://standardse.nctm.org/doeument/index.htm

National Middle School Association. (1999). Components of an exemplary middle school. Westerfield, Ohio.

Sandman, R.S. (1974). Mathematics attitude and MAI mser's manual. University of Minnesota, Minneapolis, Minnesota: Minnesota Research and Evaluation Center.

Schoenfeld, Alan. (1989). Explorations of students' mathematical beliefs and behavior. Journal for Research in Mathematics Education, 20(4), 338-355.

United States Department of Education. (1998). Perspectives on education policy research: What the third international mathematics and science study (TIMMS) means for systemic school improvement. Washington, DC: Office of Educational Research and Improvement.

Wheelock, A. (1995). Standards-based reform: What does it mean for the middle grades? In Middleweb: Exploring middle school reform. Retrieved January 22, 2000, from http;//www.middleweb.com/Whlckstand.html

Denise Hill, Texas A&M University-Corpus Christi

Hill, Ed. D. is an Assistant Professor of Teacher Education after spending 19 years teaching middle school mathematics and science in the Texas public schools.
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Author:Hill, Denise
Publication:Academic Exchange Quarterly
Geographic Code:1USA
Date:Jun 22, 2004
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