An Exploration of Calculus Students’ Beliefs about Mathematics

Abraham Ayebo; Amaniel Mrutu

doi:10.29333/iejme/5728

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Abraham Ayebo ¹ ^* , Amaniel Mrutu ¹

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¹ University of Minnesota, USA^* Corresponding Author

Abstract

This study explored the mathematics beliefs of students enrolled in a first year calculus class at a Midwestern university in the United States. The Indiana Mathematics Belief Scale was administered to 162 students enrolled in a first year calculus class during the first week of school. An exploratory factor analysis (EFA) was performed to examine the factor structure of the survey instrument. Five factors were extracted: Effort, Usefulness, Difficult problems, Understanding, and Steps. Students’ responses were analyzed for inter-item correlation and internal consistency reliability (Cronbach’s α). The results were compared with similar studies conducted by Kloosterman and Stage (1992) as well as Berkaliev and Kloosterman (2009). The reliability obtained in this study was consistent with the previous studies. In particular, the Steps subscale was quite low (0.52). It might therefore make sense to drop the Steps subscale in future studies.

Keywords

mathematics
mathematics beliefs
problem solving
calculus students

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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Article Type: Research Article

INT ELECT J MATH ED, Volume 14, Issue 2, May 2019, 385-392

https://doi.org/10.29333/iejme/5728

Publication date: 05 Mar 2019

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References

Barrow, J. A., & Wood, K. E. (2006). Fenemma-Sherman Mathematics Attitude Scales: Instruements designmed to measure attitudes towards the learning of mathematics by females and males. Journal for research in Mathematics Education, 7(5), 324-326.
Berkaliev, Z., & Kloosterman, P. (2009). Undergraduate engineering majors’ beliefs about mathematics. School Science and Mathematics, 109(3), 175-182. https://doi.org/10.1111/j.1949-8594.2009.tb17953.x
Cross, D. I. (2009). Alignment, cohesion, and change: Examining mathematics teachers’ belief structures and their influence on instructional practices. Journal of Mathematics Teacher Education, 12(5), 325-346. https://doi.org/10.1007/s10857-009-9120-5
Di Martino, P., & Zan, R. (2010). ‘Me and maths’: towards a definition of attitude grounded on students’ narratives. Journal of Mathematics Teacher Education, 13(1), 27-48. https://doi.org/10.1007/s10857-009-9134-z
Dweck, C. S. (2013). Self-theories: Their role in motivation, personality, and development. Psychology press. https://doi.org/10.4324/9781315783048
Furinghetti, F., & Pehkonen, E. (2002). Rethinking characterizations of beliefs. In Beliefs: A hidden variable in mathematics education? (pp. 39-57). Springer, Dordrecht.
Hochanadel, A., & Finamore, D. (2015). Fixed and growth mindset in education and how grit helps students persist in the face of adversity. Journal of International Education Research, 11(1), 47-50. https://doi.org/10.19030/jier.v11i1.9099
House, J. D. (1995). The predictive relationship between academic self-concept, achievement expectancies, and grade performance in college calculus. The Journal of Social Psychology, 135(1), 111-112. https://doi.org/10.1080/00224545.1995.9711411
Kaiser, H. F. (1974). An index of factorial simplicity. Psychometrika, 39(1), 31-36. https://doi.org/10.1007/BF02291575
Kargar, M., Tarmizi, R. A., & Bayat, S. (2010). Relationship between mathematical thinking, mathematics anxiety and mathematics attitudes among university students. Procedia-Social and Behavioral Sciences, 8, 537-542. https://doi.org/10.1016/j.sbspro.2010.12.074
Kloosterman, P., & Stage, F. K. (1992). Measuring beliefs about mathematical problem solving. School science and mathematics, 92(3), 109-115. https://doi.org/10.1111/j.1949-8594.1992.tb12154.x
Ma, X. (1999). A meta-analysis of the relationship between anxiety toward mathematics and achievement in mathematics. Journal for Research in Mathematics Education, 30(5), 520-540. https://doi.org/10.2307/749772
Ma, X., & Kishor, N. (1997). Assessing the Relationship between Attitude toward Mathematics and Achievement in Mathematics: A Meta-Analysis. Journal for Research in Mathematics Education, 28(1), 26-47. https://doi.org/10.2307/749662
Maloney, E. A., Schaeffer, M. W., & Beilock, S. L. (2013). Mathematics anxiety and stereotype threat: shared mechanisms, negative consequences and promising interventions. Research in Mathematics Education, 15(2), 115-128. https://doi.org/10.1080/14794802.2013.797744
McLeod, D. B., & McLeod, S. H. (2002). Synthesis—beliefs and mathematics education: Implications for learning, teaching, and research. In Beliefs: A Hidden Variable in Mathematics Education? (pp. 115-123). Springer, Dordrecht.
McLeod, D. B. (1992). Research on affect in mathematics education: A reconceptualization. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 575- 596). New York: Macmillan.
Meece, J. L., Wigfield, A., & Eccles, J. S. (1990). Predictors of math anxiety and its influence on young adolescents’ course enrollment intentions and performance in mathematics. Journal of Educational Psychology, 82, 60 – 70. https://doi.org/10.1037/0022-0663.82.1.60
Pajares, F., & Graham, L. (1999). Self-efficacy, motivation constructs, and mathematics performance of entering middle school students. Contemporary educational psychology, 24(2), 124-139. https://doi.org/10.1006/ceps.1998.0991
Pehkonen, E., & Hannula, M. S. (2004). Mathematical belief research in Finland. Nordic Studies in Mathematics Education, 9(2), 23-38.
Pett, Marjorie A., Nancy R. Lackey, and John J. Sullivan. Making sense of factor analysis: The use of factor analysis for instrument development in health care research. Sage, 2003.
Pintrich, P. R. (2002). Future challenges and directions for theory and research on personal epistemology. Personal epistemology: The psychology of beliefs about knowledge and knowing, 389-414.
Sandman, R. S. (1979, April). Factors related to mathematics anxiety in the secondary school.
Paper presented at the annual meeting of the American Educational Research Association, San Francisco. Schram, C. M. (1996).
Schoenfeld, A. H. (1988). When good teaching leads to bad results: The disasters of’well-taught’mathematics courses. Educational psychologist, 23(2), 145-166. https://doi.org/10.1207/s15326985ep2302_5
Wheat, J., Tunnell, J., & Munday, R. (1991). Predicting success in college algebra: Student attitude and prior achievement. College Student Journal, 25, 240-244.
Vanayan, M., White, N., Yuen, P., & Teper, M. (1997). Beliefs and attitudes toward mathematics among third‐and fifth‐grade students: a descriptive study. School Science and Mathematics, 97(7), 345-351. https://doi.org/10.1111/j.1949-8594.1997.tb17375.x

How to cite this article

APA

Ayebo, A., & Mrutu, A. (2019). An Exploration of Calculus Students’ Beliefs about Mathematics. International Electronic Journal of Mathematics Education, 14(2), 385-392. https://doi.org/10.29333/iejme/5728

Vancouver

Ayebo A, Mrutu A. An Exploration of Calculus Students’ Beliefs about Mathematics. INT ELECT J MATH ED. 2019;14(2):385-92. https://doi.org/10.29333/iejme/5728

AMA

Ayebo A, Mrutu A. An Exploration of Calculus Students’ Beliefs about Mathematics. INT ELECT J MATH ED. 2019;14(2), 385-392. https://doi.org/10.29333/iejme/5728

Chicago

Ayebo, Abraham, and Amaniel Mrutu. "An Exploration of Calculus Students’ Beliefs about Mathematics". International Electronic Journal of Mathematics Education 2019 14 no. 2 (2019): 385-392. https://doi.org/10.29333/iejme/5728

Harvard

Ayebo, A., and Mrutu, A. (2019). An Exploration of Calculus Students’ Beliefs about Mathematics. International Electronic Journal of Mathematics Education, 14(2), pp. 385-392. https://doi.org/10.29333/iejme/5728

MLA

Ayebo, Abraham et al. "An Exploration of Calculus Students’ Beliefs about Mathematics". International Electronic Journal of Mathematics Education, vol. 14, no. 2, 2019, pp. 385-392. https://doi.org/10.29333/iejme/5728