Prospective Mathematics Teachers’ Mathematical Problem Solving Beliefs
Author(s):
Merve Kaplan (presenting / submitting) Seher Avcu Safure Bulut
Conference:
ECER 2012
Format:
Paper

Session Information

ERG SES C 06, Mathematics Education

Parallel Paper Session

Time:
2012-09-17
13:30-15:00
Room:
FCEE - Aula 2.6
Chair:

Contribution

Turkish elementary mathematics curriculum was changed based on the new studies and new approaches in 2004. In the new elementary mathematics program, problem solving is considered as an integral part of the mathematics education and it is regarded as a basic skill that should be improved in every subject (MNE, 2003).  The reason of intense emphasis given to problem solving instruction is due to the characteristics and necessity of problem solving not only for success in daily life, but also for the future of societies and improvement in the work force. Due to the unpredictable contingencies and dangerous uncertainties, as human society developed and advanced, the new problems revealed and caused the need for new ways of solving problems (Brown, 2003).
Research showed that teachers' beliefs and preferences about how to teach mathematics play a significant role in how teachers teach in the classroom environments (Ball, 1998; Grouws, 1996; Thompson, 1984; Wilkins & Brand, 2004). Moreover, teachers' actions in the classroom and the observable effects of those actions can be better understood if their thought processes are better understood (Thompson, 1984). The key component of the problem solving process is teachers since problem solving instruction can be most effective when students feel that teachers accept problem solving as an important part of the activity and teachers use problem solving in their mathematics instruction regularly (Lester, 1980).
Many researchers believe that in order to teach mathematics well, one needs to have a positive attitude toward the subject, and that the task of improving the attitudes toward mathematics of future elementary teachers begins at the university. Sherman and Christian (1999) said that improving the attitudes toward mathematics of pre-service elementary teachers is “an important concern for university education courses in order to facilitate positive mathematics attitudes in future elementary pupils” (p. 96). Hungerford (1994) cited the need to improve the mathematics education of future elementary teachers by altering curriculum and attitudes.
In this sense, prospective teachers’ understanding of problem solving abilities and their attitudes towards mathematics may be investigated. For this reason, this study will investigate prospective elementary mathematics teachers’ problem solving beliefs and attitudes towards. Thus, it is believed that the current study will contribute to future developments of mathematical problem solving in teacher education. Moreover, it is expected that learning prospective mathematics teachers’ beliefs about problem solving and attitudes towards mathematics will help educators develop future training programs for prospective and in-service mathematics teachers. The following research questions will guide the present study.
1.    Is there a significant difference in prospective elementary mathematics teachers’ problem solving beliefs with respect to gender?
2.    Is there a significant difference in prospective elementary mathematics teachers’ problem solving beliefs with respect to grade levels?
3.    Is there a significant relationship between prospective elementary mathematics teachers’ problem solving beliefs and mathematics attitudes?

Method

In the present study, the participants are the prospective mathematics teachers from the two – public and private – universities in Turkey. Participants are first, second, third and fourth graders. Data was collected from 100 prospective teachers and it is expected to collect additional data and reach approximately 140 prospective teachers in total. Data obtained from the responds of the prospective mathematics teachers to the two scales will be analyzed by two-way analysis of variance (ANOVA). The dependent variables of this study are problem solving beliefs and attitude towards mathematics. The independent variables are gender and grade level. In the data collection process, two attitude scales were conducted. Mathematics Attitude Scale has been developed by Duatepe and Çilesiz (1999). The scale constitutes 4 dimensions. The lowest correlation value in the first dimension was .55, for the second dimension 0.62, for the third dimension 0.48 and for the fourth dimension 0.51. Furthermore, Cronbach Alpha coefficient regarding the scale developed was found as 0.96. Mathematical Problem Solving Beliefs Scale has been developed by Çakıroğlu and Kayan (2008). The scale has 39 items in total. Alpha reliability of the scale was calculated as 0.87 indicating high consistency between instrument items.

Expected Outcomes

Results of the analysis in the present study are expected to show similarity with the literature. A statistically significant difference between males and females in terms of their mathematical problem solving beliefs is not expected. Considering the relationship between gender and problem solving beliefs, some of the related studies (Winocur, Schoen, & Sirowatka, 1989; Fennema, 1990) found no evidence of difference between males and females. The difference in prospective teachers’ problem solving beliefs in terms of grade levels and the relationship between mathematical attitudes and problem solving beliefs will be reported according to the analyses of the data. The results of the study intend to add outcomesto the related literature on problem solving beliefs of prospective mathematics teachers. Considering the results of the study, recommendations for teachers, prospective teachers and future researches will be given.

References

Ball, D. (1998). Research on Teacher Learning: Studying How Teachers’ Knowledge Changes. Action in Teacher Education, 10(2), 7-24. Brown, N.M. (2003). A Study of Elementary Teachers’ Abilities, Attitudes, and Beliefs about Problem Solving. Dissertation Abstracts International, 64(10), 3620. (UMI No. 3108818). Duatepe, A., &Çilesiz, S. (1999). Matematik tutumölçeğigeliştirilmesi.Hacettepe University Journal of Education, 16, 45 - 52 Grouws, D. A. (1996). Critical Issues in Problem Solving Instruction in Mathematics. In D. Zhang, T. Sawada, & J. P. Becker (Eds.), Proceedings of the China-Japan-U.S. seminar on mathematical education, 70-93, Carbondale, IL: Board of Trustees of Southern Illinois University. Hungerford, T.W. (1994). Future elementary teachers: The neglected constituency. American Mathematical Monthly, 101 (1), 15-21. Kayan, F., & Çakıroğlu, E. (2008). İlköğretim matematik öğretmen adaylarının matematiksel problem çözmeye yönelik inançları. Hacettepe University Journal of Education, 35, 218-226 Lester, F. K. (1980). Problem Solving: Is it a Problem?. In M. M. Lindsquist (Ed.), Selected Issues in Mathematics, 29-45, NCTM, Reston VA. Ministry of National Education. MNE. (2003). Üçüncü uluslararasi matematik ve fen bilgisi çalışması raporu, Milli Eğitim Bakanlığı Eğitim Araştırma ve Geliştirme Dairesi Başkanlığı., Ankara. Sherman, H.J., & Christian, M. (1999). Mathematics attitudes and global self-concept: An investigation of the relationship. College Student Journal, 33, 95-101. Thompson, A.G. (1984). The Relationship of Teachers’ Conceptions of Mathematics and Mathematics Teaching to Instructional Practice. Educational Studies in Mathematics, 15(2), 105-127. Wilkins, J., & Brand, B. (2004). Change in Pre-service Teachers’ Beliefs: An evaluation of a mathematics methods course. School Science & Mathematics, 104(5), 226-232.

Author Information

Merve Kaplan (presenting / submitting)
Baskent University, Turkey
Aksaray University, Turkey
Middle East Technical University, Turkey

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