The Development and Validation of Mathematical Thinking Beliefs (MTB) Instrument

Saoud Alhunaini; Kamisah Osman; Naser Abdurab

doi:10.29333/ejmste/11213

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Saoud Alhunaini ¹, Kamisah Osman ¹ ^* , Naser Abdurab ²

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¹ Faculty of Education, Universiti Kebangsaan Malaysia, MALAYSIA² Faculty of Education, International Islamic University Malaysia, MALAYSIA^* Corresponding Author

Abstract

Mathematical thinking beliefs are a significant element in supporting teachers’ practices of learning and teaching school mathematics. Most prior researches on mathematics beliefs have focused on teachers’ beliefs about learning and teaching mathematics in general. This research aimed to validate a Mathematical Thinking Belief instruments (MTB). The instrument was distributed to 523 mathematics teachers in Omani public schools. These teachers were asked to write their opinion in an instrument with a 5-point Likert scale. Exploratory factor analysis and confirmatory factor analysis have been applied to test the MTB using AMOS 25.0. All constructs show acceptable internal consistency reliability. The model meet a good model fit for the mathematical thinking beliefs measurement model through different fit index tests such as CMINDF, CFI, GFI, SRMR, RMSEA, and TLI. The results show that all indices of fit criteria were achieved. It is also indicated that acceptable validity, construct reliability and variance extracted values.

Keywords

mathematical thinking
teachers’ beliefs
problem solving

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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

EURASIA J Math Sci Tech Ed, 2021, Volume 17, Issue 11, Article No: em2024

https://doi.org/10.29333/ejmste/11213

Publication date: 08 Sep 2021

Article Views: 2290

Article Downloads: 2428

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Declaration of Conflict of Interest: No conflict of interest is declared by author(s).

Data sharing statement: Data supporting the findings and conclusions are available upon request from the corresponding author(s).

References

Abdullah, A., Fadil, S., Abdurahman, S., & Mohd, L. (2019). Emerging patterns and problems of higher-order thinking skills (HOTS) mathematical problem-solving in the form-three assessment (PT3). South African Journal of Education, 29(2), 1-18. https://doi.org/10.15700/saje.v39n2a1552
Acar-Erdol, T., & Yıldızl, H. (2018). Classroom assessment practices of teachers in Turkey. International Journal of Instruction 11(3), 587-602. https://doi.org/10.12973/iji.2018.11340a
Aljaberi, N., & Gheith, E. (2018). Ins-ervice mathematics teachers’ beliefs about teaching, learning and nature of mathematics and their mathematics teaching practices. Journal of Education and Learning, 7(5), 156. https://doi.org/10.5539/jel.v7n5p156
Alkharusi, H., Aldhafri, S., Al-Hosni, K., Al-Busaidi, S., Al-Kharusi, B., Ambusaidi, A., & Alrajhi, M. (2017). Development and validation of a scale for measuring mathematics teaching self-efficacy for teachers in the Sultanate of Oman. International Journal of Instruction 10(3), 143-158. https://doi.org/10.12973/iji.2017.10310a
Al-Mahrooqi, R., Denman, C., Al-Siyabi, J., & Al-Maamari, F. (2015). Characteristics of a good EFL Teacher: Omani EFL teacher and student perspectives. SAGE Open, 5(2), 1-15. https://doi.org/10.1177/2158244015584782
Anderson, J. (2009). Using NAPLAN items to develop students’ thinking skills and build confidence. Australian Mathematics Teacher 65(4), 17-23.
Anthony, G., Hunter, J., & Hunter, R. (2015). Supporting prospective teachers to notice students’ mathematical thinking through rehearsal activities. Mathematics Teacher Education and Development 17(2), 7-24.
Bal, A. P. (2015). Examination of the mathematical problem-solving beliefs and success levels of primary school teacher candidates through the variables of mathematical success and gender. Kuram ve Uygulamada Egitim Bilimleri 15(5), 1373-1390.
Bates, A. B., Latham, N., & Kim, J. (2011). Linking preservice teachers’ mathematics self-efficacy and mathematics teaching efficacy to their mathematical performance. School Science and Mathematics 111(7), 325-333. https://doi.org/10.1111/j.1949-8594.2011.00095.x
Brady, K. (2014). Towards a fresh understanding of the relationship between teacher beliefs about mathematics and their classroom practices. In M. Anderson, M. Cavanagh, & A. Prescott (Eds.), Proceedings of the 37th annual conference of the Mathematics Education Research Group of Australasia (pp. 103-110). MERGA.
Brown, T. A. (2014). Confirmatory factor analysis for applied research. Guilford Publications.
Burton, L. 1984. Mathematical thinking: The struggle for meaning. Journal for Research in Mathematics Education 15(1), 35-49. https://doi.org/10.5951/jresematheduc.15.1.0035
Byrne, B. M. (2016). Structural equation modeling with AMOS: Basic concepts, applications, and programming. Routledge. https://doi.org/10.4324/9781315757421
Celiki, H., & Ozdemir, F. (2020). Mathematical thinking as a predictor of critical thinking dispositions of pre-service mathematics teachers. International Journal of Progressive Education, 16(4), 81-98. https://doi.org/10.29329/ijpe.2020.268.6
Chigeza, P. (2013). Translating between and within representations: Mathematics as lived experiences and interactions. In V. Steinle, L. Ball, & Bardini (Eds.), Proceeding of the 36th Annual Conference of Mathematics Education Group of Australia (pp. 178-185). Mathematics Education Research Group of Australasia. MERGA.
Haciomeroglu, G. (2013). Mathematics anxiety and mathematical beliefs: What is the relationship in elementary pre-service teachers?. Undergraduate Mathematics Preparation of School Teachers 5, 1-9.
Hair, J. F., Black, W. C., Babin, B. J., & Anderson, R. E. (2014). Multivariate data analysis. Pearson Education Limited.
Hongboontri, C., & Keawkhong, N. (2014). School culture: Teachers’ beliefs, behaviors, and instructional practices. Australian Journal of Teacher Education, 39(5), 66-88. https://doi.org/10.14221/ajte.2014v39n5.7
Hudson, B., Henderson, S., & Hudson, A. (2015). Developing mathematical thinking in the primary classroom: Liberating students and teachers as learners of mathematics. Journal of Curriculum Studies, 47(3), 374-398. https://doi.org/10.1080/00220272.2014.979233
Karaman, P., & Sahin, C. (2017). Adaptation of teachers’ conceptions and practices of formative assessment scale into Turkish culture and a structural equation modeling. International Electronic Journal of Elementary Education, 10(2), 185-194. https://doi.org/10.26822/iejee.2017236114
Keith, T. Z., Fine, J. G., Taub, G. E., Reynolds, M. R., & Kranzler, J. H. (2006). Higher order, multisample, confirmatory factor analysis of the wechsler intelligence scale for children (4th ed.): What does it measure? School Psychology Review, 35(1), 108-127.
Kline, R. B. (2015). Principles and practice of structural equation modeling. The Guilford Press.
Kul, U., & Celik, S. (2017). Exploration of pre-service teachers’ beliefs in relation to mathematics teaching activities in classroom-base. International Journal of Research in Education and Science (IJRES) 3(1), 245-257.
Lesh, R., Cramer, K., Doerr, H., Post, T., & Zawojewski, J. (2003). Model development sequences. In R. Lesh & H. Doerr (Eds.), Beyond constructivism: A models and modelling perspective on mathematics problem solving; learning and teaching (pp. 35-58). Lawrence Erlbaum Associates, Inc. https://doi.org/10.4324/9781410607713
Lui, A. M., & Bonner, S. M. (2016). Preservice and inservice teachers’ knowledge, beliefs, and instructional planning in primary school mathematics. Teaching and Teacher Education, 56(2), 1-13. https://doi.org/10.1016/j.tate.2016.01.015
Maoto, S., Masha, K., & Mokwana, L. (2018). Teachers’ learning and assessing of mathematical processes with emphasis on representations, reasoning and proof. Pythagoras, 39(1), a373. https://doi.org/10.4102/pythagoras.v39i1.373
Mccluskey, C., Mulligan, J., & Mitchelmore, M. (2016). The role of reasoning in the Australian curriculum: Mathematics. In B. White, M. Chinnappan, & S. Trenholm (Eds.), Proceedings of the 39th annual conference of the Mathematics Education Research Group of Australasia (pp. 447-454). MERGA.
Memnun, S., & Katranc, Y. (2012). A research on the beliefs about mathematics learning and teacher efficacy of prospective teachers in Turkey. World Journal of Education, 2(6), 66-78. https://doi.org/10.5430/wje.v2n6p66
Mistima, S., Zakaria, E., & Nordin, N. (2011). A confirmatory factor analysis of mathematics beliefs scale in a malaysian context. Australian Journal of Basic and Applied Sciences, 5, 555-560.
Moss, C., & Archer, J. (2014). Accreditation not aggravation. ALM International Journal 9(92), 79-83.
Mumcui, H. Y., & Aktürk, T. (2017). An analysis of the reasoning skills of pre-service Teachers in the context of mathematical thinking. European Journal of Education Studies, 3(5), 225-254.
NCII. (2016). Principles for designing intervention in mathematics. Office of Special Education, U.S. Department of Education.
NCTM. (2000). Principles and standards for school mathematics. The National Council of Teachers of Mathematics, Inc.
OECD. (2000). The PISA 2000 assessment of reading, mathematical and scientific literacy.
Pajares, M. F. (1992). Teachers’ beliefs and educational research: Cleaning up a messy construct. Review of Educational Research, 62(3), 307-332. https://doi.org/10.3102/00346543062003307
Palraj, S., DeWitt, D., & Alias, N. (2017). Teachers beliefs in problem solving in Rural Malaysian secondary schools. Malaysian Online Journal of Educational Technology, 5(4), 45-57.
Peker, M., & Ulu, M. (2018). The effect of pre-service mathematics teachers’ beliefs about mathematics teaching-learning on their mathematics teaching anxiety. International Journal of Instruction, 11(3), 249-264. https://doi.org/10.12973/iji.2018.11318a
Philipp, R. (2007). Mathematics teachers’ beliefs and affect. In F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 257-315). Information Age Publishing Inc.
Philipp, R., Thanheiser, E., & Clement, L. (2002). The role of a children’s mathematical thinking experience in the preparation of prospective elementary school teachers. International Journal of Educational Research, 37(2), 195-210. https://doi.org/10.1016/S0883-0355(02)00060-5
Pourdavood, R., McCarthy, K., & McCafferty, T. (2020). The impact of mental computation on children’s mathematical communication, problem solving, reasoning, and algebraic thinking. Athens Journal of Education, 7(3), 241-254. https://doi.org/10.30958/aje.7-3-1
Privitera, G. J. (2014). Survey and correlational research designs. In Research methods for the behavioral sciences (pp. 227-240).
Purnomo, Y. W. (2017). A scale for measuring teachers’ mathematics-related beliefs: A validity and reliability study. International Journal of Instruction, 10(2), 2-38. https://doi.org/10.12973/iji.2017.1022a
Reyes-Cedeno, C. C., Rivas-Cun, H. I., Espinoza-Cevallos, C. E., & Rojas-Garcia, C. R. 2019. Assessment of the practices for early mathematics thinking in preschools of Pasaje city, Ecuador. European Journal of Educational Research, 8(4), 1063-1070. https://doi.org/10.12973/eu-jer.8.4.1063
Salazar, D. A. (2012). Enhanced-Group Moore Method: Effects on van Hiele Levels of Geometric Understanding, Proof-Construction Performance and Beliefs. US-China Education Review, 6, 594-605.
Saragih, S., & Napitupulu, E. (2015). Developing student-centered learning model to improve high order mathematical thinking ability. International Education Studies, 8(6), 104-112. https://doi.org/10.5539/ies.v8n6p104
Siemon, D., Day, L., Stephens, M., Horne, M., Callingham, R., Watson, J., Seah, R., & Siemon, D. (2017). Reframing mathematical futures: Using learning progressions to support mathematical thinking in the middle years. In A. Downton, S. Livy, & J. Hall (Eds.), Proceedings of the 40th Annual Conference of the Mathematics Education Research Group of Australasia (pp. 646). MERGA.
Tabachnick, B. G., & Fidell, L. S. (2007). Using multivariate statistics (5th ed.). Pearson Education, Inc.
Ünlü, M., & Ertekin, E. (2013). The relationship between mathematics teaching self-efficacy and mathematics self-efficacy. Procedia - Social and Behavioral Sciences 106, 3041-3045. https://doi.org/10.1016/j.sbspro.2013.12.350
Uyangör, S. M. (2019). Investigation of the mathematical thinking processes of students in mathematics education supported with graph theory. Universal Journal of Educational Research, 7(1), 1-9. https://doi.org/10.13189/ujer.2019.070101
Xenofontos, C., & Kyriakou, A. (2017). Prospective elementary teachers’ beliefs about collaborative problem solving and dialogue in mathematics. Mathematics Teacher Education and Development, 19(2), 142-158.
Yavuz Mumcu, H., & Cansız Aktaş, M. (2019). The effect of the use of mathematics course in terms of prospective teachers’ attitudes toward mathematics and their beliefs on the nature, teaching, and learning of mathematics. Pegem Eğitim ve Öğretim Dergisi, 9(3), 697-728. https://doi.org/10.14527/pegegog.2019.023
Yong, H., & Sam, L. (2008). Implementing school-based assessment: The mathematical thinking assessment (MATA). Buku Koleksi Bahan Seminar Inovasi Pedagogi IPBL Tahun 2008, (pp. 73-88), Batu Lintang, Kuching, Sarawak, 28 August.

How to cite this article

APA

Alhunaini, S., Osman, K., & Abdurab, N. (2021). The Development and Validation of Mathematical Thinking Beliefs (MTB) Instrument. Eurasia Journal of Mathematics, Science and Technology Education, 17(11), em2024. https://doi.org/10.29333/ejmste/11213

Vancouver

Alhunaini S, Osman K, Abdurab N. The Development and Validation of Mathematical Thinking Beliefs (MTB) Instrument. EURASIA J Math Sci Tech Ed. 2021;17(11):em2024. https://doi.org/10.29333/ejmste/11213

AMA

Alhunaini S, Osman K, Abdurab N. The Development and Validation of Mathematical Thinking Beliefs (MTB) Instrument. EURASIA J Math Sci Tech Ed. 2021;17(11), em2024. https://doi.org/10.29333/ejmste/11213

Chicago

Alhunaini, Saoud, Kamisah Osman, and Naser Abdurab. "The Development and Validation of Mathematical Thinking Beliefs (MTB) Instrument". Eurasia Journal of Mathematics, Science and Technology Education 2021 17 no. 11 (2021): em2024. https://doi.org/10.29333/ejmste/11213

Harvard

Alhunaini, S., Osman, K., and Abdurab, N. (2021). The Development and Validation of Mathematical Thinking Beliefs (MTB) Instrument. Eurasia Journal of Mathematics, Science and Technology Education, 17(11), em2024. https://doi.org/10.29333/ejmste/11213

MLA

Alhunaini, Saoud et al. "The Development and Validation of Mathematical Thinking Beliefs (MTB) Instrument". Eurasia Journal of Mathematics, Science and Technology Education, vol. 17, no. 11, 2021, em2024. https://doi.org/10.29333/ejmste/11213