Early-years future teachers’ mathematical beliefs as determinants of performance in primary mathematics

Adeneye Olarewaju Awofala(1*), Oludola Sarah Sopekan(2)

(1) Department of Science and Technology Education, University of Lagos,
(2) Department of Arts and Social Sciences Education, University of Lagos,
(*) Corresponding Author

Abstract

One construct that lies in between the cognitive and affective domains of mathematics education is belief and this concept is rarely investigated in the Nigerian mathematics education community. Thus, an investigation of early-years future teachers’ mathematical beliefs as determinants of performance in primary mathematics within the blueprint of the quantitative method of the descriptive survey research design was conducted. Three research questions were addressed and secondary data relating to performance in mathematics of 320 early-years future teachers were retrieved from their records at the Department of Arts and Social Sciences Education, University of Lagos, Nigeria. One other instrument labeled Mathematical Beliefs Scale was employed for the collection of key data connected to the mathematical beliefs. The collected data were condensed and explored with the principal components factor analysis, multiple regression analysis, and independent samples t-test. Results showed that mathematical beliefs measured using the Mathematical Beliefs Scale are a multidimensional construct with four-factor structure: emotional and developmental commitment in learning of mathematics; self-assurance and philosophies concerning one's subjective mathematical aptitude; beliefs about mathematics; and mathematical problem-solving beliefs. These factors show adequate and excellent reliabilities as computed using Cronbach alpha. Also, gender was not a factor in early-years future teachers' mathematical beliefs even at the subscale level and the four factors of the mathematical belief scale predicted early-years future teachers' performance in primary mathematics. In line with these results, it is recommended that early-years future teachers be taught in a constructivist manner so that they can imbibe constructivist beliefs capable of engendering better learning of mathematics.

Keywords

Early-years future teachers, mathematical beliefs, performance, primary mathematics

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References

Aksu, H. H. (2008). Öğretmen adaylarının matematik öğretimine yönelik öz-yeterlilik inançları. Abant İzzet Baysal Üniversitesi Eğitim Fakültesi Dergisi, 8(2), 161–170.

Ambrose, R. (2004). Initiating change in prospective elementary school teachers’ orientations to mathematics teaching by building on beliefs. Journal of Mathematics Teacher Education, 7(2), 91–119. https://doi.org/10.1023/B:JMTE.000002 1879.74957.63

Anderson, J. (1997). Teachers’ reported use of problem-solving teaching strategies in primary mathematics classrooms. In F. Biddulph & K. Carr (Eds.), People in mathematics education. Proceedings of the 20th Annual Conference of the Mathematics Education Research Group of Australasia (pp. 50–57). Rotorua, NZ: MERGA.

Awofala, A. O. A. & Anyikwa, B. E. (2014). Assessing Adult Learner’s Numeracy as Related to Gender and Performance in Arithmetic. Journal of New Approaches in Educational Research (NAER Journal), 3(2), 83–92. https://doi.org/10.7821/naer.3.2.83-92

Awofala, A. O. A. (2017). Assessing senior secondary school students’ mathematical proficiency as related to gender and performance in mathematics in Nigeria. International Journal of Research in Education and Science, 3(2), 488–502. https://doi.org/10.21890/ijres.327908

Awofala, A. O. A., & Awolola, S. A. (2011). Coping with new mathematics teacher’s beliefs in a conflicting milieu of curriculum transform. In I. O. S. Abonyi (Ed.) Proceedings of 52nd Annual Conference of the Science Teachers Association of Nigeria on Reforms in Science, Technology, Engineering and Mathematics (pp. 309–315). HEBN Publishers Plc.

Beaton, A. E., Mullis, I. V. S., Martin, M. O., Gonzalez, E. J., Kelly, D. L., Smith, T. A. (1996). Mathematics achievement in the middle school years. Boston: Center for the Study of Testing, Evaluation, and Educational Policy, Boston College.

Benbow, R. M. (1993). Tracing Mathematical Beliefs of Preservice Teachers through Integrated Content-Methods Courses. Proceedings of the Annual Conference of the American Educational Research Association. ERIC Document Reproduction Service No. ED 388638.

Block, J. H., & Hazelip, K. (1995). Teachers’ beliefs and belief systems. In L. W. Anderson (Ed.), International encyclopedia of teaching and teacher education (2nd ed., pp.25-28). New York: Pergamon Press.

Boz, N. (2008). Turkish Pre-Service Mathematics Teachers’ Beliefs About Mathematics Teaching. Australian Journal of Teacher Education, 33(5), 66–80. https://doi.org/10.14221/ajte.2008v33n5.5

Burkhardt, H., Fraser, R., & Ridgway, J. (1990). The dynamics of curriculum change. In I. Wirszup & R. Streit (Eds.), Development in school mathematics education around the world (pp. 3–29). Reston, VA: NCTM.

Buzeika, A. (1996). Teachers’ beliefs and practice: The chicken or the egg? In P. C. Clarkson (Ed.), Technology in mathematics Education. Proceedings of the 19th Annual Conference of the Mathematics Education Research Group of Australasia (pp. 93–100). Melbourne: MERGA

Çam, A. (2015). Primary Pre-Service Teachers’ Epistemological Beliefs and their Teaching and Learning Experiences. Eurasia Journal of Mathematics, Science & Technology Education, 11(2), 381–390. https://doi.org/10.12973/eurasia.2015.1351a

Cattel, R. B. (1996). The scree test for the number of factors. Multivariate Behavioral Research, 1(2), 245–276. https://doi.org/10.1207/s15327906mbr0102_10

Civil, M. (1990). “You only do Math in Math”: A Look at Four Prospective Teachers’ Views about Mathematics. For the Learning of Mathematics, 10(1), 7–9. Retrieved From https://www.jstor.org/stable/40247968

Dionne, J. (1984). The perception of mathematics among elementary school teachers. In J. Moser (Ed.), Proceedings of the 6th Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (PME) (pp. 223–228). Madison (WI): University of Wisconsin.

Ernest, P. (1989a). The impact of beliefs on the teaching of mathematics. In P. Ernest (Ed.), Mathematics teaching: The state of art (pp. 249–254). New York: Falmer.

Ernest, P. (1989b). The knowledge, beliefs and attitudes of the mathematics teacher: A model. Journal of Education for Teaching, 15(1), 13–34. https://doi.org/10.1080/0260747890150102

Ernest, P. (1991). The Philosophy of Mathematics Education. Hampshire (UK): The Falmer Press.

Foss, D. H., & Kleinsasser, R. C. (1996). Preservice elementary teachers’ views of pedagogical and mathematical content knowledge. Teaching and Teacher Education, 12(4), 429–442. https://doi.org/10.1016/0742-051X(95)00049-P

Frank, M. L. (1990). What myths about mathematics are held and conveyed by teachers? Arithmetic Teacher, 37(5), 10–12.

Fullan, M. & Stegelbauer, S. (1991). The new meaning of educational change. New York: Cassell.

Furinghetti, F., & Pehkonen, E. (2002). Rethinking characterizations of beliefs. In Beliefs: A hidden variable in mathematics education? (pp. 39–57). https://doi.org/10.1007/0-306-47958-3_3

Furinghetti, F. (1996). A theoretical framework for teachers’ conceptions. In E. Pehkonen (Ed.), Current State of Research on Mathematical Beliefs III. Proceedings of the MAVI-3 Workshop (pp.19–25). University of Helsinki. Department of Teacher Education. Research Report 170.

Goldin, G., Rösken, B., & Törner, G. (2009). Beliefs–no longer a hidden variable in mathematical teaching and learning processes. In J. Masses & W. Schlogmann (Eds.), Beliefs and attitudes in mathematics education (pp. 1-18). Rotterdam, The Netherlands: Sense Publishers. https://doi.org/10.1163/9789087907235_002

Gómez-Chacón, I. M., García-Madruga, J. A., Rodríguez, R., Vila, J. Ó., & Elosúa, M. R. (2011). Mathematical beliefs and cognitive reflection: Do they predict academic achievement? In B. Roesken, & M. Casper (Eds.), Current State of Research on Mathematical Beliefs XVII. Proceedings of the MAVI-17 (pp. 64-73). Ruhr-Universität Bochum, Germany.

Gómez-Chacón, I. M., & García-Madruga, J. A. (2009). Mathematical beliefs questionnaire (Creemat). In I+D+i project: Cognition and education: working memory, reading comprehension and reasoning, from the Spanish Ministry of Science and Innovation.

Grossman, P. and S. S. S. (1995). Content as context: The role of school subjects in secondary school teaching. Educational Researcher, 24(8), 5–23. https://doi.org/10.2307/1176887

Hacıömeroğlu, G., & Şahin-Taşkın, Ç. (2010). Sınıf öğretmeni adaylarının matematik öğretimi yeterlik inançları. Uludağ Üniversitesi Eğitim Fakültesi Dergisi, 23(2), 539–555.

Handal, B., & Herrington, A. (2003). Mathematics teachers’ beliefs and curriculum reform. Mathematics Education Research Journal, 15(1), 59–69. https://doi.org/10.1007/BF03217369

Handal, B. (2003). Teachers’ mathematical beliefs: A review. The Mathematics Educator, 13(2), 47–57. Retrieved From http://tme.journals.libs.uga.edu/index.php/ tme/article/view/131

House, J. D. (2006). Mathematics beliefs and achievement of elementary school students in Japan and the United States: Results from the Third International Mathematics and Science Study. The Journal of Genetic Psychology, 167(1), 31–45. https://doi.org/10.3200/GNTP.167.1.31-45

Işıksal, M., Kurt, G., Doğan, O., & Çakıroğlu, E. (2007). İlköğretim Matematik Öğretmen Adaylarının Epistemolojik Kavramlamaları: Üniversite ve Sınıf Düzeyinin Etkisi. İlköğretim Online, 6(2), 313–321.

Kagan, D. M. (1992). Implication of research on teacher belief. Educational Psychologist, 27(1), 65–90. https://doi.org/10.1207/s15326985ep2701_6

Kaiser, H. F. (1960). The application of electronic computers to factor analysis. Educational and Psychological Measurement, 20(1), 141–151. https://doi.org/10.1177/001316446002000116

Koehler, M. S. & Grouws, D. A. (1992). Mathematics teaching practices and their effects. In D. A. Grouws (Ed.), Handbook of research in on mathematics teaching and learning (pp. 115-126). New York: Macmillan.

McLeod, D. (1992). Research on affect in mathematics education: A reconceptualization. In D. Grows (Ed.), Handbook of research on mathematics teaching and learning (pp. 575– 596). New York: McMillan

Memnun, D. S., & Katranci, 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

Nespor, J. (1987). The role of beliefs in the practice of teaching. Journal of Curriculum Studies, 19(4), 317–328. https://doi.org/10.1080/0022027870190403

Op’t Eynde, P., & De Corte, E. (2003). Students’ Mathematics-Related Belief Systems: Design and Analysis of a Questionnaire. Paper presented at the 2003 Annual Meeting of the American Educational Research Association, pp.21-25, Chicago.

Op’t Eynde, P., De Corte, E., & Verschaffel, L. (2002). Framing students’ mathematics-related beliefs: A quest for conceptual clarity and a comprehensive categorization. In G.C. Leder, E. Pehkonen, & G. Törner (Eds.), Beliefs: A hidden variable in mathematics education? (pp. 13-37). Dordrecht, The Netherlands: Kluwer Academic Publishers. https://doi.org/10.1007/0-306-47958-3_2

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

Pehkonen, E. and Pietilä, A. (2003). On the relation between beliefs and knowledge in mathematics education. CERME3, Bellaria, Italy.

Pehkonen, E., & Törner, G. (1996). Mathematical beliefs and different aspects of their meaning. International Reviews on Mathematical Education (ZDM), 28(4), 101–108.

Purnomo. W., Suryadi, D., & Darwis, S. (2016). Examining pre-service elementary school teacher beliefs and instructional practices in mathematics class. International Electronic Journal of Elementary Education, 8(4), 629–642. Retrieved From https://www.iejee.com/index.php/IEJEE/article/view/137

Purnomo, Y. W. (2017). The complex relationship between teachers’ mathematics-related beliefs and their practices in mathematics class. The New Educational Review, 47(1), 200–210. https://doi.org/10.15804/tner.2017.47.1.16

Rokeach, M. (1968). Beliefs, attitudes, and values. San Francisco (Ca): Jossey-Bass.

Schoenfeld, A. H. (1983). Beyond the purely cognitive: Belief systems, social cognitions, and metacognitions as driving forces in intellectual performance. Cognitive Science, 7(4), 329–363. https://doi.org/10.1016/S0364-0213(83)80003-2

Schoenfeld, A. H. (1985). Mathematical Problem Solving. Orlando (FL.): Academic Press.

Schoenfeld, A. H. (1987). What’s all the fuss about metacognition? In A.H. Schoenfeld (Ed.), Cognitive Science and Mathematics Education (pp. 189–215). Hillsdale (NJ): Lawrence Erlbaum Associates

Shi, Q., Zhang, S., & Lin, E. (2014). Relationships of new teachers’ beliefs and instructional practices: Comparisons across four countries. Action in Teacher Education, 36(4), 322–341. https://doi.org/10.1080/01626620.2014.948228

Siswono, T. Y. E., Kohar, A. W., Kurniasari, I., & Hartono, S. (2018). Inconsistency among beliefs, knowledge, and teaching practice in mathematical problem solving: A case study of a primary teacher. Southeast Asian Mathematics Education Journal, 7(2), 27–39. Retrieved From http://journal.qitepinmath.org/index.php/seamej/article/ view/51

Skott, J. (2010). Shifting the direction of belief research: from beliefs to patterns of participation. In Pinto, M.F. & Kawasaki, T.F. (Eds) Proceedings of the 34th Conference of the International Group for Psychology of Mathematics Education (pp. 193-200). Belo Horizonte, Brazil: PME.

Sosniak, L. A., Ethington, C. A., & Varelas, M. (1991). Teaching mathematics without a coherent point of view: Findings from the IEA Second International Mathematics Study. J. Curriculum Studies, 23(2), 119–131. https://doi.org/10.1080/0022027910230202

Southwell, B., & Khamis, M. (1992). Beliefs about mathematics and mathematics education. In K. Owens, B. Perry, & B. Southwell (Eds.) Space, the first and final frontier. Proceedings of the 15th Annual Conference of the Mathematics Research Group of Australasia (pp. 497–509). Sydney: MERGA.

Stage, F. K., & Kloosterman, P. (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

Thompson, A. (1992). Teachers’ Beliefs and Conceptions: A Synthesis of the Research. In D. A. Grouws (Ed.), Handbook of Research on Mathematics Teaching and Learning (pp. 127–146). New York: Macmillan

Thompson, A. G. (1991). The development of teachers’ conceptions of mathematics teaching. Proceedings of the 13th Annual Conference of the North American Chapter of the International Group for the Psychology of Mathematics Education. (ERIC Document Reproduction Service No. ED 352274).

Xenofontos, C. (2018). Greek-Cypriot elementary teachers’ epistemological beliefs about mathematics. Teaching and Teacher Education, 70(1), 47–57. https://doi.org/10.1016/j.tate.2017.11.007

Xie, S., & Cai, J. (2018). Chinese Teachers’ Beliefs About Mathematics Teaching. In The 21st Century Mathematics Education in China (pp. 413–427). https://doi.org/10.1007/978-3-662-55781-5_20

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