Teachers’ mathematics knowledge has been known to have a significant impact on instructional practices. This paper discusses research on teachers’ mathematics knowledge. The paper has been summarised in five main areas: (a) the role of subject matter knowledge in teaching and learning, (b) teachers’ beliefs about mathematics teaching and learning, (c) beliefs and beliefs-in-practice: inconsistencies, (d) teacher education and its impact on instructional practices, and (e) future research on teachers’ mathematics knowledge. The review indicated that teachers are critical factors in the learning of mathematics and the extents of their content and pedagogical knowledge do determine students’ achievement. Also, the paper acceded to the view that, a teacher’s memories from the school years is a central influencing factor that affects its mathematics related beliefs, hence there is a need to enhance pre-service teachers’ positive attitude towards mathematics during training. The paper suggested further areas of research should look at: different theoretically-and empirically distinction in content knowledge for teaching and investigate their relationship, separately and in combination, to student achievement; whether mathematics teachers’ knowledge affects their lesson planning strategies and whether the provision of ‘mathematical knowledge for teaching’ by teacher training institutions improve pre-service teachers’ beliefs about mathematics and mathematics teaching. The paper concluded that, mathematics teacher education programme should provide pre-service teachers with awareness of conception of mathematics which may influence their teaching.
| [1] | Akinsola, M.K. (1999): STM Teacher Education: Some Themes of General Interest. In Abimbade, A. (Ed). Teaching and Teacher Preparation in the 21st Century. Book of Reading in Honour of Prof. T.A. Balogun. Department of Teacher Education. Pp. 196-202. |
| [2] | Akinsola, M.K. (2009). Comparison of Prospective and Practicing Teachers’ Mathematics Efficacy Beliefs Regarding Mathematics Teaching and Classroom Management. In Jürgen Maaß & Wolfgang Schlöglmann (Ed.) Beliefs and Attitudes in Mathematics Education: New Research Results. Sense Publishers. Holland, 135-148 |
| [3] | Akinsola, M.K. (2008). Relationship of some psychological variables in predicting problem solving ability of in-service mathematics teachers. The Montana Mathematics Enthusiasts, Vol.5, No 1, pp 79-100. |
| [4] | Akinsola, M.K. (2009). Comparison of Prospective and Practicing Teachers’ Mathematics Efficacy Beliefs Regarding Mathematics Teaching and Classroom Management. In Jürgen Maaß & Wolfgang Schlöglmann (Ed.) Beliefs and Attitudes in Mathematics Education: New Research Results. Sense Publishers, Holland. 135-148. |
| [5] | Akinsola, M.K and Ajiboye, J.O. (2009). School reform: A case study of Primary Education in Botswana. In James, V. U.& Etim, J.S. (Eds.). Educational Reform in Africa: Essays on Curriculum, Libraries, Counseling, and Grades Levels. The Edwin Mellen Press, 225-234 |
| [6] | Akinsola, M.K. (2013). Helping Teacher Tame Underachievement in Mathematics: The Attitude Dimension. Lead paper presented at the Oyo State Mathematical Association of Nigeria Conference held at The Trenchard Hall, University of Ibadan, Ibadan, Nigeria |
| [7] | Alexander, R., Rose, J., & Woodhead, C. (1992). Curriculum organization and classroom practice in primary school: A discussion paper. London: Her Majesty’s Stationary Office. |
| [8] | American Council of Education, (1999). To touch the future: Transforming the way teachers are taught. An action agenda for college and university presidents. Washington, DC: American Council on Education. |
| [9] | Argyris, C., & Schon, D. A. (1974). Theory in practice: Increasing professional effectiveness. London: Jossey-Bass. |
| [10] | Askew, M., Brown, M., Rhodes, V., Johnson, D., & William, D. (1997). Effective teachers of Numeracy. London: King’s College. |
| [11] | Aubrey, C. (19997). Teaching in the early years: An investigation into teachers’ subject knowledge. London: Falmer Press. |
| [12] | Australian Association of Mathematics Teachers. (2000). Consultation draft descriptors of excellence in teaching mathematics. Adelaide: AAMT |
| [13] | Ball, D. L., Hill, H. C., & Bass, H (2005). Knowing mathematics for teaching. Who knows mathematics well enough to teach third grade, and how can we decide? Available online: www-personal.umich.edu/~dball/ [Date of access: November 12, 2008]. |
| [14] | Ball, D. L. (1988). Knowledge and reasoning in mathematical pedagogy: Examining what prospective teachers bring to teacher education. Unpublished doctoral dissertation. Michigan State University, East Lancing. |
| [15] | Ball, D. L. (1990). Prospective elementary and secondary teachers’ understanding of division. Journal for research in mathematics education, 21, 132-144.View Article |
| [16] | Ball, D. L., Lubienski, S., & Mewborn, D.(2001). Research on teaching mathematics: The unsolved problem of teachers’ mathematical knowledge. In V. Richardson (Ed.), Handbook of research on teaching (pp. 433-456). New York, NY: Macmillan. |
| [17] | Ball, D. L., & McDiarmid, G. W. (1990). The subject-matter preparation of teachers. In W. R. Houston and M. H. J. Sikula (Eds.), Handbook of research on teacher education (pp. 437-449). New York: Macmillan. |
| [18] | Boaler, J. (1998). Open and closed mathematics: Students experiences and understanding. Journal for research in mathematics education, 1, 41-62.View Article |
| [19] | Bramald, R., Hardman, F., & Leat, D. (1995). Initial teacher trainees and their views of teaching and learning. Teaching and teacher education, 11(1), 23-31.View Article |
| [20] | Brophy, J. E. (1991). Conclusion to advances in research on teaching: Teachers’ knowledge of subject matter as it relates to teaching practice. In J. E. Brophy (Ed.), Advances in research on teaching: Teachers’ subject matter knowledge and classroom instruction (pp. 347-362). Greenwich CT: JAI Press. |
| [21] | Brown, M., Askew, M., Millett, A., & Rhodes, V. (2003). The key role of educational research in the development and evaluation of the National Numeracy Strategy. British Educational Research Journal, 29, 655-672.View Article |
| [22] | Brown, T. (2003). Mathematical identity in initial teacher training. Available on line: http://onlinedb.terc.edu/PME2003/PDF/RR_brown_T.pdf. |
| [23] | Brown, C. A. (1985). A study of the socialization to teaching of a beginning mathematics teacher. Unpublished doctoral dissertation, University of Georgia, Athens, GA., USA. |
| [24] | Brown, s., & McIntyre, D. (1993). Making sense of teaching. Buckingham: Open University Press. |
| [25] | Carpenter, T. P., Fennema, E. & Franke, M. L. (1996). Cognitively Guided Instruction: A knowledge base for reform in Primary Mathematics instruction. Elementary school Journal, 97, 1, 3-20.View Article |
| [26] | Carpenter, T. P., Fennema, E., Peterson, P., Chiang, C., & Loef, M (1989). Using knowledge of children’s mathematics thinking in classroom teaching: An experimental study. American Educational Research Journal, 26, 4, 499531.View Article |
| [27] | Chaney, B. (1995). Student outcomes and the preparation of eighth-grade teachers in science and mathematics: NSF/NELS:88 teacher transcript analysis. Rockville, MD: Westat. |
| [28] | Clarke, B. (2003). Supporting teachers in understanding, assessing and developing children's mathematics through sharing children's thinking. Available online: www.nku.edu/~sheffield!bclarke.html [Date of access: November 7,2003]. |
| [29] | Cobb, P. (2002). Epistemological world views, subject matter contexts, and the institutional setting of teaching. Issues in education. Contributions from Educational psychology, 8 (2), 149-157. |
| [30] | Cooney, T. J. (1999).Conceptualizing teachers’ way of knowing. Educational Studies in Mathematics, 38, 163-187.View Article |
| [31] | Cooney, T., Shealy, E. B., & Arvold, B. (1998). Conceptualizing belief structures of pre- service secondary mathematics teachers. Journal for research in mathematics education, 3, 306-333.View Article |
| [32] | Cooney, T. J. (1985). A beginning teacher’s view of problem solving. Journal for research in mathematics education, 16 (5), 324-336.View Article |
| [33] | Daskalogianni, K., & Simpson, A. (2000). Towards a definition of attitude: The relationship between affective and cognitive in pre-university students. In T. Nakahara and M. Koyama (Eds.), Proceedings of the 24th conference of the international group for the psychology of mathematics education (pp. 217-224), Vol. 2, Hirishima, Japan. |
| [34] | Day, C. (1999). Developing teachers: The challenges of lifelong learning. London: Falmer. |
| [35] | Dembo, M. (2001). Learning to teach is not enough. Future teachers also need to learn how to learn. Teacher Education Quarterly, 23-24. |
| [36] | DfEE, (1998). Teaching: High status, High standards: Circular 4/98. London: HMSO. |
| [37] | Ernest, P. (1989). The knowledge, beliefs, and attitudes of the mathematics teacher: A model. Journal of education for teaching, 15, 1, 13-34.View Article |
| [38] | Fennema, E., & Franke, M. L. (1992). Teachers’ knowledge and its impact. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 147- 164). New York: Macmillan. |
| [39] | Fennema, E., & Romberg, T. A. (1999). Mathematics classrooms that promote understanding. Mahwah, NJ: Lawrence Erlbaum. |
| [40] | Franke, M. L. (1990). What myth about mathematics are held and conveyed by teachers? Arithmetic teacher, 37 (5) 10-12. |
| [41] | Furinghetti, F., & Pehkonen, E. (2002). Rethinking characterizations of beliefs. In Leder, G., Pehkonen, E., and Torner, G. (Eds.), Beliefs: A hidden variable in mathematics education? 31, 39-57. Dordrecht, Kluwer. |
| [42] | Gellert, U. (2000). Mathematics instruction in safe space: Prospective elementary teachers’ views of mathematics education. Journal of mathematics teacher education, 3, 251-270.View Article |
| [43] | Goulding, M. (2003). An investigation into the mathematical knowledge of primary teacher trainees. In J. Williams (Ed.), Proceedings of the British Society for Research into Learning mathematics. University of York. UK. |
| [44] | Government of Botswana (1994). The Revised National Policy on Education. Government Paper NO. 2 of 1994. Gaborone: Government Printers. |
| [45] | Government of Botswana (1993). Report of the National Commission on Education. Gaborone. Government Printers. |
| [46] | Greenwald, R., Hedges, L. V., & Laine, R. D. (1996). The effect of school resources on student achievement. Review of Educational Research, 6, 361-396.View Article |
| [47] | Hanushek, E. A. (1996). A more complete picture of school resource policies. Review of Educational Research, 66, 397-409.View Article |
| [48] | Harbison, R. W., & Hanushek, E. A. (1992). Educational performance for the poor: Lessons from rural northeast Brazil. Oxford, England: Oxford University Press. PubMed |
| [49] | Hare, A. Y. (1999). Revealing what urban early childhood teachers think about mathematics and how they teach it: Implications for practice. Doctoral dissertation, |
| [50] | Hill, C. H., Rowan, B., & Ball, D. L. (2005). Effects of teachers’ mathematical knowledge for teaching on student achievement. American Educational Research Journal, 42, 2, 371-406.View Article |
| [51] | Hodgen, J. (2003). Recent UK research into prospective primary teachers’ mathematics subject knowledge: A response. In J. Williams (Ed.), Proceedings of the British society for research into the learning of mathematics (pp.103-108). Vol. 23, Kings College: London. |
| [52] | Howie, S. (2001). Mathematics and science performance in Grade 8 in South Africa 1998/1999: TIMSS-R 1999. South Africa: Human Sciences Research Council. Pretoria. |
| [53] | Hoyles, C. (1992). Illuminations and reflections: Teachers, methodologies and mathematics. In W. Geelin and K. Graham (Eds.), Proceedings of the 16th Conference of the Internal Group for the Psychology of Mathematics Education (PME). Durham, NH., USA: University of New Hampshire, Vol. 3, pp. 263-286. |
| [54] | Huckstep, P., Rowland, T., Thwaites, A. (2002). Primary teachers’ mathematics content knowledge: What does it look like in the classroom? A paper presented at the Annual Conference of the British Educational Research Association. University of Exeter. UK. |
| [55] | Jones, D., Henderson, E., & Cooney T. (1986). Mathematics teachers’ beliefs about mathematics and about teaching mathematics. In G. Lappan, and R. Even, (Eds.), Proceedings of PME-NA-8 (pp. 274-279). East Lancing MI. Michigan University. |
| [56] | Joram, E., & Gabriele, A. (1998). Pre-service teachers’ prior beliefs: Transforming obstacles into opportunities. Teaching and teacher education, 14 (2), 175-191.View Article |
| [57] | Kaasila, R. (2000). An insight into the role of pupils. The significance of school recollections in the formation of the conceptions and teaching practices of mathematics for pre- service teachers. Rovaniemi: Acta Universitatis Lapponiensis 32. |
| [58] | Kagan, D. M. (1992). Professional growth among pre-service and beginning teachers. Review of educational research, 62, 129-169. View Article |
| [59] | Levitt, K. E. (2001). An analysis of elementary teachers’ beliefs regarding the teaching and learning of science. Science education, 86, 1-22.View Article |
| [60] | Lindgren, L. (1995). Pre-service teachers’ beliefs and conception about mathematics and teaching mathematics. Tampere University, Department of Teacher education. |
| [61] | Lortie, D. (175). School teacher: a sociological study. University of Chicago Press, Chicago. |
| [62] | Ma, L. (1999). Knowing and teaching elementary mathematics: Teachers’ understanding of fundamental mathematics in China and United States. Mahwah, NJ: Erlbaum. |
| [63] | Mason, J., & Spence, M. (1999). Beyond mere knowledge of mathematics: The importance of knowing-to act in the moment. Educational studies in mathematics, 38, 135-161.View Article |
| [64] | McDiarmid, G. W., Ball, D. L., & Anderson, C. W. (1989). Why staying ahead one chapter doesn’t really work: Subject-specific pedagogy. In M. C. Reynolds (Ed.), Knowledge base for the beginning teacher (pp. 193-205). New York: Pergamon. |
| [65] | Middleton, J. A. (1995). A study of intrinsic motivation in the mathematics classroom: A personal construct approach. Journal for research in mathematics education, 26 (3), 254-279.View Article |
| [66] | Muijs, D., & Reynolds, D. (2002). Teachers’ beliefs and behaviors: What really matters? Journal of classroom interaction, 2, 3-15. |
| [67] | Mullens, J. E., Murname, R. J., & Willet, J. B. (1996). The contributions of training and subject knowledge to teaching effectiveness: A multilevel analysis of longitudinal evidence from Belize. Comparative education review, 40, 139-157.View Article |
| [68] | National Council of Teachers of Mathematics. (2000). Principles and standards for teaching mathematics. . Reston, VA; Author |
| [69] | National Council of Teachers of Mathematics. (1991). Professional standards for teaching school mathematics. Reston, VA; Author |
| [70] | National Research Council. (1996). National science education standards. Washington, DC: National Academy Press. |
| [71] | National Research Council (1989). Everybody counts: A report on the future of mathematics education. Washington: National Academy Press. |
| [72] | National Commission on Teaching and America’s Future. (1996). What matters most: Teaching for America’s future. New York: National Council of Teachers of Mathematics. |
| [73] | Olafson, L. & Schraw, G. (2006). Teachers’ beliefs and practices within and across domains. International journal of educational research, 45, 71-84.View Article |
| [74] | Pajares, F. (1992). Teachers’ beliefs and educational research: Cleaning up a messy construct. Review of educational research, 62, 307-332.View Article |
| [75] | Pendaeli, J., Ogunnyi, M. B., & Mosothwane, M. (1993). Strategies for the improvement of performance in science and mathematics at all levels in education system of Botswana. Gaborone: Botswana Educational Research Association. |
| [76] | Pietila, A. (2002). Pre-service elementary teachers’ views of mathematics: The role mathematics experiences in forming the views of mathematics. University of Helsinki. Department of teacher education. Research report 238. |
| [77] | Pinto, M., & Tall, D. (1996). Student teachers’ conceptions of the rational numbers. In L. Puig and A. Gutierrez (Eds.), Proceedings of the 20th Conference of the Internal Group for the Psychology of Mathematics Education (PME). Valencia, Spain: University of Valencia, Vol. 4, pp. 139-146. |
| [78] | Post, T., Harel, G., Behr, M., & Lesh, R. (1988). Intermediate teachers’ knowledge of rational number concepts. In E. Fennema, T. P. Carpenter, & S. J. Lamon (Eds.), Integrating research on teaching and learning mathematics (pp. 177-198). Albany, NY: Sunny Press. |
| [79] | Powell, R. R. (1992). The influence of prior experiences on pedagogical constructs of traditional and non-traditional pre-service teachers. Teaching and teacher education, 8, 225-238.View Article |
| [80] | Prawat, R. S. (1992). Teachers’ beliefs about teaching and learning: A constructivist perspective. American journal of education, 100(3), 354-395.View Article |
| [81] | Raymond, A. M. (1997). Inconsistency between a beginning elementary school teacher’s mathematics beliefs and teaching practices. Journal for research in mathematics education, 28, 550-576.View Article |
| [82] | Remillard, J., & Bryans, M. (2004). Teachers' orientations towards mathematics curriculum materials: implications for teacher learning. Journal for research in mathematics education, 35(5), 352-388.View Article |
| [83] | Richardson, V. (2003). Preservice teachers’ beliefs. Paper presented at the American Educational Research Association, Chicago. |
| [84] | Rowan, B., Chiang, F., & Miller, R. J. (1997). Using research on employees’ performance to study the effects of teachers on students’ achievement. Sociology of Education, 70, 256-284.View Article |
| [85] | Saeed, M., & Mahmood, K. (2002). Assessing competency of Pakistani primary school teachers in mathematics, science, and pedagogy. International journal of educational management, 16, 190-195.View Article |
| [86] | Schoenfeld, A. H. (2002). How can we examine the connections between teachers’ world views and their educational practices? Issues in education. Contributions from Educational psychology, 8 (2), 229-232. |
| [87] | Seldon, A. (2003). Two research traditions separated by a common subject: Mathematics and mathematics education. Mathematics Department Technical Report No. 2002-2. |
| [88] | Tennessee Technological University Shaw, K. (1989). Constructs of teacher ideal and actual beliefs about mathematics understanding: Three case studies. Unpublished doctoral dissertation, University of Georgia, Athens, GA., USA. |
| [89] | Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 67, 4-14.View Article |
| [90] | Shulman, L. S. (1987). Knowledge and teaching: Foundation of the new reform. Harvard educational review, 1, 1-22. |
| [91] | Simon, M. (1993). Prospective elementary teachers’ knowledge of division. Journal for research in mathematics education, 24, 233-254.View Article |
| [92] | Simmons, M. (1993). The effective teaching mathematics. New York: Longman. |
| [93] | Swafford, J. O., Jones, G. A., Thornton, C. A., Stump, S. L., & Miller, D. R. (1999). The impact on instructional practice of a teacher change model. Journal of research and development in education, 32, 69-82. |
| [94] | Taylor, N., & Vinjevold, P. (1999). Teaching and learning in South African schools. In N. Taylor and P. Vinjevold (Eds.), Getting learning right: report of the President’s education initiative research project (pp. 131-162). Braamfontein: Joint Education Trust. |
| [95] | Thompson, A. G. (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. |
| [96] | Thompson, A. G. (1984). The relationship of teachers’ conceptions of mathematics and mathematics teaching to instructional practice. Educational studies in mathematics, 15, 105-112.View Article |
| [97] | Verschaffel, L. (1996). Pre-service teachers’ conceptions and beliefs about the role of real- world knowledge in arithmetic word problem solving. In L. Puig and A. Gutierrez (Eds.), Proceedings of the 20th Conference of the Internal Group for the Psychology of Mathematics Education (PME). Valencia, Spain: University of Valencia, Vol. 4, pp. 387-394. |
| [98] | Wilson, S. M., Shulman, L. S., & Richert, A. (1987). 150 different ways of knowing: Representations of knowledge in teaching. In J. Calderhead (Ed.), Exploring teachers’ thinking (pp. 104-124). Sussex, England: Holt, Rinehart & Winston. |
| [99] | Wilcox-Herzog, A. (2002). Is there a link between teachers’ beliefs and behaviors? Early education and development, 13 (1), 81-106.View Article |
| [100] | Zhihui, F. (1996). A review of research on teachers’ beliefs and practices. Educational research, 38, 47-65.View Article |
