Abstract
This article describes a study that investigates preschool teachers’ knowledge of their young students’ number conceptions and the teachers’ related self-efficacy beliefs. It also presents and illustrates elements of a professional development program designed explicitly to promote this knowledge among preschool teachers. Results indicated that teachers’ knowledge of students’ number conceptions improved and that their related self-efficacy increased. Furthermore, prior to participating in the programs, a significant negative correlation between knowledge and self-efficacy was reported. However, no significant correlation was found after the program.
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References
Allinder, R. M. (1994). The relationship between efficacy and the instructional practices of special education teachers and consultants. Teacher Education and Special Education, 17(2), 86–95.
An, S., Kulm, G., & Wu, Z. (2004). The pedagogical content knowledge of middle school mathematics teachers in China and the US. Journal of Mathematics Teacher Education, 7, 145–172.
Ashton, P. T., & Webb, R. B. (1986). Making a difference: Teachers’ sense of efficacy and student achievement. New York: Longman.
Ball, D., Thames, M., & Phelps, G. (2008). Content knowledge for teaching. Journal of Teacher Education, 59(5), 389–407.
Bandura, A. (1986). Social foundations of thought and action: A social cognitive theory. Englewood Cliffs, NJ: Prentice Hall.
Baroody, A. J. (1987). Children’s mathematical thinking: A developmental framework for preschool, primary, and special education teachers. New York: Teacher’s College Press.
Baroody, A. J., Lai, M. L., & Mix, K. S. (2006). The development of young children’s early number and operation sense and its implications for early childhood education. In B. Spodek & O. Saracho (Eds.), Handbook of research on the education of young children (2nd ed., pp. 187–221). Mahwah, NJ: Erlbaum.
Baroody, A. J., & Wilkins, J. L. M. (1999). The development of informal counting, number, and arithmetic skills and concepts. In J. V. Copley (Ed.), Mathematics in the early years (pp. 48–65). Reston, VA: National Council of Teachers of Mathematics.
Bates, A. B., Latham, N., & Kim, J. A. (2011). Linking preservice teachers’ mathematics self-efficacy and mathematics teaching efficacy to their mathematical performance. School Science and Mathematics, 111(7), 325–333.
Bobis, J., Clarke, B., Clarke, D., Thomas, G., Wright, B., Young-Loveridge, J., et al. (2005). Supporting teachers in the development of young children’s mathematical thinking: Three large scale cases. Mathematics Education Research Journal, 16(3), 27–57.
Brady, S., Gillis, M., Smith, T., Lavalette, M., Liss-Bronstein, L., Lowe, E., et al. (2009). First grade teachers’ knowledge of phonological awareness and code concepts: Examining gains from an intensive form of professional development and corresponding teacher attitudes. Reading and Writing, 22(4), 425–455.
Briars, D., & Siegler, R. S. (1984). A featural analysis of preschoolers counting knowledge. Developmental Psychology, 20(4), 607–618.
Carpenter, T. P., Fennema, E., Peterson, P. L., Chiang, C. P., & Loef, M. (1989). Using knowledge of children’s mathematics thinking in classroom teaching: An experimental study. American Educational Research Journal, 26(4), 499–531.
Clements, D. H., & Sarama, J. (2007). Effects of a preschool mathematics curriculum: Summative research on the Building Blocks project. Journal for Research in Mathematics Education, 38, 136–163.
Clements, D., Sarama, J., Spitler, M., Lange, A., & Wolfe, C. B. (2011). Mathematics learned by young children in an intervention based on learning trajectories: A large-scale cluster randomized trial. Journal for Research in Mathematics Education, 42, 127–166.
Coladarci, T. (1992). Teachers’ sense of efficacy and commitment to teaching. Journal of Experimental Education, 60, 323–337.
Dellinger, A. B., Bobbett, J. J., Olivier, D. F., & Ellett, C. D. (2008). Measuring teachers’ self-efficacy beliefs: Development and use of the TEBS-Self. Teaching and Teacher Education, 24(3), 751–766.
Even, R., & Tirosh, D. (1995). Subject matter knowledge and knowledge about students as sources of teacher presentations of the subject matter. Educational Studies in Mathematics, 29(1), 1–20.
Farran, D. C., Lipsey, M. W., Watson, B., & Hurley, S. (2007). Balance of content emphasis and child content engagement in an early reading first program. In Paper presented at the American Educational Research Association, Chicago, IL.
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. 147–165). New York: Macmillan Publishing Company.
Fuson, K. C. (1988). Children’s counting and concepts of number. New York: Springer.
Fuson, K. C., & Hall, J. (1982). ‘The acquisition of early number word meanings: A conceptual analysis and review. In H. P. Ginsburg (Ed.), Children’s mathematical thinking (pp. 49–107). New York: Academic Press.
Fuson, K. C., Richards, J., & Briars, D. J. (1982). The acquisition and elaboration of the number word sequence. In C. J. Brainerd (Ed.), Children’s logical and mathematical cognition (pp. 33–92). New York: Springer.
Geary, D. C., Bow-Thomas, C. C., & Yao, Y. (1992). Counting knowledge and skill in cognitive addition: A comparison of normal and mathematically disabled children. Journal of Experimental Child Psychology, 54(3), 372–391.
Gelman, R., & Gallistel, C. (1978). The child’s understanding of number. Cambridge: Harvard University Press.
Ginsburg, H. P., Jang, S., Preston, M., VanEsselstyn, D., & Appel, A. (2004). Learning to think about early childhood mathematics education: A course. In C. Greenes & J. Tsankova (Eds.), Challenging young children mathematically (pp. 40–56). Boston, MA: National Council of Supervisors of Mathematics.
Ginsburg, H. P., Lee, J. S., & Boyd, J. S. (2008). Mathematics education for young children: What it is and how to promote it (pp. 1–22). XXII(I): Social Policy Report.
Hackett, G., & Betz, N. (1989). An exploration of the mathematics self-efficacy/mathematics performance correspondence. Journal for Research in Mathematics Education, 20(3), 261–273.
Halvorsen, A., Lee, V., & Andreade, F. (2009). A mixed-method study of teachers’ attitudes about teaching in urban and low-income schools. Urban Education, 44(2), 181–224.
Han, Y., & Ginsburg, H. P. (2001). Chinese and English mathematics language: The relation between linguistic clarity and mathematics performance. Mathematical Thinking and Learning, 3(2–3), 201–220.
Israel national mathematics preschool curriculum (INMPC) (2008). Retrieved April 7, 2009, from http://meyda.education.gov.il/files/Tochniyot_Limudim/KdamYesodi/Math1.pdf.
Maher, C. (2008). Video recording as pedagogical tools in mathematics teacher education. In D. Tirosh & T. Wood (Eds.), International handbook of mathematics teacher education: Tools and processes in mathematics teacher education (Vol. 2, pp. 65–83). Rotterdam: Sense Publishers.
Mayer, A. (2008). Expanding opportunities for high academic achievement: An international Baccalaureate diploma program in an urban high school. Journal of Advanced Academics, 19(2), 202–235.
Mulligan, J. T., Prescott, A., Papic, M., & Mitchelmore, M. (2006). Improving early numeracy through a pattern and structure mathematics awareness program (PASMAP). In Building connections: Theory, research and practice (Proceedings of the 28th annual conference of the Mathematics Education Research Group of Australia) (pp. 376–383).
National Association for the Education of Young Children & National Council of Teachers of Mathematics (NAEYC & NCTM) (2002). Position statement. Early childhood mathematics: Promoting good beginnings. Available: www.naeyc.org/resources/position_statements/psmath.htm.
Piaget, J., Inhelder, B., & Szeminska, A. (1960). The child’s conception of geometry. London: Routledge and Kegan Paul.
Schifter, D. (1998). Learning mathematics for teaching: From the teacher’s seminar to the classroom. Journal for Mathematics Teacher Education, 1(1), 55–87.
Schoenfeld, A. H., & Kilpatrick, J. (2008). Toward a theory of proficiency in teaching mathematics. In D. Tirosh & T. Wood (Eds.), The international handbook of mathematics teacher education: Tools and processes in mathematics teacher education (Vol. 2, pp. 321–354). Rotterdam: Sense Publishers.
Seo, K. H., & Ginsburg, H. P. (2004). What is developmentally appropriate in early childhood mathematics education? Lessons from new research. In D. H. Clements, J. Sarama, & A. M. DiBiase (Eds.), Engaging young children in mathematics: Standards for early childhood mathematics education (pp. 91–104). Hillsdale, NJ: Erlbaum.
Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4–14.
Skaalvik, E. M., & Skaalvik, S. (2007). Dimensions of teacher self-efficacy and relations with strain factors, perceived collective teacher efficacy, and teacher burnout. Journal of Educational Psychology, 99(3), 611.
Starkey, P., Klein, A., & Wakeley, A. (2004). Enhancing young children’s mathematical knowledge through a pre-kindergarten mathematics intervention. Early Childhood Research Quarterly, 19, 99–120.
Tirosh, D., & Tsamir, P. (2008). Starting right: Mathematics in preschool. Unpublished research report. In Hebrew.
Tirosh, D., Tsamir, P., Levenson, E., Tabach, M., & Barkai, R. (2011). Prospective and practicing preschool teachers’ mathematics knowledge and self-efficacy: Identifying two and three dimensional figures. In 17th MAVI (Mathematical Views) conference. Bochum, Germany. Retrieved May 7, 2012 from http://www.ruhr-uni-bochum.de/ffm/Lehrstuehle/Roesken/maviarticles.html.
Törner, G. (2002). Mathematical beliefs. In G. C. Leder, E. Pehkonen, & G. Törner (Eds.), Beliefs: A hidden variable in mathematics education? (pp. 73–94). The Netherlands: Kluwer.
Tsamir, P., Tirosh, D., & Levenson, E. (2011). Special issue: Windows to early childhood mathematics teacher education. Journal for Mathematics Teacher Education, 14(2), 89–92.
Tsamir, P., Tirosh, D., Levenson, E., Barkai, R., & Tabach, M. (in press). Facilitating proficient mathematics teaching in Preschool. In Y. Li & J. N. Moschkovich (Eds.), Proficiency and beliefs in learning and teaching mathematics—learning from Alan Schoenfeld and Günter Toerner.
Tsamir, P., Tirosh, D., Levenson, E., Tabach, M., & Barkai, R. (2014). Employing the CAMTE framework: Focusing on preschool teachers’ knowledge and self-efficacy related to students’ conceptions. In C. Benz, B. Brandt, U. Kortenkamp, G. Krummheuer, S. Ladel & R. Vogel (Eds.), Early mathematics learning—selected papers from the POEM 2012 conference (pp. 291–306). New York: Springer.
Tschannen-Moran, M., & Hoy, A. (2007). The differenetial antecedents of self-efficacy beliefs of novice and experienced teachers. Teaching and Teacher Education, 23, 944–956.
Wheatley, K. F. (2002). The potential benefits of teacher efficacy doubts for educational reform. Teaching and Teacher Education, 18(1), 5–22.
Zimmerman, B., Bandura, A., & Martinez-Pons. (1992). Self-motivation for academic attainment: The role of self-efficacy beliefs and personal goal setting. American Educational Research Journal, 29, 663–676.
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This study was supported by the Israel Science Foundation (Grant No. 654/10).
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Tsamir, P., Tirosh, D., Levenson, E. et al. Developing preschool teachers’ knowledge of students’ number conceptions. J Math Teacher Educ 17, 61–83 (2014). https://doi.org/10.1007/s10857-013-9260-5
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DOI: https://doi.org/10.1007/s10857-013-9260-5