Patterns in Kindergarten: Teachers' Knowledge of Content and Students and Associated Self-Efficacy Beliefs
PDF

How to Cite

Schreiber, I. (2020). Patterns in Kindergarten: Teachers’ Knowledge of Content and Students and Associated Self-Efficacy Beliefs. Scientia in Educatione, 11(1), 69-81. https://doi.org/10.14712/18047106.1543

Abstract

The present study engages in sixty kindergarten teachers' knowledge and self-efficacy related to patterns. Two aspects are examined: Teachers' pedagogical knowledge of content and students (specifically, what is easy or difficult for the children and what their typical errors are) as well as teachers' self-efficacy in their knowledge. These aspects are explored about two types of patterns - a repeating pattern and a growing pattern. The results pertaining to the repeating pattern show that teachers have knowledge of children's typical errors. However, they have partial knowledge of what is easy or difficult for the children: they tend to underestimate children's performance. Regarding the growing pattern, teachers have partial knowledge of both children's typical errors and of what is easy or difficult for them: they tend to overestimate children's performance. The results may have implications for teachers' education and guidance, especially novice teachers.

https://doi.org/10.14712/18047106.1543
PDF

References

Ball, D. L., Thames, M.H., & Phelps, G. (2008). Content knowledge for teaching – What makes it special? Journal of Teacher Education, 59(5), 389–407. https://doi.org/10.1177/0022487108324554

Ball, D. L., & Wilson, S.M. (1990). Knowing the subject and learning to teach it: Examining assumptions about becoming a mathematics teacher. National Center for Research on Teacher Education, Michigan State University.

Bandura, A. (1977). Self-efficacy: Toward a unifying theory of behavioral change. Psychological Review, 84(2), 191–215. https://doi.org/10.1037/0033-295X.84.2.191

Bandura, A. (1986). Social foundations of thought and action: A social cognitive. Englewood Cliffs, NJ: Prentice-Hall. https://doi.org/10.1017/S0813483900008238

Brouwers, A., & Tomic, W. (2000). A longitudinal study of teacher burnout and perceived self- efficacy in classroom management. Teacher and Teaching Education, 16(2), 239–253. https://doi.org/10.1016/S0742-051X(99)00057-8

Burton, G.M. (1982). Patterning: Powerful play. School Science and Mathematics, 82(1), 38–44. https://doi.org/10.1111/j.1949-8594.1982.tb17161.x

Chiu, M., & Klassen, R. M. (2010). Effects on teachers’ self-efficacy and job satisfaction: Teacher gender, years of experience and job stress. Journal of Educational Psychology, 102(3), 741–756. https://doi.org/10.1037/a0019237

Clements, D.H. (2001). Mathematics in the preschool. Teaching Children Mathematics, 7(5), 270–275.

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(2), 136–163.

Clements, D.H., & Sarama, J. (2011). Early childhood mathematics intervention. Science, 333(6045), 968–970. https://doi.org/10.1126/science.1204537

Cohen, D.K., & Ball, D.L. (1990). Relations between policy and practice: a commentary. Educational Policy and Analysis, 12(3), 331–338. https://doi.org/10.3102/01623737012003331

Dellinger, A., Bobbett, J., Olivier, D., & Ellett, C. (2008). Measuring teachers’ self-efficacy beliefs: Development and use of the TEBS-Self. Teaching and Teacher Education, 24(3), 751–766. https://doi.org/10.1016/j.tate.2007.02.010

Economopoulos, K. (1998). What comes next? The mathematics of pattern in kindergarten. Teaching Children Mathematics, 5(4), 230–233.

Fox, J. (2005a). Connecting algebraic development to mathematical patterning in early childhood. In P. Grootenboer., R. Zevenbergen, & M. Chinnappan (Eds.), Proceedings of the 29th Annual Conference of the Mathematics Education Research Group of Australia (Vol. 1, pp. 221–228). MERGA.

Fox, J. (2005b). Child initiated mathematical patterning in the pre-compulsory years. In H. L. Chick, & J. L. Vincent (Eds.), Proceedings of the 29th International Conference for the Psychology of Mathematics Education (2, pp. 313–320). PME.

Garrick, R., Threlfall, J., & Orton, A. (1999). Pattern in the nursery. In A. Orton (Ed.), Pattern in the teaching and learning of mathematics (pp. 1–17). Cassel.

Gibbs, W. (1999). Pattern in the classroom. In A. Orton (Ed.), Pattern in the teaching and learning of mathematics (pp. 207–221). Cassel.

Greenes, C., Ginsburg, H.P., & Balfanz, R. (2004). Big mathematics for little kids. Early Childhood Research Quarterly, 19(1), 159–166. https://doi.org/10.1016/j.ecresq.2004.01.010

Guo, Y., Justice, L.M., Sawyer, B., & Tompkins, V. (2011). Exploring factors related to preschool teachers’ self-efficacy. Teaching and Teacher Education, 27(5), 961–968. https://doi.org/10.1016/j.tate.2011.03.008

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. https://doi.org/10.2307/749515

Hill, H. C., Ball, D. L., & Schilling, S. G. (2008). Unpacking pedagogical concept knowledge: Conceptualizing and measuring teachers’ topic-specific knowledge for students. Journal for Research in Mathematics Education, 39(4), 372–400.

Jacobs, R.V., Lamb, L.C., & Philip, R.A. (2010). Professional noticing of children’s mathematical thinking. Journal for Research in Mathematics Education, 41(2), 169–202.

Kyriakides, L., & Gagatsis, A. (2003). Assessing student problem solving skills. Structural Equation Modeling, 10(4), 609–621. https://doi.org/10.1207/S15328007SEM1004 7

Krauss, S., Baumert, J., & Blum, W. (2008). Secondary mathematics teachers’ pedagogical content knowledge and content knowledge: Validation of the COACTIV constructs. ZDM, 40(5), 873–892. https://doi.org/10.1007/s11858-008-0141-9

Lee, J. (2010). Exploring kindergarten teachers’ pedagogical content knowledge of mathematics. International Journal of Early Childhood, 42(1), 27–41. https://doi.org/10.1007/s13158-010-0003-9

Leinhardt, G. (1989). Math lessons: a contrast of novice and expert competence. Journal for Research in Mathematics Education, 20(1), 52–75. https://doi.org/10.2307/749098

McCray, J. S., & Chen, J.Q. (2012). Pedagogical content knowledge for preschool mathematics: Construct validity of a new teacher interview. Journal of Research in Childhood Education, 26(3), 291–307. https://doi.org/10.1080/02568543.2012.685123

Midgley, C., Feldlaufer, H., & Eccles, J. S. (1989). Change in teacher efficacy and student self and task-related beliefs in mathematics during the transition to junior high school. Journal of Educational Psychology, 81(2), 247–258. https://doi.org/10.1037/0022-0663.81.2.247

Moss, J., & Beatty, R. (2006). Knowledge building and knowledge forum: grade 4 students collaborate to solve linear generalization problems. In J. Novotná, H. Moraová, M. Krátká, & N. Stehlíková (Eds.), Proceedings of the 30th Conference of the International Group for the Psychology of Mathematics Education (Vol. 4, pp. 193–199). PME.

Mulligan, J.T., Prescott, A., & Mitchelmore, M. C. (2004). Children’s development of Structure in early mathematics. In Proceedings of the 28th PME International Conference (Vol. 3, pp. 393–401). Bergen University College.

Ministry of Education in Israel. (2010). Curriculum for mathematics in kindergarten. Ministry of Education, Israel. [Hebrew]

National Council of Teachers of Mathematics. (1989). Curriculum and Evaluation for school mathematics. NCTM USA.

National Council of Teachers of Mathematics. (2000). Principles and Standards for school mathematics. NCTM USA.

Papic, M., & Mulligan, J. (2007). The growth of early mathematical patterning: an intervention study. In J. Watson, & K. Beswick (Eds.), Proceedings of the 30th Annual Conference of the Mathematical Education Research Group of Australia (Vol. 2, pp. 591–600). MERGA.

Papic, M., Mulligan, J., & Mitchelmore, M. (2011). Assessing the development of preschoolers’ mathematical patterning. Journal for Research in Mathematics Education, 42(3), 237–269. https://doi.org/10.5951/jresematheduc.42.3.0237

Shulman, L. S. (1986). Those who understand: knowledge growth in teaching. Educational Researcher, 15(2), 4–14. https://doi.org/10.3102/0013189X015002004

Shulman, L. S. (1987). Knowledge and teaching: Foundations of the new reform. Harvard Educational Review, 57(1), 1–21. https://doi.org/10.17763/haer.57.1.j463w79r56455411

Starkey, P., Klein, A., & Wakeley, A. (2004). Enhancing young children’s mathematical knowledge through a pre-kindergarten mathematics intervention. Early Childhood Research Quarterly, 19(1), 99–120. https://doi.org/10.1016/j.ecresq.2004.01.002

Tchoshanov, M.A. (2011). Relationship between teacher knowledge of concepts and connections, teaching practice and student achievement in middle grades mathematics. Educational Studies in Mathematics, 76(2), 141–164. https://doi.org/10.1007/s10649-010-9269-y

Threlfall, J. (1999). Repeating pattern in the early primary years. In A. Orton (Ed.), Pattern in the teaching and learning of mathematics (pp. 18–29). Cassel.

Tirosh, D., Even, R., & Robinson, N. (1998). Simplifying algebraic expressions: Teacher awareness and teaching approaches. Educational Studies in Mathematics, 35(1), 51–64. https://doi.org/10.1023/A:1003011913153

Tschannen-Moran, M., & Woolfolk-Hoy, A. (2007). The differential antecedents of self-efficacy beliefs of novice and experienced teachers. Teaching and Teacher Education, 23(6), 944–956. https://doi.org/10.1016/j.tate.2006.05.003

Warren, E. (2005). Patterns supporting the development of early algebraic thinking. In P. Clarkson, A. Downton, D. Gronn, M. Horne, A. McDonough, R. Pierce, & A. Roche (Eds.), Proceedings of the 28th annual conference of the Mathematics Education Research Group of Australasia, Melbourne (Vol. 1, pp. 759–766). MERGA.

Warren, E., & Miller, J. (2010). Indigenous children’s ability to pattern as they enter kindergarten/pre-prep settings: an exploratory study. In L. Sparrow, B. Kissane, & C. Hurst (Eds.), Proceedings of the 33rd annual conference of the Mathematics Education Research Group of Australasia (pp. 594–601). MERGA.

Waters, J. (2007). Mathematical patterning in early childhood settings. In J. Watson, & K. Beswick (Eds.), Proceeding of the 30th Annual Conference of the Mathematical Education Research Group of Australia (Vol. 2, pp. 565–572). MERGA.

Zazkis, R., & Liljedahl, P. (2002). Generalization of patterns: the tension between algebraic thinking and algebraic notation. Educational Studies in Mathematics, 49(3), 379–402. https://doi.org/10.1023/A:1020291317178

Zhang, Y. (2015). Pedagogical content knowledge in early mathematics: What teachers know and how it associates with teaching and learning. A dissertation submitted for the degree of Ph.D. Loyola University, USA.