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

Iris Schreiber

doi:10.14712/18047106.1543

Vol 11 No 1 (2020): sciED Výzkumné stati

Vzory ve školce: Didaktické znalosti týkající se obsahu a žáků a související přesvědčení

Iris Schreiber, ¹

Kibbutzim college of education & Bar Ilan university

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

PDF (angličtina)

Jak citovat

Schreiber, I. (2020). Vzory ve školce: Didaktické znalosti týkající se obsahu a žáků a související přesvědčení. Scientia in educatione, 11(1), 69-81. https://doi.org/10.14712/18047106.1543

Stánhout citace

Abstrakt

Studie se šedesáti učiteli mateřské školy v Izraeli zkoumá dva aspekty, které mohou ovlivnit výuku „vzorů: Didaktické znalosti týkající se obsahu a žáků (konkrétně co je pro žáky jednoduché a co je obtížné a jaké jsou typické chyby) a učitelovo vnímání vlastní zdatnosti (self-efficacy). Tyto aspekty jsou analyzovány prostřednictvím dvou typů vzorů – opakující se vzor a rostoucí vzor, a porovnáním dvou skupin učitelů – začátečníci a zkušení učitelé. Výsledky týkající se opakujícího se vzoru ukazují, že učitelé mají povědomí o typických chybách žáků. Mají ovšem jen částečnou znalost toho, co je pro děti jednoduché a co obtížné. Mají tendenci výkon dětí podceňovat. Co se týče rostoucího vzoru, učitelé mají částečné znalosti typických chyb i toho, co je pro děti jednoduché a co obtížné. Mají tendenci výkon dětí přeceňovat. Co se týče učitelské zkušenosti, začátečníci mají menší důvěru ve vlastní zdatnost a menší znalosti. Výsledky mají důsledky pro vzdělávání učitelů zejména u začátečníků.

Reference

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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 Přejít na DOI Vyhledej v Google Scholar
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 Přejít na DOI Vyhledej v Google Scholar
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. Vyhledej v Google Scholar
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. Vyhledej v Google Scholar
Kyriakides, L., & Gagatsis, A. (2003). Assessing student problem solving skills. Structural Equation Modeling, 10(4), 609–621. https://doi.org/10.1207/S15328007SEM1004 7 Přejít na DOI Vyhledej v Google Scholar
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 Přejít na DOI Vyhledej v Google Scholar
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 Přejít na DOI Vyhledej v Google Scholar
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 Přejít na DOI Vyhledej v Google Scholar
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 Přejít na DOI Vyhledej v Google Scholar
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 Přejít na DOI Vyhledej v Google Scholar
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. Vyhledej v Google Scholar
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National Council of Teachers of Mathematics. (1989). Curriculum and Evaluation for school mathematics. NCTM USA. Vyhledej v Google Scholar
National Council of Teachers of Mathematics. (2000). Principles and Standards for school mathematics. NCTM USA. Vyhledej v Google Scholar
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. Vyhledej v Google Scholar
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 Přejít na DOI Vyhledej v Google Scholar
Shulman, L. S. (1986). Those who understand: knowledge growth in teaching. Educational Researcher, 15(2), 4–14. https://doi.org/10.3102/0013189X015002004 Přejít na DOI Vyhledej v Google Scholar
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 Přejít na DOI Vyhledej v Google Scholar
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 Přejít na DOI Vyhledej v Google Scholar
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 Přejít na DOI Vyhledej v Google Scholar
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. Vyhledej v Google Scholar
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 Přejít na DOI Vyhledej v Google Scholar
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 Přejít na DOI Vyhledej v Google Scholar
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. Vyhledej v Google Scholar
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. Vyhledej v Google Scholar
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. Vyhledej v Google Scholar
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 Přejít na DOI Vyhledej v Google Scholar
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. Vyhledej v Google Scholar

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[1] 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 Přejít na DOI Vyhledej v Google Scholar

[2] 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. Vyhledej v Google Scholar

[3] 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 Přejít na DOI Vyhledej v Google Scholar

[4] Bandura, A. (1986). Social foundations of thought and action: A social cognitive. Englewood Cliffs, NJ: Prentice-Hall. https://doi.org/10.1017/S0813483900008238 Přejít na DOI Vyhledej v Google Scholar

[5] 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 Přejít na DOI Vyhledej v Google Scholar

[6] 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 Přejít na DOI Vyhledej v Google Scholar

[7] 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 Přejít na DOI Vyhledej v Google Scholar

[8] Clements, D.H. (2001). Mathematics in the preschool. Teaching Children Mathematics, 7(5), 270–275. Vyhledej v Google Scholar

[9] 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. Vyhledej v Google Scholar

[10] Clements, D.H., & Sarama, J. (2011). Early childhood mathematics intervention. Science, 333(6045), 968–970. https://doi.org/10.1126/science.1204537 Přejít na DOI Vyhledej v Google Scholar

[11] 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 Přejít na DOI Vyhledej v Google Scholar

[12] 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 Přejít na DOI Vyhledej v Google Scholar

[13] Economopoulos, K. (1998). What comes next? The mathematics of pattern in kindergarten. Teaching Children Mathematics, 5(4), 230–233. Vyhledej v Google Scholar

[14] 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. Vyhledej v Google Scholar

[15] 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. Vyhledej v Google Scholar

[16] 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. Vyhledej v Google Scholar

[17] Gibbs, W. (1999). Pattern in the classroom. In A. Orton (Ed.), Pattern in the teaching and learning of mathematics (pp. 207–221). Cassel. Vyhledej v Google Scholar

[18] 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 Přejít na DOI Vyhledej v Google Scholar

[19] 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 Přejít na DOI Vyhledej v Google Scholar

[20] 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 Přejít na DOI Vyhledej v Google Scholar

[21] 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. Vyhledej v Google Scholar

[22] 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. Vyhledej v Google Scholar

[23] Kyriakides, L., & Gagatsis, A. (2003). Assessing student problem solving skills. Structural Equation Modeling, 10(4), 609–621. https://doi.org/10.1207/S15328007SEM1004 7 Přejít na DOI Vyhledej v Google Scholar

[24] 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 Přejít na DOI Vyhledej v Google Scholar

[25] 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 Přejít na DOI Vyhledej v Google Scholar

[26] 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 Přejít na DOI Vyhledej v Google Scholar

[27] 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 Přejít na DOI Vyhledej v Google Scholar

[28] 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 Přejít na DOI Vyhledej v Google Scholar

[29] 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. Vyhledej v Google Scholar

[30] 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. Vyhledej v Google Scholar

[31] Ministry of Education in Israel. (2010). Curriculum for mathematics in kindergarten. Ministry of Education, Israel. [Hebrew] Vyhledej v Google Scholar

[32] National Council of Teachers of Mathematics. (1989). Curriculum and Evaluation for school mathematics. NCTM USA. Vyhledej v Google Scholar

[33] National Council of Teachers of Mathematics. (2000). Principles and Standards for school mathematics. NCTM USA. Vyhledej v Google Scholar

[34] 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. Vyhledej v Google Scholar

[35] 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 Přejít na DOI Vyhledej v Google Scholar

[36] Shulman, L. S. (1986). Those who understand: knowledge growth in teaching. Educational Researcher, 15(2), 4–14. https://doi.org/10.3102/0013189X015002004 Přejít na DOI Vyhledej v Google Scholar

[37] 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 Přejít na DOI Vyhledej v Google Scholar

[38] 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 Přejít na DOI Vyhledej v Google Scholar

[39] 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 Přejít na DOI Vyhledej v Google Scholar

[40] 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. Vyhledej v Google Scholar

[41] 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 Přejít na DOI Vyhledej v Google Scholar

[42] 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 Přejít na DOI Vyhledej v Google Scholar

[43] 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. Vyhledej v Google Scholar

[44] 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. Vyhledej v Google Scholar

[45] 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. Vyhledej v Google Scholar

[46] 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 Přejít na DOI Vyhledej v Google Scholar

[47] 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. Vyhledej v Google Scholar

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