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Year 2019, Volume: 6 Issue: 3, 49 - 60, 01.09.2019

Abstract

References

  • Alibali, M., Knuth, E. J., Hattikudur, S., McNeil, N. M., & Stephens, A. C. (2007). A longitudinal examination of middle school students’ understanding of the equal sign and equivalent equations. Mathematical Thinking and Learning, 9(3), 221–247.
  • Alibali, M. W. (1999). How children change their minds: Strategy change can be gradual or abrupt. Developmental Psychology, 35(1): 127–145.
  • Asquith, P., Stephens, A., Knuth, E., & Alibali, M. (2007). Middle school mathematics teachers’ knowledge of students’ understanding of core algebraic concepts: Equal sign and variable. Mathematical Thinking and Learning, 9(3), 249–272.
  • Ball, D. (1990). Prospective elementary and post primary level teachers understanding of division. Journal for Research in Mathematics Education, 21(2), 132–144.
  • Bartell, T. G., Webel, C., Bowen, B. & Dyson, N. (2013). Prospective teacher learning: recognizing evidence of conceptual understanding. Journal of MathematicsTeacher Education, 16(1), 57–79.
  • Callejo, M. L. & Zapatera, A. (2017). Prospective primary teachers’ noticing of students’ understanding of pattern generalization. Journal of Mathematics Teacher Education, 20(4), 309–333.
  • Carpenter, T., Franke, M., & Levi, L. (2003). Thinking mathematically: Integrating arithmetic and algebra in elementary school. Portsmouth, NH: Heinemann.
  • Carpenter, T. P., Levi, L., Franke, M. L., & Zeringue, J. K. (2005) Algebra in elementary school: Developing relational thinking, ZDM, 37(1), 53‐59
  • Driver, M. K.,& Powell, S. R. (2015). Symbolic and nonsymbolic equivalence tasks: The influence of symbols on students with mathematics difficulty. Learning Disabilities Research and Practice, 30(3), 127–134. doi:10.1111/ldrp.12059
  • Falkner, K.P., Levi, L. & Carpenter, T.P. (1999). Children’s understanding of equality: A foundation for algebra. Teaching Children Mathematics, 6 (4), 232‐6.
  • Ferna´ndez, C., Llinares, S. & Valls, J. (2012). Learning to notice students’ mathematical thinking through on‐ line discussions. ZDM MathematicsEducation, 44(6), 747–759.
  • Fisher, M. H.; Thomas, J.; Jong, C.; Schack, E. O. & Dueber, D. (2019). Comparing preservice teachers’ professional noticing skills in elementary mathematics classrooms. School Science and Mathematics, v119 n3 p142‐149.
  • Goodwin, C. (1994). Professional vision. American Anthropologist, 96(3), 606–633.
  • Hines, E. & McMahon, M. T. (2005). Interpreting middle school students’ proportional reasoning strategies: observations from prospective teachers. School Science and Mathematics, 105(2), 88–105
  • Hitchcock, G.,& Hughes, D. (1995). Research and the teacher (2nd ed.). London: Routledge.
  • Holt, P., Mojica, G. & Confrey, J. (2013). Learning trajectories in teacher education: Sup‐porting teachers’ understandings of students’ mathematical thinking. Journal of Mathematical Behavior. 32, 103‐121. doi: 10.1016/j.jmathb.2012.12.003
  • Jacobs, V R., Franke, M. L., Carpenter, T. P., Levi, L., & Battey, D. (2007). Professional development focused on childrenʹs algebraic reasoning in elementary school. Journal for Research in Mathematics Education, 38, 258‐288
  • Jacobs, V. R., Lamb, L. & Philipp, R. A. (2010). Professional noticing of children’s mathematical thinking. Journal for Research in Mathematics Education. 41(2), 169–202.
  • Kieran, C. (1981). Concepts associated with the equality symbol. Educational Studies in Mathematics. 12(3), 317‐326
  • Kieran, C. (1992). The learning and teaching of school algebra. In D. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 390–419). New York, NY: Macmillan.
  • Knuth, E. J., Stephens, A. C., McNeil, N. M., & Alibali, M. (2006). Does understanding of the equal sign matter? Evidence from solving equations. Journal for Research in Mathematics Education. 37, 297–312.
  • Macgregor, M. & Stacey, K. (1997). Students’ understanding of algebraic notation: 11‐15. Educational Studies in Mathematics. 33, 1‐19.
  • Mason, J. (2002). Researching your own practice: The discipline of noticing. New York, NY: Routledge.
  • Matthews, P., Rittle‐Johnson, B., McEldon, K., & Taylor, R. (2012). Measure for measure: What combining diverse measures reveals about children’s understanding of the equal sign as an indicator of mathematical equality. Journal for Research in Mathematics Education. 43(3), 316–350.
  • MEB. (2005). İlköğretim hayat bilgisi, matematik, sosyal bilgiler, türkçe, fen ve teknoloji dersi öğretim programlarında değişiklik yapılması. Milli Eğitim Bakanlığı Tebliğler Dergisi. Ankara: MEB Yayınları.
  • MEB. (2018). Turkish National Education Curriculum. http://mufredat.meb.gov.tr/Dosyalar/201813017165445
  • MATEMAT%C4%B0K%20%C3%96%C4%9ERET%C4%B0M%20PROGRAMI%202018v.pdf (14.05.2019)
  • McNeil, N. M., & Alibali, M. W. (2000). Learning mathematics from procedural instruction: Externally imposed goals influence what is learned. Journal of Educational Psychology. 92, 734–744.
  • McNeil, N. M. & Alibali, M. W. (2005). Knowledge change as a function of mathematics experience: All contexts are not created equal. Journal of Cognition and Development. 6(2), 285‐306.
  • National Research Council. (1998). The nature and role of algebra in the K‐14 curriculum. Washington, DC: National Academy Press.
  • Schack, E.,Fisher, M., Thomas, J., Eisenhardt, S., Tassell, J. & Yoder, M. (2013). Prospective elementary school teachers’ professional noticing of children’s early numeracy. Journal of MathematicsTeacherEducation, 16, 379‐397.
  • Schack, E. O., Fisher, M. H., & Wilhelm, J. (Eds.). (2017). Teacher noticing—Bridging and broadening perspectives, contexts, and frameworks. New York, NY: Springer.
  • Sherin, M. G., Jacobs, V. R., & Philipp, R. A. (Eds.). (2011). Mathematics teacher noticing: Seeing through teachers’ eyes. New York: Routledge.
  • Sherman, J.,& Bisanz, J. (2009). Equivalence in symbolic and nonsymbolic contexts: Benefits of solving problems with manipulatives. Journal of Educational Psychology. 101(1), 88–100. doi:10. 1037/a0013156
  • Star, J. R.,& Strickland, S. K. (2008). Learning to observe: Using video to improve preservice mathematics teachers’ ability to notice. Journal of Mathematics Teacher Education. 11(2), 107–125.
  • Stephens, A. C. (2006). Equivalence and relational thinking: Preservice elementary teachers’ awareness of opportunities and misconceptions. Journal of Mathematics Teacher Education, 9, 249‐278. doi: 10.1007/s10857‐006‐9000‐1
  • Van Es, E.,& Sherin, M. G. (2002). Learning to notice: Scaffolding new teachers’ interpretations of classroom interactions. Journal of Technology and Teacher Education. 10(4), 571–596.
  • Van den Kieboom, Magiera & Moyer(2017). Van den Kieboom, L., Magiera, M. T. ve Moyer, J. (2017). Learning to notice student thinking about the equal sign: K‐8 pre‐service teachers’ experiences in a teacher preparation program. In E. O., Schack, M. H., Fisher, ve J. Wilhelm, (Eds.), Teacher noticing – Bridging and broadening perspectives, contexts, and frameworks, (s. 141‐159). New York, NY: Springer. doi:10.1007/978‐3‐319‐46753‐5_9
  • Yıldırım, A. & Şimşek, H. (2008). Sosyal Bilimlerde Nitel Araştırma Yöntemleri (7. Baskı). Ankara: Seçkin Yayıncılık.

Secondary School Students’Attitudes towards the Concept of Equality and Preservice Teachers’ Professional Noticing

Year 2019, Volume: 6 Issue: 3, 49 - 60, 01.09.2019

Abstract

With the understanding of importance of pedagogical content knowledge, professional noticing has become one of the research subjects of the mathematics educators for the last 10 years. This qualitative study which explores secondary school students’ solution processes regarding the concept of equation ,one of the main components of algebraic learning field and the pre-service teachers’ noticing about this is quite rich in terms of its results. The 6th, 7th, and 8th graders’ attitudes towards equations were revealed and it was found as stated in literature that students were dominantly “computational thinkers”. However, the differences in this general concept of thinking seem to make contribution to literature by involving discrete attitudes. In addition to this, the secondary findings of the study include some evidence revealing that pre-service teachers’ level of noticing accumulates at middle levels but they can be improved.

References

  • Alibali, M., Knuth, E. J., Hattikudur, S., McNeil, N. M., & Stephens, A. C. (2007). A longitudinal examination of middle school students’ understanding of the equal sign and equivalent equations. Mathematical Thinking and Learning, 9(3), 221–247.
  • Alibali, M. W. (1999). How children change their minds: Strategy change can be gradual or abrupt. Developmental Psychology, 35(1): 127–145.
  • Asquith, P., Stephens, A., Knuth, E., & Alibali, M. (2007). Middle school mathematics teachers’ knowledge of students’ understanding of core algebraic concepts: Equal sign and variable. Mathematical Thinking and Learning, 9(3), 249–272.
  • Ball, D. (1990). Prospective elementary and post primary level teachers understanding of division. Journal for Research in Mathematics Education, 21(2), 132–144.
  • Bartell, T. G., Webel, C., Bowen, B. & Dyson, N. (2013). Prospective teacher learning: recognizing evidence of conceptual understanding. Journal of MathematicsTeacher Education, 16(1), 57–79.
  • Callejo, M. L. & Zapatera, A. (2017). Prospective primary teachers’ noticing of students’ understanding of pattern generalization. Journal of Mathematics Teacher Education, 20(4), 309–333.
  • Carpenter, T., Franke, M., & Levi, L. (2003). Thinking mathematically: Integrating arithmetic and algebra in elementary school. Portsmouth, NH: Heinemann.
  • Carpenter, T. P., Levi, L., Franke, M. L., & Zeringue, J. K. (2005) Algebra in elementary school: Developing relational thinking, ZDM, 37(1), 53‐59
  • Driver, M. K.,& Powell, S. R. (2015). Symbolic and nonsymbolic equivalence tasks: The influence of symbols on students with mathematics difficulty. Learning Disabilities Research and Practice, 30(3), 127–134. doi:10.1111/ldrp.12059
  • Falkner, K.P., Levi, L. & Carpenter, T.P. (1999). Children’s understanding of equality: A foundation for algebra. Teaching Children Mathematics, 6 (4), 232‐6.
  • Ferna´ndez, C., Llinares, S. & Valls, J. (2012). Learning to notice students’ mathematical thinking through on‐ line discussions. ZDM MathematicsEducation, 44(6), 747–759.
  • Fisher, M. H.; Thomas, J.; Jong, C.; Schack, E. O. & Dueber, D. (2019). Comparing preservice teachers’ professional noticing skills in elementary mathematics classrooms. School Science and Mathematics, v119 n3 p142‐149.
  • Goodwin, C. (1994). Professional vision. American Anthropologist, 96(3), 606–633.
  • Hines, E. & McMahon, M. T. (2005). Interpreting middle school students’ proportional reasoning strategies: observations from prospective teachers. School Science and Mathematics, 105(2), 88–105
  • Hitchcock, G.,& Hughes, D. (1995). Research and the teacher (2nd ed.). London: Routledge.
  • Holt, P., Mojica, G. & Confrey, J. (2013). Learning trajectories in teacher education: Sup‐porting teachers’ understandings of students’ mathematical thinking. Journal of Mathematical Behavior. 32, 103‐121. doi: 10.1016/j.jmathb.2012.12.003
  • Jacobs, V R., Franke, M. L., Carpenter, T. P., Levi, L., & Battey, D. (2007). Professional development focused on childrenʹs algebraic reasoning in elementary school. Journal for Research in Mathematics Education, 38, 258‐288
  • Jacobs, V. R., Lamb, L. & Philipp, R. A. (2010). Professional noticing of children’s mathematical thinking. Journal for Research in Mathematics Education. 41(2), 169–202.
  • Kieran, C. (1981). Concepts associated with the equality symbol. Educational Studies in Mathematics. 12(3), 317‐326
  • Kieran, C. (1992). The learning and teaching of school algebra. In D. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 390–419). New York, NY: Macmillan.
  • Knuth, E. J., Stephens, A. C., McNeil, N. M., & Alibali, M. (2006). Does understanding of the equal sign matter? Evidence from solving equations. Journal for Research in Mathematics Education. 37, 297–312.
  • Macgregor, M. & Stacey, K. (1997). Students’ understanding of algebraic notation: 11‐15. Educational Studies in Mathematics. 33, 1‐19.
  • Mason, J. (2002). Researching your own practice: The discipline of noticing. New York, NY: Routledge.
  • Matthews, P., Rittle‐Johnson, B., McEldon, K., & Taylor, R. (2012). Measure for measure: What combining diverse measures reveals about children’s understanding of the equal sign as an indicator of mathematical equality. Journal for Research in Mathematics Education. 43(3), 316–350.
  • MEB. (2005). İlköğretim hayat bilgisi, matematik, sosyal bilgiler, türkçe, fen ve teknoloji dersi öğretim programlarında değişiklik yapılması. Milli Eğitim Bakanlığı Tebliğler Dergisi. Ankara: MEB Yayınları.
  • MEB. (2018). Turkish National Education Curriculum. http://mufredat.meb.gov.tr/Dosyalar/201813017165445
  • MATEMAT%C4%B0K%20%C3%96%C4%9ERET%C4%B0M%20PROGRAMI%202018v.pdf (14.05.2019)
  • McNeil, N. M., & Alibali, M. W. (2000). Learning mathematics from procedural instruction: Externally imposed goals influence what is learned. Journal of Educational Psychology. 92, 734–744.
  • McNeil, N. M. & Alibali, M. W. (2005). Knowledge change as a function of mathematics experience: All contexts are not created equal. Journal of Cognition and Development. 6(2), 285‐306.
  • National Research Council. (1998). The nature and role of algebra in the K‐14 curriculum. Washington, DC: National Academy Press.
  • Schack, E.,Fisher, M., Thomas, J., Eisenhardt, S., Tassell, J. & Yoder, M. (2013). Prospective elementary school teachers’ professional noticing of children’s early numeracy. Journal of MathematicsTeacherEducation, 16, 379‐397.
  • Schack, E. O., Fisher, M. H., & Wilhelm, J. (Eds.). (2017). Teacher noticing—Bridging and broadening perspectives, contexts, and frameworks. New York, NY: Springer.
  • Sherin, M. G., Jacobs, V. R., & Philipp, R. A. (Eds.). (2011). Mathematics teacher noticing: Seeing through teachers’ eyes. New York: Routledge.
  • Sherman, J.,& Bisanz, J. (2009). Equivalence in symbolic and nonsymbolic contexts: Benefits of solving problems with manipulatives. Journal of Educational Psychology. 101(1), 88–100. doi:10. 1037/a0013156
  • Star, J. R.,& Strickland, S. K. (2008). Learning to observe: Using video to improve preservice mathematics teachers’ ability to notice. Journal of Mathematics Teacher Education. 11(2), 107–125.
  • Stephens, A. C. (2006). Equivalence and relational thinking: Preservice elementary teachers’ awareness of opportunities and misconceptions. Journal of Mathematics Teacher Education, 9, 249‐278. doi: 10.1007/s10857‐006‐9000‐1
  • Van Es, E.,& Sherin, M. G. (2002). Learning to notice: Scaffolding new teachers’ interpretations of classroom interactions. Journal of Technology and Teacher Education. 10(4), 571–596.
  • Van den Kieboom, Magiera & Moyer(2017). Van den Kieboom, L., Magiera, M. T. ve Moyer, J. (2017). Learning to notice student thinking about the equal sign: K‐8 pre‐service teachers’ experiences in a teacher preparation program. In E. O., Schack, M. H., Fisher, ve J. Wilhelm, (Eds.), Teacher noticing – Bridging and broadening perspectives, contexts, and frameworks, (s. 141‐159). New York, NY: Springer. doi:10.1007/978‐3‐319‐46753‐5_9
  • Yıldırım, A. & Şimşek, H. (2008). Sosyal Bilimlerde Nitel Araştırma Yöntemleri (7. Baskı). Ankara: Seçkin Yayıncılık.
There are 39 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

Seval Deniz Kılıç This is me

Ercan Masal This is me

Publication Date September 1, 2019
Published in Issue Year 2019 Volume: 6 Issue: 3

Cite

APA Kılıç, S. D., & Masal, E. (2019). Secondary School Students’Attitudes towards the Concept of Equality and Preservice Teachers’ Professional Noticing. International Journal of Psychology and Educational Studies, 6(3), 49-60.