Research Article
BibTex RIS Cite
Year 2021, Issue: 27, 103 - 124, 31.07.2021

Abstract

References

  • Barnhart, T., & van Es, E. (2015). Studying teacher noticing: Examining the relationship among pre-service science teachers' ability to attend, analyze and respond to student thinking. Teaching and Teacher Education, 45, 83-93.
  • Blanton, M. L., & Kaput, J. J. (2005). Characterizing a classroom practice that promotes algebraic reasoning. Journal for research in mathematics education, 36(5), 412-446.
  • Brizuela, B., & Schliemann, A. (2004). Ten-year-old students solving linear equations. For the Learning of Mathematics, 24(2), 33-40.
  • 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.
  • Chazan, D. (2000). Beyond formulas in mathematics and teaching: Dynamics of the high school algebra classroom. New York, NY: Teachers College Press.
  • Crespo, S. (2002). Praising and correcting: Prospective teachers investigate their teacherly talk. Teaching and Teacher Education, 18(6), 739-758.
  • Creswell, J. W. (2007). Qualitative inquiry and research design: Choosing among five approaches (2nd Ed.). Thousand Oaks, CA: Sage Publications, Inc.
  • Erickson, F. (2011). On noticing teacher noticing. In M. Sherin, V. Jacobs, & R. Philipp (Eds.), Mathematics teacher noticing: Seeing through teachers' eyes (pp. 17-34). New York, NY: Routledge.
  • Fernández, C., Llinares, S., & Valls, J. (2013). Primary school teacher’s noticing of students’ mathematical thinking in problem solving. The Mathematics Enthusiast, 10(1), 441-468.
  • Ginsburg, H. (1997). Entering the child's mind: The clinical interview in psychological research and practice. New York, NY: Cambridge University Press.
  • Goldsmith, L. T., Seago, N. (2011). Using classroom artifacts to focus teachers’ noticing affordances and opportunities. In M. G. Sherin, V. R. Jacobs, & R. A. Philipp (Eds.), Mathematics teacher noticing: Seeing through teachers eyes (pp. 169-187). New York, NY: Routledge.
  • Ivars, P., Fernández, C., Llinares, S., & Choy, B. H. (2018). Enhancing noticing: Using a hypothetical learning trajectory to improve pre- service primary teachers’ professional discourse. EURASIA Journal of Mathematics, Science and Technology Education, 14(11), em1599.
  • Jacobs, V. R., & Ambrose, R. C. (2008). Making the most of story problems. Teaching children mathematics, 15(5), 260-266.
  • Jacobs, V. R., Lamb, L. L., & Philipp, R. A. (2010). Professional noticing of children's mathematical thinking. Journal for research in mathematics education, 41(2), 169-202.
  • Jacobs, V. R., Lamb, L. L., Philipp, R. A., & Schappelle, B. P. (2011). Deciding how to respond on the basis of children’s understandings. In M. Sherin, V. Jacobs, & R. Philipp (Eds.), Mathematics teacher noticing: Seeing through teachers’ eyes (pp. 97-116). New York, NY: Routledge.
  • Kaput, J. (1999). Teaching and learning a new algebra. In E. Fennama & T. Romberg (Eds.), Mathematics classrooms that promote understanding (pp.133-155). Mahwah, NJ: Erlbaum.
  • Kieran, C. (1992). The learning and teaching of school algebra. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 390-419). New York, NY: Macmillan.
  • Kieran, C. (2004). Algebraic thinking in the early grades: What is it? The Mathematics Educator, 8(1), 139-151.
  • Kilpatrick, J., Swafford, J., & Findell, B. (Eds.). (2001). Adding it up: Helping children learn mathematics. Washington, DC: National Academy Press.
  • LaRochelle, R., Nickerson, S. D., Lamb, L. C., Hawthorne, C., Philipp, R. A., & Ross, D. L. (2019). Secondary practising teachers' professional noticing of students' thinking about pattern generalisation. Mathematics Teacher Education and Development, 21(1), 4-27.
  • Little, J. W., & Curry, M. W. (2008). Structuring talk about teaching and learning: The use of evidence in protocol-based conversation. In L. M. Earl & H. Timperley (Eds.), Professional learning conversations: Challenges in using evidence for improvement (pp. 29-42). New York, NY: Springer.
  • Magiera, M. T., Van den Kieboom, L. A., & Moyer, J. C. (2013). An exploratory study of pre-service middle school teachers’ knowledge of algebraic thinking. Educational Studies in Mathematics, 84(1), 93-113.
  • Mason, J. (2008). Making use of children’s powers to produce algebraic thinking. In J. Kaput, D. Carraher, & M. Blanton (Eds.), Algebra in the early grades (pp. 57–94). New York, NY: Erlbaum.
  • Mason, J. (2011). Noticing: Roots and branches. In M. Sherin, V. Jacobs, & R. Philipp (Eds.), Mathematics teacher noticing: Seeing through teachers’ eyes (pp. 35-50). New York, NY: Routledge.
  • Merriam, S. B. (2009). Qualitative research: A guide to design and implementation. San Francisco, CA: Jossey-Bass.
  • Milewski, A., & Strickland, S. (2016). (Toward) developing a common language for describing instructional practices of responding: A teacher-generated framework. Mathematics Teacher Educator, 4(2), 126-144.
  • Miller, K. F. (2011). Situation awareness in teaching: What educators can learn from video-based research in other fields. In Sherin, M. G., Jacobs, V. R., & Philipp, R. A. (Eds.), Mathematics teacher noticing: Seeing through teachers’ eyes (p. 51- 65). New York, NY: Routledge.
  • Ministry of National Education (MoNE). (2018). Mathematics program [Elementary and Middle School 1, 2, 3, 4, 5, 6, 7, and 8 grades]. Ankara, Turkey: MoNE.
  • Mouhayar, R. (2019). Exploring teachers’ attention to students’ responses in pattern generalization tasks. Journal of Mathematics Teacher Education, 22(6), 575-605.
  • Mouhayar, R. R., & Jurdak, M. E. (2013). Teachers’ ability to identify and explain students’ actions in near and far figural pattern generalization tasks. Educational Studies in Mathematics, 82(3), 379-396.
  • National Council of Teachers of Mathematics (NCTM). (2000). Learning mathematics for a new century (2000 Yearbook). Reston, VA: NCTM.
  • National Council of Teachers of Mathematics (NCTM). (2014). Principles to actions: Ensuring mathematical success for all. Reston, VA: NCTM.
  • Radford, L., & Sabena, C. (2015). The question of method in a Vygotskian semiotic approach. In A. Bikner-Ahsbahs, C. Knipping, & N. Presmeg (Eds.), Approaches to qualitative research in mathematics education (pp. 157–182). New York, NY: Springer.
  • Rivera, F., & Becker, J. R. (2003). The effects of figural and numerical cues on the induction processes of preservice elementary teachers. In N. Pateman, B. Dougherty, & J. Zilliox (Eds.), Proceedings of the Joint Meeting PME and PMENA (Vol. 4, pp. 63–70). Honolulu, HA: University of Hawaii.
  • Sánchez-Matamoros, G., Fernández, C., & Llinares, S. (2019). Relationships among prospective secondary mathematics teachers’ skills of attending, interpreting and responding to students’ understanding. Educational Studies in Mathematics, 100(1), 83-99.
  • Santagata, R., Zannoni, C., & Stigler, J. W. (2007). The role of lesson analysis in pre-service teacher education: An empirical investigation of teacher learning from a virtual video-based field experience. Journal of mathematics teacher education, 10(2), 123-140.
  • Schoenfeld, A. H. (2011). Noticing matters. A lot. Now what? In M. Sherin, V. Jacobs, & R. Philipp (Eds.), Mathematics teacher noticing: Seeing through teachers' eyes (pp. 253-268). New York, NY: Routledge.
  • Sherin, M. G. (2007). The development of teachers' professional vision in video clubs. In R. Goldman, R. Pea, B. Barron, & S. J. Deny (Eds.), Video research in the learning sciences (pp. 383-395). Mahwah, NJ: Erlbaum.
  • Sherin, M. G., Jacobs, V. R., & Philipp, R. A. (Eds.). (2011). Mathematics teacher noticing: Seeing through teachers’ eyes. New York, NY: Routledge.
  • Sherin, B., & Star, J. R. (2011). Reflections on the study of teacher noticing. In M. Sherin, V. Jacobs, & R. Philipp (Eds.), Mathematics teacher noticing: Seeing through teachers' eyes (pp. 66-78). New York, NY: Routledge.
  • Simpson, A., & Haltiwanger, L. (2017). “This is the First Time I’ve Done This”: Exploring secondary prospective mathematics teachers’ noticing of students’ mathematical thinking. Journal of Mathematics Teacher Education, 20(4), 335–355.
  • Son, J. W., & Crespo, S. (2009). Prospective teachers’ reasoning and response to a student’s non-traditional strategy when dividing fractions. Journal of Mathematics Teacher Education, 12(4), 235-261.
  • 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.
  • Stevens, R., & Hall, R. (1998). Disciplined perception: Learning to see in technoscience. In M. Lampert & M. L. Blunk (Eds.), Talking mathematics in school: Studies of teaching and learning (pp. 107-149). Cambridge, UK: Cambridge University Press.
  • Stockero, S. L. (2014). Transitions in prospective mathematics teachers’ noticing. In J. Lo, K. R. Leatham, & L. R. Van Zoest (Eds.), Research trends in mathematics teacher education (pp. 239–259). New York, NY: Springer.
  • Usiskin, Z. (1988). Conceptions of school algebra and uses of variable. In A. F. Coxford & A. P. Shulte (Eds.), The ideas of algebra, K-12: 1988 Yearbook (pp. 8-19). Reston, VA: NCTM.
  • van Es, E. A., & Sherin, M. G. (2002). Learning to notice: Scaffolding new teachers’ interpretations of classroom interactions. Journal of Technology and Teacher Education, 10(4), 571-596.
  • Wager, A. A. (2014). Noticing children's participation: Insights into teacher positionality toward equitable mathematics pedagogy. Journal for Research in Mathematics Education, 45(3), 312-350.
  • Wilson, P. H., Mojica, G. F., & Confrey, J. (2013). Learning trajectories in teacher education: Supporting teachers’ understandings of students’ mathematical thinking. The Journal of Mathematical Behavior, 32(2), 103-121.
  • Yin, R. K. (2009). Case study research: Design and methods (4th Ed.). Thousand Oaks, CA: Sage Publications, Inc.

How Do Pre-service Elementary Teachers Notice Students’ Algebraic Way of Thinking in Written Works?

Year 2021, Issue: 27, 103 - 124, 31.07.2021

Abstract

The purpose of this embedded-single case study was to examine pre-service elementary teachers’ noticing expertise of students’ algebraic thinking in written works considering three skills: attention to students’ solutions, interpretation of students’ solutions, and deciding how to respond to students’ solutions. The participants in this study involved 32 pre-service teachers who were enrolled at an Elementary Teacher Education Program in a public university in Turkey. The data were utilized by pre-service elementary teachers’ responses to four students’ solutions to a figural pattern task and were analyzed using the framework developed by Jacobs et al. (2010). The analysis indicated although the pre-service teachers could not provide robust evidence of attention and interpretation, they could be able to provide robust evidence of deciding how to respond. Specifically, the percentage of pre-service teachers demonstrating robust evidence was greatest in the skill of deciding how to respond, then interpreting, with attending having the lowest percentage of pre-service teachers demonstrating robust evidence.

References

  • Barnhart, T., & van Es, E. (2015). Studying teacher noticing: Examining the relationship among pre-service science teachers' ability to attend, analyze and respond to student thinking. Teaching and Teacher Education, 45, 83-93.
  • Blanton, M. L., & Kaput, J. J. (2005). Characterizing a classroom practice that promotes algebraic reasoning. Journal for research in mathematics education, 36(5), 412-446.
  • Brizuela, B., & Schliemann, A. (2004). Ten-year-old students solving linear equations. For the Learning of Mathematics, 24(2), 33-40.
  • 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.
  • Chazan, D. (2000). Beyond formulas in mathematics and teaching: Dynamics of the high school algebra classroom. New York, NY: Teachers College Press.
  • Crespo, S. (2002). Praising and correcting: Prospective teachers investigate their teacherly talk. Teaching and Teacher Education, 18(6), 739-758.
  • Creswell, J. W. (2007). Qualitative inquiry and research design: Choosing among five approaches (2nd Ed.). Thousand Oaks, CA: Sage Publications, Inc.
  • Erickson, F. (2011). On noticing teacher noticing. In M. Sherin, V. Jacobs, & R. Philipp (Eds.), Mathematics teacher noticing: Seeing through teachers' eyes (pp. 17-34). New York, NY: Routledge.
  • Fernández, C., Llinares, S., & Valls, J. (2013). Primary school teacher’s noticing of students’ mathematical thinking in problem solving. The Mathematics Enthusiast, 10(1), 441-468.
  • Ginsburg, H. (1997). Entering the child's mind: The clinical interview in psychological research and practice. New York, NY: Cambridge University Press.
  • Goldsmith, L. T., Seago, N. (2011). Using classroom artifacts to focus teachers’ noticing affordances and opportunities. In M. G. Sherin, V. R. Jacobs, & R. A. Philipp (Eds.), Mathematics teacher noticing: Seeing through teachers eyes (pp. 169-187). New York, NY: Routledge.
  • Ivars, P., Fernández, C., Llinares, S., & Choy, B. H. (2018). Enhancing noticing: Using a hypothetical learning trajectory to improve pre- service primary teachers’ professional discourse. EURASIA Journal of Mathematics, Science and Technology Education, 14(11), em1599.
  • Jacobs, V. R., & Ambrose, R. C. (2008). Making the most of story problems. Teaching children mathematics, 15(5), 260-266.
  • Jacobs, V. R., Lamb, L. L., & Philipp, R. A. (2010). Professional noticing of children's mathematical thinking. Journal for research in mathematics education, 41(2), 169-202.
  • Jacobs, V. R., Lamb, L. L., Philipp, R. A., & Schappelle, B. P. (2011). Deciding how to respond on the basis of children’s understandings. In M. Sherin, V. Jacobs, & R. Philipp (Eds.), Mathematics teacher noticing: Seeing through teachers’ eyes (pp. 97-116). New York, NY: Routledge.
  • Kaput, J. (1999). Teaching and learning a new algebra. In E. Fennama & T. Romberg (Eds.), Mathematics classrooms that promote understanding (pp.133-155). Mahwah, NJ: Erlbaum.
  • Kieran, C. (1992). The learning and teaching of school algebra. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 390-419). New York, NY: Macmillan.
  • Kieran, C. (2004). Algebraic thinking in the early grades: What is it? The Mathematics Educator, 8(1), 139-151.
  • Kilpatrick, J., Swafford, J., & Findell, B. (Eds.). (2001). Adding it up: Helping children learn mathematics. Washington, DC: National Academy Press.
  • LaRochelle, R., Nickerson, S. D., Lamb, L. C., Hawthorne, C., Philipp, R. A., & Ross, D. L. (2019). Secondary practising teachers' professional noticing of students' thinking about pattern generalisation. Mathematics Teacher Education and Development, 21(1), 4-27.
  • Little, J. W., & Curry, M. W. (2008). Structuring talk about teaching and learning: The use of evidence in protocol-based conversation. In L. M. Earl & H. Timperley (Eds.), Professional learning conversations: Challenges in using evidence for improvement (pp. 29-42). New York, NY: Springer.
  • Magiera, M. T., Van den Kieboom, L. A., & Moyer, J. C. (2013). An exploratory study of pre-service middle school teachers’ knowledge of algebraic thinking. Educational Studies in Mathematics, 84(1), 93-113.
  • Mason, J. (2008). Making use of children’s powers to produce algebraic thinking. In J. Kaput, D. Carraher, & M. Blanton (Eds.), Algebra in the early grades (pp. 57–94). New York, NY: Erlbaum.
  • Mason, J. (2011). Noticing: Roots and branches. In M. Sherin, V. Jacobs, & R. Philipp (Eds.), Mathematics teacher noticing: Seeing through teachers’ eyes (pp. 35-50). New York, NY: Routledge.
  • Merriam, S. B. (2009). Qualitative research: A guide to design and implementation. San Francisco, CA: Jossey-Bass.
  • Milewski, A., & Strickland, S. (2016). (Toward) developing a common language for describing instructional practices of responding: A teacher-generated framework. Mathematics Teacher Educator, 4(2), 126-144.
  • Miller, K. F. (2011). Situation awareness in teaching: What educators can learn from video-based research in other fields. In Sherin, M. G., Jacobs, V. R., & Philipp, R. A. (Eds.), Mathematics teacher noticing: Seeing through teachers’ eyes (p. 51- 65). New York, NY: Routledge.
  • Ministry of National Education (MoNE). (2018). Mathematics program [Elementary and Middle School 1, 2, 3, 4, 5, 6, 7, and 8 grades]. Ankara, Turkey: MoNE.
  • Mouhayar, R. (2019). Exploring teachers’ attention to students’ responses in pattern generalization tasks. Journal of Mathematics Teacher Education, 22(6), 575-605.
  • Mouhayar, R. R., & Jurdak, M. E. (2013). Teachers’ ability to identify and explain students’ actions in near and far figural pattern generalization tasks. Educational Studies in Mathematics, 82(3), 379-396.
  • National Council of Teachers of Mathematics (NCTM). (2000). Learning mathematics for a new century (2000 Yearbook). Reston, VA: NCTM.
  • National Council of Teachers of Mathematics (NCTM). (2014). Principles to actions: Ensuring mathematical success for all. Reston, VA: NCTM.
  • Radford, L., & Sabena, C. (2015). The question of method in a Vygotskian semiotic approach. In A. Bikner-Ahsbahs, C. Knipping, & N. Presmeg (Eds.), Approaches to qualitative research in mathematics education (pp. 157–182). New York, NY: Springer.
  • Rivera, F., & Becker, J. R. (2003). The effects of figural and numerical cues on the induction processes of preservice elementary teachers. In N. Pateman, B. Dougherty, & J. Zilliox (Eds.), Proceedings of the Joint Meeting PME and PMENA (Vol. 4, pp. 63–70). Honolulu, HA: University of Hawaii.
  • Sánchez-Matamoros, G., Fernández, C., & Llinares, S. (2019). Relationships among prospective secondary mathematics teachers’ skills of attending, interpreting and responding to students’ understanding. Educational Studies in Mathematics, 100(1), 83-99.
  • Santagata, R., Zannoni, C., & Stigler, J. W. (2007). The role of lesson analysis in pre-service teacher education: An empirical investigation of teacher learning from a virtual video-based field experience. Journal of mathematics teacher education, 10(2), 123-140.
  • Schoenfeld, A. H. (2011). Noticing matters. A lot. Now what? In M. Sherin, V. Jacobs, & R. Philipp (Eds.), Mathematics teacher noticing: Seeing through teachers' eyes (pp. 253-268). New York, NY: Routledge.
  • Sherin, M. G. (2007). The development of teachers' professional vision in video clubs. In R. Goldman, R. Pea, B. Barron, & S. J. Deny (Eds.), Video research in the learning sciences (pp. 383-395). Mahwah, NJ: Erlbaum.
  • Sherin, M. G., Jacobs, V. R., & Philipp, R. A. (Eds.). (2011). Mathematics teacher noticing: Seeing through teachers’ eyes. New York, NY: Routledge.
  • Sherin, B., & Star, J. R. (2011). Reflections on the study of teacher noticing. In M. Sherin, V. Jacobs, & R. Philipp (Eds.), Mathematics teacher noticing: Seeing through teachers' eyes (pp. 66-78). New York, NY: Routledge.
  • Simpson, A., & Haltiwanger, L. (2017). “This is the First Time I’ve Done This”: Exploring secondary prospective mathematics teachers’ noticing of students’ mathematical thinking. Journal of Mathematics Teacher Education, 20(4), 335–355.
  • Son, J. W., & Crespo, S. (2009). Prospective teachers’ reasoning and response to a student’s non-traditional strategy when dividing fractions. Journal of Mathematics Teacher Education, 12(4), 235-261.
  • 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.
  • Stevens, R., & Hall, R. (1998). Disciplined perception: Learning to see in technoscience. In M. Lampert & M. L. Blunk (Eds.), Talking mathematics in school: Studies of teaching and learning (pp. 107-149). Cambridge, UK: Cambridge University Press.
  • Stockero, S. L. (2014). Transitions in prospective mathematics teachers’ noticing. In J. Lo, K. R. Leatham, & L. R. Van Zoest (Eds.), Research trends in mathematics teacher education (pp. 239–259). New York, NY: Springer.
  • Usiskin, Z. (1988). Conceptions of school algebra and uses of variable. In A. F. Coxford & A. P. Shulte (Eds.), The ideas of algebra, K-12: 1988 Yearbook (pp. 8-19). Reston, VA: NCTM.
  • van Es, E. A., & Sherin, M. G. (2002). Learning to notice: Scaffolding new teachers’ interpretations of classroom interactions. Journal of Technology and Teacher Education, 10(4), 571-596.
  • Wager, A. A. (2014). Noticing children's participation: Insights into teacher positionality toward equitable mathematics pedagogy. Journal for Research in Mathematics Education, 45(3), 312-350.
  • Wilson, P. H., Mojica, G. F., & Confrey, J. (2013). Learning trajectories in teacher education: Supporting teachers’ understandings of students’ mathematical thinking. The Journal of Mathematical Behavior, 32(2), 103-121.
  • Yin, R. K. (2009). Case study research: Design and methods (4th Ed.). Thousand Oaks, CA: Sage Publications, Inc.
There are 50 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

Sümeyra Doğan Coşkun

Publication Date July 31, 2021
Published in Issue Year 2021 Issue: 27

Cite

APA Doğan Coşkun, S. (2021). How Do Pre-service Elementary Teachers Notice Students’ Algebraic Way of Thinking in Written Works?. Eğitimde Nitel Araştırmalar Dergisi(27), 103-124.
AMA Doğan Coşkun S. How Do Pre-service Elementary Teachers Notice Students’ Algebraic Way of Thinking in Written Works?. Derginin Amacı ve Kapsamı. July 2021;(27):103-124.
Chicago Doğan Coşkun, Sümeyra. “How Do Pre-Service Elementary Teachers Notice Students’ Algebraic Way of Thinking in Written Works?”. Eğitimde Nitel Araştırmalar Dergisi, no. 27 (July 2021): 103-24.
EndNote Doğan Coşkun S (July 1, 2021) How Do Pre-service Elementary Teachers Notice Students’ Algebraic Way of Thinking in Written Works?. Eğitimde Nitel Araştırmalar Dergisi 27 103–124.
IEEE S. Doğan Coşkun, “How Do Pre-service Elementary Teachers Notice Students’ Algebraic Way of Thinking in Written Works?”, Derginin Amacı ve Kapsamı, no. 27, pp. 103–124, July 2021.
ISNAD Doğan Coşkun, Sümeyra. “How Do Pre-Service Elementary Teachers Notice Students’ Algebraic Way of Thinking in Written Works?”. Eğitimde Nitel Araştırmalar Dergisi 27 (July 2021), 103-124.
JAMA Doğan Coşkun S. How Do Pre-service Elementary Teachers Notice Students’ Algebraic Way of Thinking in Written Works?. Derginin Amacı ve Kapsamı. 2021;:103–124.
MLA Doğan Coşkun, Sümeyra. “How Do Pre-Service Elementary Teachers Notice Students’ Algebraic Way of Thinking in Written Works?”. Eğitimde Nitel Araştırmalar Dergisi, no. 27, 2021, pp. 103-24.
Vancouver Doğan Coşkun S. How Do Pre-service Elementary Teachers Notice Students’ Algebraic Way of Thinking in Written Works?. Derginin Amacı ve Kapsamı. 2021(27):103-24.