Noticing Student Mathematical Thinking: Self-Contemplation of a Pre-Service Teacher

Serife Sevinc 1 * , Enrique Galindo 2
More Detail
1 Mathematics and Science Education, Middle East Technical University, Ankara, TURKEY
2 Mathematics Education, Indiana University Bloomington, Indiana, USA
* Corresponding Author
EUR J SCI MATH ED, Volume 10, Issue 2, pp. 154-169. https://doi.org/10.30935/scimath/11489
Published: 03 January 2022
OPEN ACCESS   1887 Views   1328 Downloads
Download Full Text (PDF)

ABSTRACT

This study focused on a pre-service teacher’s self-contemplations about the two opportunities provided in a field experience course, Formative Assessment Interviews (FAIs) and Model Building (MB), which were designed to support pre-service teachers developing the skills of noticing students’ mathematical thinking. In the field experience, pre-service teachers conducted FAIs with a pair of children and participated in MB sessions to hypothesize students’ mathematical thinking. The findings suggest that although the pre-service teacher, Gloria, experienced some challenges, FAIs and MBs created a supportive medium for the pre-service teacher’s development of noticing student thinking and appreciating the value of this practice, which is important to gain in teacher education.
Keywords: pre-service teacher education, noticing student thinking, field experience, formative assessment interview, mathematics education

CITATION

Sevinc, S., & Galindo, E. (2022). Noticing Student Mathematical Thinking: Self-Contemplation of a Pre-Service Teacher. European Journal of Science and Mathematics Education, 10(2), 154-169. https://doi.org/10.30935/scimath/11489

REFERENCES

  • Alatorre, S., & Sáiz, M. (2009). Teachers and triangles. In V. Durand-Guerrier, S. Soury-Lavergne, & F. Arzarello (Eds.), Proceedings of CERME 6-working group 10 (pp. 1980-1900). INRP.
  • Amador, J. M., & Carter, I. S. (2018). Audible conversational affordances and constraints of verbalizing professional noticing during prospective teacher lesson study. Journal of Mathematics Teacher Education, 21, 5-34. https://doi.org/10.1007/s10857-016-9347-x
  • An, S., & Wu, Z. (2012). Enhancing mathematics teachers’ knowledge of students’ thinking from assessing and analyzing misconceptions in homework. International Journal of Science and Mathematics Education, 10(3), 717-753. https://doi.org/10.1007/s10763-011-9324-x
  • 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
  • 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. https://doi.org/10.1016/j.tate.2014.09.005
  • Carpenter, T. P., Fennema, E., & Romberg, T. A. (Eds.). (1993). Rational numbers: An integration of research. Lawrence Erlbaum Associates.
  • Carpenter, T. P., Fennema, E., Franke, M. L, Levi, L., & Empson, S. B. (2000). Cognitively guided instruction: A research-based teacher professional development program for elementary school mathematics (National Center for Improving Student Learning and Achievement in Mathematics and Science, Report No. 003). Wisconsin Centre for Education Research. The University of Wisconsin-Madison.
  • Chung, H. Q., & van Es, E. A. (2014). Pre-service teachers’ use of tools to systematically analyze teaching and learning, Teachers and Teaching: Theory and Practice, 20(2), 113-135. https://doi.org/10.1080/13540602.2013.848567
  • Creswell, J. W. (2007). Qualitative inquiry and research design: Choosing among five approaches. Thousand Oaks, CA: Sage.
  • Da Ponte, J. P., & Chapman, O. (2006). Mathematics teachers’ knowledge and practices. In A. Gutiérrez & P. Boero (Eds.), Handbook of research on the psychology of mathematics education: Past, present and future (pp. 461-494). Sense Publishers. https://doi.org/10.1163/9789087901127_017
  • Danielowich, R. M. (2014). Shifting the reflective focus: Encouraging student teacher learning in video-framed and peer-sharing contexts, Teachers and Teaching: Theory and Practice, 20(3), 264-288. https://doi.org/10.1080/13540602.2013.848522
  • Doerr, H. M., & Lesh, R. (2003). A modeling perspective on teacher development. In R. Lesh & H. M. Doerr (Eds.), Beyond constructivism: A models and modeling perspective (pp. 125-140). Lawrence Erlbaum Associates.
  • Fennema, E., Carpenter, T. P., & Franke, M. L. (1992). Cognitively guided instruction. The Teaching and Learning of Mathematics, 1(2), 5-9.
  • Grossman, P. L. (1990). The making of a teacher: Teacher knowledge and teacher education. New York: Teachers College Press.
  • Grossman, P., Hammerness, K., & McDonald, M. (2009). Redefining teaching, re‐imagining teacher education, Teachers and Teaching: Theory and Practice, 15(2), 273-289. https://doi.org/10.1080/13540600902875340
  • Gutiérrez, A., & Jaime, A. (1998). On the assessment of the Van Hiele levels of reasoning. Focus on Learning Problems in Mathematics, 20, 27-46.
  • Hershkowitz, R., & Vinner, S. (1984). Children’s concepts in elementary geometry: A reflection of teacher’s concepts? In B. Southwell (Ed.), Proceedings of the 8th PME International Conference (pp. 63-69). Darlinghurst, Australia: Mathematical Association of New South.
  • Hodson, E., Smith, K., & Brown, T. (2012). Reasserting theory in professionally based initial teacher education, Teachers and Teaching: Theory and Practice, 18(2), 181-195. https://doi.org/10.1080/13540602.2012.632269
  • Jacobs, V. R., Lamb, L. L., & Philipp, R. A. (2010). Professional noticing of children’s mathematical thinking. Journal for Research in Mathematics Education, 41, 169-202. https://doi.org/10.5951/jresematheduc.41.2.0169
  • Jenkins, O. F. (2010). Developing teachers’ knowledge of students as learners of mathematics through structured interviews. Journal of Mathematics Teacher Education, 13(2), 141-154. https://doi.org/10.1007/s10857-009-9129-9
  • Kleinknecht, M., & Gröschner, A. (2016). Fostering preservice teachers’ noticing with structures video feedback: Results of an online- and video-based intervention study. Teaching and Teacher Education, 59, 45-56. https://doi.org/10.1016/j.tate.2016.05.020
  • Kleinknecht, M., & Schneider, J. (2013). What do teachers’ think and feel when analyzing videos of themselves and other teachers teaching? Teaching and Teacher Education, 33, 13-23. https://doi.org/10.1016/j.tate.2013.02.002
  • Koellner-Clark, K., & Lesh, R. (2003). A modeling approach to describe teacher knowledge. In R. Lesh & H. M. Doerr (Eds.), Beyond constructivism: A models and modeling perspective (pp. 159-173). Lawrence Erlbaum Associates.
  • Korthagen, F. A. J., & Wubbels, T. (2001). Learning from practice. In Linking practice and theory: The pedagogy of realistic teacher education (pp. 32-50). Mahwah, NJ: Lawrence Erlbaum. https://doi.org/10.4324/9781410600523
  • Lee, M. Y. (2018). Further investigation into the quality of teachers’ noticing expertise: A proposed framework for evaluating teachers’ models of students’ mathematical thinking. EURASIA Journal of Mathematics, Science and Technology Education, 14(11), 1-15. https://doi.org/10.29333/ejmste/92019
  • Lesh, R. (2006). New directions for research on mathematical problem solving. http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.554.5643&rep=rep1&type=pdf
  • Lesh, R., & Lehrer, R. (2003). Models and modeling perspectives on the development of students and teachers. Mathematical Thinking and Learning, 5(2, 3), 109-129. https://doi.org/10.1080/10986065.2003.9679996
  • Lewis, C. (2000). Lesson study: The core of Japanese professional development [Paper presentation]. Annual Meeting of the American Educational Research Association, New Orleans, LA, USA.
  • Lingefjärd, T. (2002). Teaching and assessing mathematical modeling. Teaching Mathematics and Its Applications, 21(2), 75-83. https://doi.org/10.1093/teamat/21.2.75
  • Mayer, D., & Marland, P. (1997). Teachers’ knowledge of students: A significant domain of practical knowledge? Asia-Pacific Journal of Teacher Education, 25, 17-34. https://doi.org/10.1080/1359866970250103
  • McCaughtry, N. (2005). Elaborating pedagogical content knowledge: What it means to know students and think about teaching, Teachers and Teaching: Theory and Practice, 11(4), 379-395. https://doi.org/10.1080/13450600500137158
  • McDuffie, A. R., Foote, M. Q., Bolson, C., Turner, E. E., Aguirre, J. M., Bartell, T. G., Drake, C., & Land, T. (2014). Using video analysis to support prospective K-8 teachers’ noticing of students’ multiple mathematical knowledge bases. Journal of Mathematics Teacher Education, 17, 245-270. https://doi.org/10.1007/s10857-013-9257-0
  • Norton, A., McCloskey, A., & Hudson, R. A. (2011). Prediction assessments: Using video-based predictions to assess prospective teachers’ knowledge of students’ mathematical thinking, Journal of Mathematics Teacher Education, 14, 305-325. https://doi.org/10.1007/s10857-011-9181-0
  • Patton, M. Q. (2002). Qualitative research and evaluation methods (3rd ed.). Sage.
  • Paulus, T., Lester, J., & Dempster, P. (2014). Digital tools for qualitative research. Sage. https://doi.org/10.4135/9781473957671
  • Roller, S. (2016). What they notice in video: A study of prospective secondary mathematics teachers learning to teach. Journal of Mathematics Teacher Education, 19, 477-498. https://doi.org/10.1007/s10857-015-9307-x
  • Sadler, D. R. (2005). Interpretations of criteria‐based assessment and grading in higher education, Assessment & Evaluation in Higher Education, 30(2), 175-194. https://doi.org/10.1080/0260293042000264262
  • Saldaña, J. (2009). The coding manual for qualitative researchers. Sage Publications.
  • Sánchez-Matamoros, G., Fernández, C., & Llinares, S. (2015). Developing pre-service teachers’ noticing of students’ understanding of the derivative concept. International journal of science and mathematics education, 13(6), 1305-1329. https://doi.org/10.1007/s10763-014-9544-y
  • Schorr, R., &; Lesh, R. (2003). A modeling approach for providing teacher development. In R. A. Lesh & H. M. Doerr (Eds.), Beyond constructivism: Models and modeling perspectives on mathematics problem solving; learning; and teaching (pp. 141-158). Lawrence Erlbaum.
  • Schwartz, C. (2015). Developing the practice of teacher questioning through a K-2 elementary mathematics field experience, Investigations in Mathematics Learning, 7(3), 30-50. https://doi.org/10.1080/24727466.2015.11790344
  • 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), 1-22. https://doi.org/10.17763/haer.57.1.j463w79r56455411
  • 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, 107-125. https://doi.org/10.1007/s10857-007-9063-7
  • Steffe, L. P. (1991). The constructivist teaching experiment: Illustrations and implications. In E. von Glasersfeld (Ed.), Radical constructivism in mathematics education (pp. 177-194). Kluwer. https://doi.org/10.1007/0-306-47201-5_9
  • Steffe, L. P., & Cobb, P. (1983). Cognitive development and children’s solutions to verbal arithmetic problems: A critique. Journal for Research in Mathematics Education, 14, 74-76. https://doi.org/10.2307/748799
  • Steffe, L. P., & Thompson, P. W. (2000). Teaching experiment methodology: Underlying principles and essential elements. In R. Lesh & A. E. Kelly (Eds.), Research design in mathematics and science education (pp. 267-307). Erlbaum.
  • Stockero, S., Rupnow, R. L., & Pascoe, A. E. (2017). Learning to notice important student mathematical thinking in complex classroom interactions. Teaching and Teacher Education, 63, 384-395. https://doi.org/10.1016/j.tate.2017.01.006
  • Tang, S. Y. F., & Chow, A. W. K. (2007). Communicating feedback in teaching practice supervision in a learning-oriented field experience assessment framework. Teaching and Teacher Education, 23, 1066-1085. https://doi.org/10.1016/j.tate.2006.07.013
  • 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, 571-596.
  • van Es, E. A., & Sherin, M. G. (2008). Mathematics teachers’ “learning to notice” in the context of a video club. Teaching and Teacher Education, 24, 244-276. https://doi.org/10.1016/j.tate.2006.11.005
  • Weiland, I., Hudson, R., & Amador, J. (2014). Preservice formative assessment interviews: The development of competent questioning. International Journal of Science and Mathematics Education, 12, 329-352. https://doi.org/10.1007/s10763-013-9402-3