Experienced Elementary Teachers’ Processes for Interpreting Artifacts of Student Thinking

Yıl 2019, Cilt: 6 Sayı: 3, 124 - 143, 30.09.2019

Tiffany Hill

Öz

Consensus exists in mathematics education that
classroom assessment is an essential component of effective practice; however,
the importance of teacher interpretation of student thinking in the assessment
process is often overlooked. The purpose of this interpretative qualitative
research study was to examine teachers’ interpretations of artifacts of student
thinking. In particular, we sought to understand the personal resources
teachers used to construct their interpretations. Nine experienced and professionally
active teachers participated in two interviews. The first interview was
semi-structured and focused on the participants’ professional experiences,
conceptions of assessment, and assessment practices. The second interview was
task-based and involved participants in the interpretation of student artifacts
collected from second grade students in the area of place value. The results
indicate that teachers applied to the act of interpretation a complex, but
personal awareness of student thinking that influenced interpretation,
including: (a) conceptions of levels of student performance, (b) expectations
for student performance, and (c) awareness of common student difficulties.
These results provide support for the conclusion that professional development
related to classroom assessment should address the interpretative process of
examining student artifacts, with emphasis on developing personal resources
used in this process. 

Anahtar Kelimeler

formative assessment, summative assessment, interpretation of student thinking

Kaynakça

• Ball, D. L. (1993). With an eye on the mathematical horizon: Dilemmas of teaching elementary school mathematics. Elementary School Journal, 93(4), 373-397.
• Ball, D. L. (1997). What do students know? Facing challenges of distance, context, and desire in trying to hear children. In B. J. Biddle, T. L. Good, & I.
• Goodson. (Eds.), International handbook of teachers and teaching (pp. 769-818). Netherlands: Kluwer Academic.
• Ball, D. L. (2001). Teaching, with respect to mathematics and students. In T. Wood, B. S. Nelson, & J. Warfield (Eds.), Beyond classical pedagogy: Teaching elementary school mathematics (pp. 11-22). Mahwah, NJ: Lawrence Erlbaum.
• Berliner, D. C. (1986). In pursuit of the expert pedagogue. Educational Researcher, 15(7), 5-13.
• Black, P., & William, D. (1998). Assessment and classroom learning. Assessment in Education: Principles, Policy, and Practice, 5, 7-74.
• Boeije, H. (2002). A purposeful approach to the constant comparative method in the analysis of qualitative interviews. Quality and Quantity, 36, 391-409.
• Carpenter, T. P., & Fennema, E. (1991). Research and cognitively guided instruction. In E. Fennema,T. P. Carpenter, & S. J. Lamon (Eds.), Integrating research on teaching and learning mathematics (pp. 1–16). Albany, NY: State University of New York Press.
• Carpenter, T. P., & Fennema, E. (1992). Cognitively guided instruction: Building on the knowledge of students and teachers. In W. Secada (Ed.), Curriculum reform: The case of mathematics education in the United States. Special issue of International Journal of Educational Research (pp. 457-470). Elmsford, NY: Pergamon Press.
• Clement, J. (2000). Analysis of clinicial interviews: Foundations and model viability. In A. E. Kelly & R. A. Lesh (Eds.), Handbook of reearch design in mathematics and science education (pp. 547-589). Mahwah, NJ: Lawrence Erlbaum.
• Cobb, P. (1996). Where is the mind? A coordination of sociocultural and cognitive constructivist perspectives. In C. Fosnot (Ed.), Constructivism: Theory, perspectives, and practice (pp. 34-52). New York, NY: Teachers College Press.
• Crespo, S. (2000). Seeing more than right and wrong answers: Prospective teachers’ interpretations of students’ mathematical work. Journal of Mathematics Teacher Education, 3, 155-181.
• Daro, P., Mosher, F. A., & Corcoran, T. (2011). Learning trajectories in mathematics: A foundation for standards, curriculum, assessment, and instruction (Report No. RR-68). Philadelphia, PA: Consortium for Policy Research in Education.
• Doerr, H.M., Goldsmith, L.T. & Lewis, C.C. (2010). Mathematics professional development brief. NCTM Research brief. Reston, Va.: National Council of Teachers of Mathematics.
• Ebby, C. B. (2015a). How do Teachers Make Sense of Student Work for Instruction? Paper presented at National Council of Teachers of Mathematics Research Conference, Boston, Massachusetts.
• Ebby, C. B & Sam, C. (2015b). Understanding How Math Teachers Make Sense of Student Work. Paper presented at the Annual Meeting of the American Educational Research Association, Chicago.
• Ericsson, K. A., & Simon, H. A. (1993). Protocol anlaysis: Verbal reports as data. Cambridge, MA: Massachusetts Institute of Technology.
• Ernest, P. (1991). The philosophy of mathematics education. London, England. Routledge.
• Ernest, P. (2010). Reflections on theories of learning. In B. Sriraman & L. English (Eds.), Theories of mathematics education: Seeking new frontiers (pp. 39-47). Heidelberg, Germany: Springer.
• Even, R. (2005). Using assessment to inform instructional decisions: How hard can it be? Mathematics Education Research Journal, 17(3), 45-61.
• Even, R., & Tirosh, D. (2008). Teacher knowledge and understanding of students’ learning and thinking. In L. D. English (Ed.), Handbook of international research in mathematics education (pp. 202-222). New York, NY: Routledge.
• Even, R. & Wallach, T. (2003). On student observation and student assessment. In L. Bragg, C. Campbell, G. Herbert & J. Mousley (Eds.), Mathematics Education Research: Innovation, Networking, Opportunity: Proceedings of the 26th Annual Conference of Mathematics Education Research Group of Austrailia (Vol. 1, pp. 316-323). Melbourne, Austrilia: Deakin Univeristy.
• Even, R. & Wallach, T. (2004). Between student observation and student assessment: A critical reflection. Canadian Journal of Science, Mathematics, and Technology Education, 4(4), 483-495.
• Heid, M. K., Blume, G. W., Zbiek, R. M., & Edwards, B. S. (1999). Factors that influence teachers learning to do interviews to understand students’ mathematical understandings. Educational Studies in Mathematics, 37, 223-249.
• Hines, E., & McMahon, M. T. (2005). Interpreting middle school students’ proportional reasoning strategies: Observations from PSTs. School Science and Mathematics, 105(2), 88-105.
• Jacobs, V., Lamb, L. L. C., & Philipp, R. (2010). Professional noticing of children's mathematical thinking. Journal for Research in Mathematics Education, 41(2), 169-202.
• Kazemi, E., & Franke, M. L. (2004). Teacher learning in mathematics: Using student work to promote collective inquiry. Journal of Mathematics Teacher Education, 7, 203-235.
• Kingston, N., & Nash, B. (2011). Formative assessment: A meta-analysis and a call for research. Educational Measurement: Issues and Practice, 30, 28-37.
• Lannin, J. & van Garderen, D. (2009). A Study of the Struggling Learner's Knowledge and Development for Number and Operation (Award No. 0918060). National Science Foundation, Discovery Research K-12.
• Lincoln, Y. S., & Guba, E. G. (1985). Naturalistic inquiry. Newbury Park, CA: Sage.
• Merriam, S. B. (2009). Qualitative research and case study applications in education. San Francisco, CA: Jossey-Bass.
• Miles, M. B., & Huberman, A. M. (1994). Qualitative data analysis: A methods sourcebook (2nd ed.). Thousand Oaks, CA: Sage.
• Miles, M. B., Huberman, A. M., & Saldaña, J. (2014). Qualitative data analysis: A methods sourcebook (3rd ed.). Thousand Oaks, CA: Sage.
• Morgan, C., & Watson, A. (2002). The interpretative nature of teachers’ assessment of students’ mathematics: Issues for equity. Journal for Research in Mathematics Education, 33(2), 78-110.
• Morris, A. (2006). Assessing pre-service teachers’ skills for analyzing teaching. Journal of Mathematics Teacher Education, 9(5), 471–505.
• National Council of Teachers of Mathematics. (2000). Principles and standards for school Mathematics. Reston, VA: National Council of Teachers of Mathematics.
• National Council of Teachers of Mathematics. (2014). Principles to actions: Ensuring mathematical success for all. Reston, VA: National Council of Teachers of Mathematics.
• National Research Council. (2000). How people learn: Brain, mind, experience, and school. Washington, DC: National Academy Press.
• National Research Council. (2001). Adding it up: Helping children learn mathematics. Washington, DC: National Academy Press.
• Otero, V. K. (2006). Moving beyond the ''get it or don't'' conception of formative assessment. Journal of Teacher Education, 57(3), 247-255.
• Patton, M. Q. (2002). Qualitative research & evaluation methods (3rd ed.). Thousand Oaks, CA: Sage.
• Pellegrino, J., Chudowsky, N., & Glaser, R. (2001). Knowing what students know: The science and design of educational assessment. Washington, DC: National Academy Press.
• Romberg, T., & Carpenter, T. (1986). Research on teaching and learning mathematics: Two disciplines of scientific inquiry. In M. Wittrock (Ed.), Handbook of research on teaching. (pp. 850-873). New York, NY: Macmillan Publishing Company.
• Schack, E. O., Fisher, M. H., Thomas, J. N., Eisenhardt, S., Tassell, J., & Yoder, M. (2013). Prospective elementary school teachers professional noticing of children’s early numeracy. Journal of Mathematics Teacher Education. Advance online publication.
• Schifter, D. (2001). Learning to see the invisible: What skills and knowledge are needed to engage with students’ matheamtical ideas?. In T. Wood, B. S.
• Nelson, & J. Warfield (Eds.), Beyond classical pedagogy: Teaching elementary school mathematics (pp. 11-22). Mahwah, NJ: Lawrence Erlbaum.
• Simon, M. A. (2000). Constructivism, mathematics teacher education, and research in mathematics teacher development. In L. P. Steffe & P. W. Thompson (Eds.), Radical constructivism in action: Building on the pioneering work of Ernst von Glasersfeld (pp. 213-230). New York, NY: Taylor and Francis.
• Sleep, L., & Boerst, T. A. (2012). Preparing beginning teachers to elicit and interpret students' mathematical thinking. Teaching and Teacher Education, 28(7), 1038-1048.
• Son, J. (2010). How PSTs interpret and respond to student errors: Ratio and proportion in similar rectangles. Advance online publication. doi:10.1007/s10649-013-9475-5
• Son, J., & Crespo, S. (2009). Prospective teachers’ reasoning and response to a student’s non-traditional strategy when dividing fractions. Journal of Mathematics Teacher Education, 12, 235-261.
• Sowder, J. T. (2007). The mathematical education and development of teachers. In F. K. Lester Jr (Ed.), Second handbook of research on mathematics teaching and learning (pp. 157-223). Charlotte, NC: Information Age Publishing.
• Spitzer, S. M., Phelps, C. M., Beyers, J. E. R., Johnson, D. Y., & Sieminski, E. M. (2011). Developing prospective elementary teachers’ abilities to identify evidence of student mathematical achievement. Journal of Mathematics Teacher Education, 14, 67-87.
• Steffe, L. P., & Thompson, P. W. (2000). Interaction or intersubjectivity? A reply to Lerman. Journal for Research in Mathematics Education, 31(2), 191-209.
• Steffe, L. P., von Glasersfeld, E., Richards, J., & Cobb, P. (1983). Children’s counting types: Philosophy, theory and application. New York, NY: Praeger Scientific.
• Sztajin, P., Confrey, J., Wilson, P. H., & Edgington, E. (2012). Learning trajectory based instruction: Toward a theory of teaching. Educational Researcher, 41(5), 147–56.
• Van Dooren, W., Verschaffell, L., & Onghena, P. (2002). The impact of preservice teachers’ content knowledge on their evaulation of students’ strategies for solving arithmetic and algebra word problems. Journal for Research in Mathematics Eductation, 33(5), 319-351.
• Wallach, T., & Even, R. (2005). Hearing students: The complexity of understanding what they are saying, showing, and doing. Journal of Mathematics Teacher Education, 8(5), 393-417.
• Watson, A. (1999). Paradigmatic conflics in informal mathematics assessment as sources of social inequity. Educational Review, 51(2), 105-115.
• Whitenack, J. W., Knipping, N., Novinger, S., Coutts, L., & Standifer, S. (2000). Teachers' mini-case studies of children's mathematics. Journal of Mathematics Teacher Education, 3, 101-123.
• Wilson, P. H., Lee, H. S., & Hollebrands, K. F. (2011). Understanding prospective mathematics teachers’ processes for making sense of students’ work with technology. Journal for Research in Mathematics Education, 42(1), 39-64.