# Prediction assessments: Using video-based predictions to assess prospective teachers’ knowledge of students’ mathematical thinking

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## Abstract

In order to evaluate the effectiveness of an experimental elementary mathematics field experience course, we have designed a new assessment instrument. These video-based prediction assessments engage prospective teachers in a video analysis of a child solving mathematical tasks. The prospective teachers build a model of that child’s mathematics and then use that model to predict how the child will respond to a subsequent task. In this paper, we share data concerning the evolution and effectiveness of the instrument. Results from implementation indicate moderate to high degrees of inter-rater reliability in using the rubric to assess prospective teachers’ models and predictions. They also indicate strong correlation between participation in the experimental course and prospective teachers’ performances on the video-based prediction assessments. Such findings suggest that prediction assessments effectively evaluate the pedagogical content knowledge that we are seeking to foster among the prospective teachers.

## Keywords

Teacher knowledge Instrument development Video Preservice teacher education Pedagogical content knowledge## Notes

### Acknowledgments

The research reported in this paper was supported by a DR-K12 grant from the National Science Foundation (NSF), under grant number DRL-0732143. The authors wish to thank all the members of the IMB research team, as well as Dionne Cross, who collaborated with us in collecting data.

## References

- Arbaugh, F., & Brown, C. A. (2005). Analyzing mathematical tasks: A catalyst for change?
*Journal of Mathematics Teacher Education,**8*(6), 499–536.CrossRefGoogle Scholar - Ball, D. L. (1994, November).
*Developing mathematics reform: What don’t we know about teacher learning*—*but would make good working hypotheses?*Paper presented at Conference on Teacher Enhancement in Mathematics K–6, Arlington, VA.Google Scholar - Carpenter, T. P., Fennema, E., Peterson, P. L., & Carey, D. A. (1988). Teachers’ pedagogical content knowledge of students’ problem solving in elementary arithmetic.
*Journal for Research in Mathematics Education,**19*, 385–401.CrossRefGoogle Scholar - Chamberlin, M. T. (2005). Teachers’ discussions of students’ thinking: Meeting the challenge of attending to students’ thinking.
*Journal of Mathematics Teacher Education,**8*, 141–170.CrossRefGoogle Scholar - Cochran-Smith, M., & Zeichner, K. M. (Eds.). (2005).
*Studying teacher education: The report of the AERA panel on research and teacher education*. Mahwah, NJ: Lawrence Erlbaum.Google Scholar - Confrey, J. (1988).
*Multiplication and splitting: Their role in understanding exponential functions.*Paper presented at the tenth annual meeting of the North American chapter of the international group for the psychology of mathematics education, DeKalb, IL.Google Scholar - Confrey, J. (1993). Learning to see children’s mathematics: Crucial challenges in constructivist reform. In K. Tobin (Ed.),
*Constructivist perspectives in science and mathematics*(pp. 299–321). Washington, DC: American Association for the Advancement of Science.Google Scholar - Confrey, J. (1994). Splitting, similarity and rate of change: A new approach to multiplication and exponential functions. In G. Harel & J. Confrey (Eds.),
*The development of multiplicative reasoning in the learning of mathematics*(pp. 291–330). Albany: State University of New York.Google Scholar - Confrey, J., & Lachance, A. (2000). Transformative teaching experiments through conjecture driven research design. In A. E. Kelly & R. A. Lesh (Eds.),
*Handbook of research design in mathematics and science education*(pp. 231–265). Mahwah, NJ: Lawrence Erlbaum.Google Scholar - Crespo, S. (2000). Seeing more than right and wrong answers: Prospective teachers’ interpretations of students’ mathematical work.
*Journal of Mathematics Teacher Education,**3*(2), 155–181.CrossRefGoogle Scholar - Crespo, S., & Nicol, C. (2003). Learning to investigate students’ mathematical thinking: The role of student interviews. In N. A. Pateman, B. J. Dougherty, & J. Zilliox (Eds.),
*Proceedings of the 2003 joint meeting of PME and PMENA*(Vol. 2, pp. 261–267). Honolulu: College of Education, University of Hawaii.Google Scholar - Davis, B. (1997). Listening for differences: An evolving conception of mathematics teaching.
*Journal for Research in Mathematics Education,**28*(3), 355–376.CrossRefGoogle Scholar - diSessa, A. A. (2007). An interactional analysis of clinical interviewing.
*Cognition and Instruction,**25*(4), 523–565.CrossRefGoogle Scholar - Education Commission of the States. (2003a). Eight questions on teacher preparation: What does the research say? Retrieved July, 2006, from www.ecs.org/tpreport.
- Education Commission of the States. (2003b). Eight questions on teacher preparation: What does the research say? A summary of the findings. Retrieved July, 2006, from http://www.ecs.org/ecsmain.asp?page=/html/educationIssues/teachingquality/tpreport/.
- Educational Testing Service (2006). State requirements. Retrieved June 27, 2006, from http://www.ets.org/portal/site/ets/menuitem.22f30af61d34e9c39a77b13bc3921509/vgnextoid=d378197a484f4010VgnVCM10000022f95190RCRD.
- Fennema, E., Carpenter, T. P., Franke, M. L., Levi, L., Jacobs, V. R., & Empson, S. B. (1996). A longitudinal study of learning to use children’s thinking in mathematics instruction.
*Journal for Research in Mathematics Education,**27*, 403–434.CrossRefGoogle Scholar - Franke, M. L., Carpenter, T. P., Levi, L., & Fennema, E. (2001). Capturing teachers’ generative change: A follow-up study of professional development in mathematics.
*American Educational Research Journal,**38*(3), 653–689.CrossRefGoogle Scholar - Goodman, L., & Kruskal, W. (1954). Measures of associations for cross-validations.
*Journal of the American Statistical Association,**49*, 732–764.CrossRefGoogle Scholar - Hill, H. C., Ball, D. L., & Schilling, S. G. (2008). Unpacking pedagogical content knowledge: Conceptualizing and measuring teachers’ topic-specific knowledge of students.
*Journal for Research in Mathematics Education,**39*(4), 372–400.Google Scholar - Hill, H. C., Schilling, S. G., & Ball, D. L. (2004). Developing measures of teachers’ mathematics knowledge for teaching.
*Elementary School Journal,**105*, 11–30.CrossRefGoogle Scholar - Kane, T. J., Rockoff, J. E., & Staiger, D. O. (2006). What does certification tell us about teacher effectiveness? Evidence from New York City. Retrieved July, 2006, from http://gseweb.harvard.edu/news/features/kane/nycfellowsmarch2006.pdf.
- Kersting, N. (2008). Using video clips of mathematics classroom instruction as item prompts to measure teachers’ knowledge of teaching mathematics.
*Educational and Psychological Measurement,**68*(5), 845–861.CrossRefGoogle Scholar - Koirala, H. P., Davis, M., & Johnson, P. (2008). Development of a performance assessment task and rubric to measure prospective secondary school mathematics teachers’ pedagogical content knowledge and skills.
*Journal of Mathematics Teacher Education,**11*, 127–138.CrossRefGoogle Scholar - Landis, J. R., & Koch, G. G. (1977). The measurement of observer agreement for categorical data.
*Biometrics,**33*, 159–174.CrossRefGoogle Scholar - Lewis, C. C. (2000, April).
*Lesson study: The core of Japanese professional development.*Invited presentation to the Special Interest Group on Research in Mathematics Education at the annual meeting of the American Educational Research Association, New Orleans, LA.Google Scholar - No Child Left Behind of 2001. (2001, January). Public Law No. 107–110, 107th Congress. Retrieved from http://www.ed.gov/legislation/ESEA02/.
- Norton, A. H., & McCloskey, A. (2008). Teaching experiments and professional development.
*Journal of Mathematics Teacher Education,**11*(4), 285–305.CrossRefGoogle Scholar - Olive, J. (2000). Computer tools for interactive mathematical activity in the elementary school.
*International Journal of Computers for Mathematics Learning,**5*, 241–262.CrossRefGoogle Scholar - Philipp, R. A., Ambrose, R., Lamb, L. L. C., Sowder, J. T., Schappelle, B. P., Sowder, L., et al. (2007). Effects of early field experiences on the mathematical content knowledge and beliefs of prospective elementary school teachers: An experimental study.
*Journal for Research in Mathematics Education,**38*(5), 438–476.Google Scholar - Piaget, J. (1970).
*Science of education and the psychology of the child*. New York: Viking Press.Google Scholar - Schifter, D. (1998). Learning mathematics for teaching: From the teachers’ seminar to the classroom.
*Journal for Mathematics Teacher Education,**1*(1), 55–87.CrossRefGoogle Scholar - Shulman, L. S. (1986). Those who understand: A conception of teacher knowledge.
*American Educator,**10*(1), 9–15.Google Scholar - 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.CrossRefGoogle Scholar - Steffe, L. P. (1991). Mathematics curriculum design: A constructivist’s perspective. In L. P. Steffe & T. Wood (Eds.),
*International perspectives on transforming early childhood mathematics education*(pp. 389–398). Hillsdale, NJ: Lawrence Erlbaum.Google Scholar - Steffe, L. P., & Thompson, P. W. (2000). Teaching experiment methodology: Underlying principles and essential elements. In A. E. Kelly & R. A. Lesh (Eds.),
*Handbook of research design in mathematics and science education*(pp. 267–306). Mahwah, NJ: Lawrence Erlbaum.Google Scholar - Steinberg, R., Empson, S. B., & Carpenter, T. P. (2004). Inquiry into children’s mathematical thinking as a means to teacher change.
*Journal of Mathematics Teacher Education,**7*(3), 237–267.CrossRefGoogle Scholar - Stockero, S. L. (2008). Using a video-based curriculum to develop a reflective stance in prospective mathematics teachers.
*Journal of Mathematics Teacher Education,**11*, 373–394.CrossRefGoogle Scholar - Thompson, P. W., Carlson, M. P., & Silverman, J. (2007). The design of tasks in support of teachers’ development of coherent mathematical meanings.
*Journal of Mathematics Teacher Education,**10*, 415–432.CrossRefGoogle Scholar - Vacc, N. N., & Bright, G. W. (1999). Elementary preservice teachers’ changing beliefs and instructional use of children’s mathematical thinking.
*Journal for Research in Mathematics Education,**30*, 89–110.CrossRefGoogle Scholar - 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.Google Scholar - Van Es, E. A., & Sherin, M. G. (2008). Mathematics teachers’ “learning to notice” in the context of a video club.
*Journal of Technology and Teacher Education*,*24*(2), 244–276.Google Scholar - von Glasersfeld, E., & Steffe, L. P. (1991). Conceptual models in educational research and practice.
*Journal of Educational Thought,**25*(2), 91–103.Google Scholar - Wallach, T., & Even, R. (2005). Hearing students: The complexity of understanding what they are saying, showing, and doing.
*Journal of Mathematics Teacher Education,**8*, 393–417.CrossRefGoogle Scholar - Wright, R. J. (2000). Professional development in recovery education. In L. P. Steffe & P. W. Thompson (Eds.),
*Radical constructivism in action: Building on the pioneering work of Ernst von Glasersfeld*(pp. 134–151). London: Falmer.Google Scholar