Abstract
This set of comparative case studies examined three teachers’ enactments of a mathematics replacement unit to teach concepts of rate and linear function using SimCalc. The cases were drawn from a larger set of 37 teachers in a randomized experimental study that documented a significant main effect on student achievement. The goal was to identify the learning resources that supported students’ opportunities to make conceptual connections and the various configurations of learning resources among classrooms. Content Maps of lessons were created to model the content that was expressed in whole-group recitations. Two of the teachers had high gains, but used different configurations of learning resources to realize them. In contrast, the third teacher had a mean class gain that was below average, despite an MKT score that was among the highest in the treatment sample. In any case, no teacher implemented the curriculum in ways that were completely consistent with SimCalc developers’ vision. Scaling up instructional innovations entails trade-offs. Understanding these trade-offs can help educators recognize successful, “good enough” enactments of curriculum.
Keywords
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- 1.
All data collection, summaries, and transcripts were completed by mathematics education doctoral students Theodore Chao, Steven Greenstein, Luz Maldonado, and Jessica Pierson Bishop at the University of Texas Austin.
- 2.
Each teacher’s mean achievement gain is consistent with the phenomenon of regression to the mean between Years 1 and 2 of the study. That is, in Year 2 of the study, each mean gain was closer to the mean of the entire sample than in Year 1. None of the mean achievement gains appear to be a result of a ceiling effect.
- 3.
The number of letters in a student’s pseudonym indicates achievement level on pretest: 3 for low, 4 for medium, 5 for high.
- 4.
Although the class’s relatively low mean pretest score may seem to have put the class at a disadvantage for learning gains, the experiment found no significance differences in mean gain scores across differential pretest scores (Roschelle et al., 2010b).
References
Bransford, J., Brown, A., & Cocking, A. (1999). How people learn: brain, mind, experience, and school. Washington: National Academy Press.
Cohen, D., Raudenbush, S. W., & Ball, D. (2003). Resources, instruction, and research. Educational Evaluation and Policy Analysis, 25(2), 119–142.
Cohen, E., & Goodlad, J. (1994). Designing groupwork: strategies for the heterogeneous classroom. New York: Teachers College Press.
Gresalfi, M. (2009). Taking up opportunities to learn: constructing dispositions in mathematics classrooms. Journal of the Learning Sciences, 18(3), 327–369.
Grubb, N. (2008). Multiple resources, multiple outcomes: testing the improved school finance with NELS88. American Educational Research Journal, 45(1), 104–144.
Hiebert, J., & Grouws, D. (2007). The effects of classroom mathematics teaching on students’ learning. In F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 371–404). Charlotte: Information Age Publishing.
Hill, H., Rowan, B., & Ball, D. (2005). Effects of teachers’ mathematical knowledge for teaching on student achievement. American Educational Research Journal, 42(2), 371–406.
McLaughlin, M. (1976). Implementation as mutual adaptation: change in classroom organization. Teachers College Record, 77(3), 339–351.
Mercer, N. (2000). Words and minds. New York: Routledge.
Novak, J. D. (1990). Concept mapping: a useful tool for science education. Journal of Research in Science Teaching, 27(10), 937–949.
Roschelle, J., Pierson, J., Empson, S. B., Shechtman, N., Dunn, M., & Tatar, D. (2010a). Equity in scaling up simCalc: investigating differences in student learning and classroom implementation. In K. Gomez, L. Lyons, & J. Radinsky (Eds.), Learning in the disciplines. Proceedings of the 9th international conference of the learning sciences (Vol. 1, pp. 333–340). Chicago: University of Illinois at Chicago.
Roschelle, J., Shechtman, N., Tatar, D., Hegedus, S., Hopkins, B., Empson, S. B., & Knudsen, J. (2010b). Integration of technology, curriculum, and professional development for advancing middle-school mathematics: three large-scale studies. American Educational Research Journal, 47(4), 833–878.
Roschelle, J., Tatar, D., & Kaput, J. (2008). Getting to scale with innovations that deeply restructure how students come to know mathematics. In E. A. Kelly, R. Lesh, & J. Y. Baek (Eds.), Handbook of design research methods in education (pp. 369–395). New York: Routledge.
Shechtman, N., Roschelle, J., Hartel, G., & Knudsen, J. (2010). Investigating links from teacher knowledge, to classroom practice, to student learning in the instructional system of the middle school mathematics classroom. Cognition and Instruction, 28(3), 317–359.
Webb, N., & Palinscar, A. S. (1996). Group processes in the classroom. In D. C. Berliner & R. C. Calfee (Eds.), Handbook of educational psychology (pp. 841–873). New York: Macmillan.
Winnicott, D. W. (1971). Playing and reality. London: Tavistock.
Acknowledgements
We would like to thank Theodore Chao and Jessica Pierson Bishop for assistance in data collection and analysis, and Jennifer Knudsen, Nicole Shechtman, and the rest of the Scale Up research team at SRI International and Virginia Tech for insightful comments during all phases of the research. The material presented here is based on work supported by the National Science Foundation under Grant Number 04-37861 to SRI International (PI: Jeremy Roschelle). Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.
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Empson, S.B., Greenstein, S., Maldonado, L., Roschelle, J. (2013). Scaling Up Innovative Mathematics in the Middle Grades: Case Studies of “Good Enough” Enactments. In: Hegedus, S., Roschelle, J. (eds) The SimCalc Vision and Contributions. Advances in Mathematics Education. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-5696-0_14
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