From the laboratory to the classroom: Creating and implementing a research-based curriculum around the use of comparison Courtney Pollack, Harvard University Dr. Jon R. Star, Harvard University I. Abstract This poster presents a research program that seeks to improve educational practice and student learning in mathematics by developing, implementing, and testing curriculum materials built on findings from cognitive science. We convey the process of conducting experimental classroom studies built on lab-based cognitive science research and the subsequent design and implementation of a supplemental first-year algebra curriculum based on comparison. II. Learning & comparison: Cognitive science research There is a great deal of cognitive research showing the benefits of comparison for learning in young children (e.g., Loewenstein & Gentner, 2001; Oakes & Ribar, 2005) and adults (e.g., Gentner, Loewnstein, & Thompson, 2003; Namy & Gentner, 2002). Yet, little of this type of research has been done in classrooms. Building on these findings, we engaged in small-scale experimental classroom studies to explore the benefits of comparison for students’ learning of mathematics, focusing on equation solving. IV. Curriculum Design and Development During 2008-2009, we worked with a small group of expert teachers to transform our experimental materials (see Figure 1) into a supplementary Algebra I curriculum that embodied the principles derived from previous experimental research (see Figure 2). Side-by-side comparison Labeled solution steps Prompts to identify similarities & differences Principles of comparison III. Experimental classroom research Our experimental research showed positive effects of comparison on student learning in controlled settings. Two-year randomized controlled trial Pilot testing Curriculum design Experimental classroom studies Cognitive science research Figure 1. Experimental comparison materials from Rittle-Johnson & Star (2007) “Infuse” comparison into first-year algebra classes Facilitate comparison of and reflection on multiple strategies Goals About 80 “worked example pairs” Characters: Alex and Morgan Four comparison types Which is better? Why does it work? How do they differ? Which is correct? Discussion phases Understand, compare, make connections Help teachers facilitate comparison conversations Supplementary materials Usability Beyond linear equation solving to include Algebra I content New comparison type: Correct versus incorrect Scope 7th grade students Worked examples side-by-side Compare side-by-side or reflect sequentially Comparison condition: Greater procedural knowledge and flexibility Rittle-Johnson & Star (2007) 7th and 8th grade students What you compare matters Solution methods: largest gains in conceptual knowledge and flexibility Problem types: Support both to a lesser extent Rittle-Johnson & Star (2009) How does comparison affect student learning in real classroom environments? V. Pilot testing During the 2009-2010 school year, we worked with 12 middle and high school teachers to test our materials in classrooms. VI. Randomized controlled trials Our revised materials are currently being tested using about 80 first-year algebra classrooms across Massachusetts. One-week summer PD Comparison activities Create own worked example pairs Model teaching with comparison Tasks Use materials 1-2 x per week Videotape 2 x per month Submit log after material use (e.g., time spent, student learning, teacher satisfaction) Student assessments Feedback Ongoing feedback throughout the year Student and teacher end-of-year interviews Pilot year Figure 2. Worked example from comparison curriculum VII. Conclusion Atkinson, Derry, Renkl, and Wortham (2000) acknowledge the gap between mathematics research in controlled laboratory settings and the relevance of its findings to classroom settings. They note that lab findings cannot alone improve classroom practice, but that “controlled experimental research grounded in cognitive science has substantially improved educational practice,” (p. 184). We hope to illustrate one way that building on experimental research can improve educational practice and student learning, by extending the benefits of learning through comparison to authentic classroom settings. References Atkinson, R. K., Derry, S. J., Renkl, A., & Wortham, D. (2000). Learning from examples: Instructional principles from the worked examples research. Review of Educational Research, 70(2), 181-214. Gentner, D., Loewnstein, J., & Thompson, L. (2003). Learning and transfer: A general role of analogical encoding. Journal of Educational Psychology, 95(2), 393-408. Loewenstein, J., & Gentner, D. (2001). Spatial mapping in preschoolers: Close comparisons facilitate far mappings. Journal of Cognition and Development, 2, 189–219. Namy, L. L., & Gentner, D. (2002). Making a silk purse out of two sow’s ears: Young children’s use of comparison in category learning. Journal of Experimental Psychology: General, 131, 5-15. Oakes, L. M., & Ribar, R. J. (2005). A comparison of infants’ categorization in paired and successive presentation familiarization tasks. Infancy, 7, 85–98. Rittle-Johnson, B. & Star, J. R. (2007). Does comparing solution methods facilitate conceptual and procedural knowledge? An experimental study on learning to solve equations. Journal of Educational Psychology, 99(3), 561-574. Rittle-Johnson, B. & Star, J. R. (2009). Compared with what? The effects of different comparisons on conceptual knowledge and procedural flexibility for equation solving. Journal of Educational Psychology, 101(3), 529-544. Figure 3. Take-away page excerpt from the revised curriculum We are currently finishing data collection of videos, logs, and student assessments for the first year of the RCT. We will continue to collect data during the 2011-2012 school year. Based on our pilot year feedback, we expanded our curriculum to include 150 worked example pairs. We also added a second page for each (see Figure 3).