Contrasting Cases

Publications & Presentations

Project papers

Star, J.R., Kenyon, M., Joiner, R., & Rittle-Johnson, B. (in press). Comparison helps students learn to solve equations. Mathematics Teacher. request articleRequest a copy of this paper
Yakes, C., & Star, J.R. (in press). Using comparison to develop teachers' flexibility in algebra. Journal of Mathematics Teacher Education. request articleRequest a copy of this paper
Star, J.R., Kenyon, M., Joiner, R., & Rittle-Johnson, B. (in press). Comparison helps students learn to be better estimators. Teaching Children Mathematics. request articleRequest a copy of this paper
Rittle-Johnson, B., Star, J.R., & Durkin, K. (in press). The importance of familiarity when comparing examples: Impact on conceptual and procedural knowledge of equation solving. Journal of Educational Psychology. request articleRequest a copy of this paper
Star, J.R., & Newton, K.J. (in press). The nature and development of experts' strategy flexibility for solving equations. ZDM - The International Journal on Mathematics Education. request articleRequest a copy of this paper
Star, J.R., Rittle-Johnson, B., Lynch, K., & Perova, N. (in press). The role of prior knowledge and comparison in the development of strategy flexibility: The case of computational estimation. ZDM - The International Journal on Mathematics Education. request articleRequest a copy of this paper
Star, J.R., & Rittle-Johnson, B. (2009). Making algebra work: Instructional strategies that deepen student understanding, within and between representations. ERS Spectrum, 27(2), 11-18. request articleDownload this paper
Rittle-Johnson, B, & Star, J.R. (2009). Compared to what? The effects of different comparisons on conceptual knowledge and procedural flexibility for equation solving. Journal of Educational Psychology,101(3), 529-544. request articleRequest a copy of this paper
Star, J.R., & Rittle-Johnson, B. (2009). It pays to compare: An experimental study on computational estimation. Journal of Experimental Child Psychology, 102, 408-426. request articleRequest a copy of this paper
Star, J.R. & Rittle-Johnson, B. (2008). Flexibility in problem solving: The case of equation solving. Learning and Instruction, 18, 565-579 request articleRequest a copy of this paper
Star, J.R. (2008, April). It pays to compare! Using comparison to help build students’ flexibility in mathematics. The Center for Comprehensive School Reform and Improvement Newsletter, 1-4 request articleDownload this paper
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. request articleRequest a copy of this paper
Rittle-Johnson, B. & Star, J. (2007). Compared to what? How different types of comparison facilitate transfer in mathematics. In D. S. McNamara & G. Trafton (Eds.), Proceedings of the 29th Meeting of the Cognitive Science Society. (pp. 21-22). Austin, TX: Cognitive Science Society. request articleDownload this paper

 

Other relevant publications by project faculty

Newton, K. J. (2009). Instructional practices related to prospective elementary school teachers’ motivation for fractions. Journal of Mathematics Teacher Education, 12(2), 89-109. request articleRequest a copy of this paper
Newton, K. J. (2008). An extensive analysis of elementary preservice teachers' knowledge of fractions. American Educational Research Journal, 45(4), 1080-1110. request articleRequest a copy of this paper
Star, J.R. (2007). Foregrounding procedural knowledge. Journal for Research in Mathematics Education, 38(2), 132-135. request articleRequest a copy of this paper
Jones, K. K., & Byrnes, J. P. (2006). Characteristics of students who benefit from high-quality mathematics instruction. Contemporary Educational Psychology, 31, 328-343. request articleRequest a copy of this paper
Rittle-Johnson, B. (2006). Promoting transfer: The effects of direct instruction and self-explanation. Child Development, 77(1), 1-15. request articleRequest a copy of this paper
Star, J.R., & Seifert, C. (2006). The development of flexibility in equation solving. Contemporary Educational Psychology, 31, 280-300. request articleRequest a copy of this paper
Rittle-Johnson, B. & Koedinger, K.R. (2005). Investigating Knowledge Scaffolds to Support Mathematical Problem Solving. Cognition and Instruction, 23(3), 313-349. request articleRequest a copy of this paper
Star, J.R. (2005). Reconceptualizing procedural knowledge. Journal for Research in Mathematics Education, 36(5), 404-411. request articleRequest a copy of this paper
Rittle-Johnson, B., Siegler, R.S. & Alibali, M.W. (2001). Developing conceptual understanding and procedural skill in mathematics: An iterative process. Journal of Educational Psychology, 93, 346-362. request articleRequest a copy of this paper
Rittle-Johnson, B. & Alibali, M.W. (1999). Conceptual and procedural knowledge of mathematics: Does one lead to the other? Journal of Educational Psychology, 91, 1-16. request articleRequest a copy of this paper
Rittle-Johnson, B. & Siegler, R.S. (1998). The relation between conceptual and procedural knowledge in learning mathematics: A review. In C. Donlan (Ed.), The development of mathematical skill (pp. 75-110). Hove, UK: Psychology Press. request articleRequest a copy of this paper

 

Project presentations

Rittle-Johnson, B. & Star, J. (2008, June). It pays to compare: Effectively using comparison to support student learning of algebra. Invited talk presented at the Institute for Education Sciences Research Conference, Washington, D.C. request articleDownload this presentation
Star, J.R. & Rittle-Johnson, B. (2008, March). The role of comparison in the development of flexible knowledge of computational estimation. Paper presented at the annual meeting of the American Educational Research Association, New York City. request articleDownload this presentation
Rittle-Johnson, B., & Star, J.R. (2007, October). When it pays to compare: Benefits of comparison in mathematics classrooms. Paper presented at the fifth biennial of the Cognitive Development Society, Santa Fe, New Mexico. request articleDownload this presentation
Star, J.R., & Rittle-Johnson, B. (2007, August). Contrasting cases in mathematics support procedural flexibility and conceptual knowledge. Paper presented at the European Association of Research on Learning and Instruction 12th Biennial Conference, Budapest, Hungary. request articleDownload this presentation
Rittle-Johnson, B. & Star, J.R. (2007, August). Compared to what? How different types of comparison affect transfer in mathematics. Paper presented at the annual meetings of the Cognitive Science Society, Nashville, TN. request articleDownload this presentation
Star, J.R., Rittle-Johnson, B., Lee, K., Samson, J., & Chang, K. (2007, June). When it pays to compare: Experimental evidence for when and how comparison facilitates mathematics learning. Poster presented at the Institute for Education Sciences Research Conference, Washington, D.C. request articleDownload this presentation
Star, J.R. (2007, May). Improving students’ flexibility in algebra: The benefits of comparison. Invited address, California Algebra Forum, San Diego, CA. request articleDownload this presentation
Star, J.R., Lee, K., Chang, K., Rittle-Johnson, B., & Glasser, H. (2007, April). Investigating student thinking about estimation: What makes a good estimate? Paper presented at the annual meeting of the American Educational Research Association, Chicago, IL. request articleDownload this presentation
Star, J.R., Chang, K., Lee, K., & Rittle-Johnson, B. (2007, April). The benefits of comparison in learning to solve equations. Poster presented at the annual meeting of the American Educational Research Association, Chicago, IL. request articleDownload this presentation
Star, J.R., & Rittle-Johnson, B. (2007, April). Does comparison support transfer of knowledge? Investigating student learning of algebra. Paper presented at the annual meeting of the American Educational Research Association, Chicago, IL. request articleDownload this presentation
Rittle-Johnson, B., Star, J.R., Glasser, H., & Lee, K. (2006, June). Does using contrasting cases increase problem solving, flexibility, and conceptual knowledge? An experimental study on early algebra learning. Poster presented at the Institute for Education Sciences Research Conference, Washington, D.C. request articleDownload this presentation
Rittle-Johnson, B., & Star, J.R. (2006, April). Explaining contrasting solution methods supports problem-solving flexibility and transfer. Paper presented at the annual meeting of the American Educational Research Association, San Francisco, California. request articleDownload this presentation
Rittle-Johnson, B., & Star, J.R. (2005, October). Contrasting examples in mathematics lessons support flexible and transferable knowledge. Paper presented at fourth biennial meeting of the Cognitive Development Society, San Diego, California. request articleDownload this presentation

 

Other documents

Helping Teachers to Use and Students to Learn from Contrasting Examples: A Scale-up Study in Algebra I National Science Foundation Research and Evaluation on Education in Science Engineering (REESE), $2,006,604. Jon R. Star, PI; Bethany Rittle-Johnson and Kristie J. Newton, co-PIs. August, 2008 – August, 2013.
Using Contrasting Examples to Support Procedural Flexibility and Conceptual Understanding in Mathematics Institute for Education Sciences Cognition and Student Learning Research Program, $1,025,137. Jon R. Star and Bethany Rittle-Johnson, co-PIs, August, 2005 – August, 2009.

For more information, contact:

compare@gse.harvard.edu

Participating institutions:

Harvard Graduate School of EducationHarvard Graduate School of Education

Temple UniversityTemple University

Vanderbilt UniversityVanderbilt University

Funded by:

National Science Foundation
Institute of Education Sciences