Jon R. Star

Collaborative Research: Leveraging Comparison and Explanation of Multiple Strategies (CEMS) to Improve Algebra Learning (2016-2019)
National Science Foundation

This project focuses on fundamental research on learning in STEM and on STEM learning environments. We theorize that productive learning of algebra is supported by reflection on multiple solution strategies through comparison and explanation of the reasons behind the strategies (Comparison and Explanation of Multiple Strategies: CEMS). Existing theories of algebra learning focus on building conceptual knowledge and place less emphasis on how students gain expertise with symbolic strategies. Working with symbolic strategies is essential in algebra learning, including knowing multiple strategies for solving a problem, selecting the most appropriate procedure for a given problem and understanding the conceptual rationale behind commonly used strategies. In small-scale studies, we found that redesigning lessons on equation solving to integrate a CEMS approach supported greater equation solving knowledge than completing the lessons without a CEMS approach (e.g., Rittle-Johnson & Star, 2007; Rittle-Johnson, Star, & Durkin, 2012). Further, a preliminary set of supplemental materials to support a CEMS approach within a variety of lessons within the Algebra I curriculum has been developed, with evidence that classroom teachers can implement the materials with good fidelity (Star et al., 2015).
Across three years, we propose to work with teachers to integrate a CEMS approach into four Algebra I units. In Year 1, we will work with a small number of teachers to refine our existing CEMS materials, to integrate the materials into their curriculum, and to validate outcome measures that assess multiple types of knowledge (e.g., procedural flexibility, conceptual knowledge and procedural knowledge). In Year 2, we will determine the effects of our materials versus a “business as usual” control. In Year 3, we will again study the effects of the CEMS approach versus business as usual, but with a larger group of teachers; we will also study the quality of implementation and impact on student outcomes after treatment teachers have gained some proficiency with the CEMS approach. Using both quantitative and qualitative analyses, we will evaluate the hypotheses that: a) Classroom teachers can successfully and consistently integrate a CEMS approach in their algebra instruction, b) Students’ procedural flexibility, procedural knowledge, and conceptual knowledge for a variety of algebra topics can be reliably assessed and each type of knowledge is positively related and predictive of one another over time, and c) Integrating a CEMS approach supports better procedural flexibility, conceptual knowledge, and procedural knowledge for a variety of algebra topics (units) than business as usual instruction.

BPC-DP: Deploying a Vertically-Integrated Computing Curriculum to At-Risk Students (2011-2013)
National Science Center

Star's role on this project will be to supervise and mentor his doctoral student advisee Emmanuel Schanzer. Schanzer will be responsible for all aspects of the project, including design and piloting of instruments, data collection and analysis, and results dissemination. Note that the data collected as part of this project are intended to be used for Schanzer's dissertation and other publications and presentations.

Maciejewski, W., & Star, J.R. (in press). Developing flexible procedural knowledge in undergraduate calculus. Research in Mathematics Education. doi: 10.1080/14794802.2016.1148626,(forthcoming)

Star, J.R., & Verschaffel, L. (in press). Providing support for student learning: Recommendations from cognitive science for the teaching of mathematics. In J. Cai (Ed.), Handbook of Research on Mathematics Teaching and Learning (3rd ed). Reston, VA: National Council of Teachers of Mathematics.,(forthcoming)

Star, J.R., & Rittle-Johnson, B. (2016). Toward an educational psychology of mathematics education. In E. Anderman & L. Corno (Eds.), Handbook of Educational Psychology (3rd ed., pp. 257-268). New York: Taylor & Francis.,(2016)

Star, J. R. (2016). Small steps forward: Improving mathematics instruction incrementally. Phi Delta Kappan, 97, 58-62. doi: 10.1177/0031721716641651,(2016)

Star, J.R., Pollack, C., Durkin, K., Rittle-Johnson, B., Lynch, K., Newton, K., & Gogolen, C. (2015). Learning from comparison in algebra. Contemporary Educational Psychology, 40, 41-54. doi: dx.doi.org/10.1016/j.cedpsych.2014.05.005,(2015)

Star, J.R., Newton, K., Pollack, C., Kokka, K., Rittle-Johnson, B., & Durkin, K. (2015). Student, teacher, and instructional characteristics related to students' gains in flexibility. Contemporary Educational Psychology, 41, 198-208. doi: dx.doi.org/10.1016/j.cedpsych.2015.03.001,(2015)

Star, J.R., & Pollack, C. (2015). Inhibitory control and mathematics learning: Definitional and operational considerations. ZDM - The International Journal on Mathematics Education, 47(5), 859-863. doi: 10.1007/s11858-015-0716-1,(2015)

Rittle-Johnson, B., Schneider, M., & Star, J.R. (2015). Not a one-way street: Bi-directional relations between procedural and conceptual knowledge of mathematics. Educational Psychology Review, 27(4), 587-597. doi: 10.1007/s10648-015-9302-x,(2015)

Star, J.R., Chen, J., Taylor, M., Durkin, K., Dede, C., & Chao, T. (2014). Evaluating technology-based strategies for enhancing motivation in mathematics. International Journal of STEM Education, 1:7. doi:10.1186/2196-7822-1-7.,(2014)

Lynch, K. & Star, J.R. (2014). Exploring teachers' implementation of comparison in Algebra I. Journal of Mathematical Behavior, 35, 144-163. doi: dx.doi.org/10.1016/j.jmathb.2014.07.003,(2014)

Lynch, K., & Star, J.R. (2014). Teachers' views about multiple strategies in middle and high school mathematics. Mathematical Thinking and Learning, 16(2), 85-108. doi: 10.1080/10986065.2014.889501.,(2014)

Star, J. R., Caronongan, P., Foegen, A., Furgeson, J., Keating, B., Larson, M. R., Lyskawa, J., McCallum, W. G., Porath, J., & Zbiek, R. M. (2014). Teaching Strategies for Improving Algebra Knowledge in Middle and High School Students (NCEE 2014-4333). Washington, DC: National Center for Education Evaluation and Regional Assistance (NCEE), Institute of Education Sciences, U.S. Department of Education.,(2014)

Lynch, K., & Star, J.R. (2014). Views of struggling students on instruction incorporating multiple strategies in Algebra I: An exploratory study. Journal for Research in Mathematics Education, 45(1), 6-18.,(2014)

Star, J.R., & Kokka, K. (2013). Using strategic interruptions to effectively integrate whole class and small group instruction in mathematics. The Mathematics Educator (Singapore), 14 (1&2), 1-20.,(2013)

Murray, E., & Star, J.R. (2013). What do secondary prospective mathematics teachers need to know? Content courses connecting secondary and tertiary mathematics. Notices of the American Mathematical Society, 60(10), 1297-1299.,(2013)

Newton, K.J., & Star, J.R. (2013). Exploring the nature and impact of model teaching with worked example pairs. Mathematics Teacher Educator, 2(1), 86-102.,(2013)

Star, J.R., & Stylianides, G.J. (2013). Procedural and conceptual knowledge: Exploring the gap between knowledge type and knowledge quality. Canadian Journal of Science, Mathematics, and Technology Education, 13(2), 169-181.,(2013)

Rittle-Johnson, B., Star, J.R., & Durkin, K. (2012). Developing procedural flexibility: When should multiple procedures be introduced? British Journal of Educational Psychology, 82, 436-455.,(2012)

Schneider, M., Rittle-Johnson, B., & Star, J.R. (2011). Relations between conceptual knowledge, procedural knowledge, and procedural flexibility in two samples differing in prior knowledge. Developmental Psychology, 47(6), 1525-1538.,(2011)

Yakes, C., & Star, J.R. (2011). Using comparison to develop teachers' flexibility in algebra. Journal of Mathematics Teacher Education, 14, 175-191.,(2011)

Star, J.R., Kenyon, M., Joiner, R., & Rittle-Johnson, B. (2010). Comparing pays off! Mathematics Teacher, 103(8), 608-612.,(2010)

Star, J.R., Kenyon, M., Joiner, R., & Rittle-Johnson, B. (2010). Comparison helps students learn to be better estimators. Teaching Children Mathematics, 16(9), 557-563.,(2010)

Newton, K., Star, J.R., & Lynch, K. (2010). Exploring the development of flexibility in struggling algebra students. Mathematical Thinking and Learning, 12(4), 282-305.,(2010)

Star, J.R., & Newton, K.J. (2009). The nature and development of experts' strategy flexibility for solving equations. ZDM - The International Journal on Mathematics Education, 41, 557-567.,(2009)

Rittle-Johnson, B., Star, J.R., & Durkin, K. (2009). The importance of prior knowledge when comparing examples: Impact on conceptual and procedural knowledge of equation solving. Journal of Educational Psychology, 101(4), 836-852.,(2009)

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.,(2009)

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.,(2009)

Gersten, R., Beckmann, S., Clarke, B., Foegen, A., Marsh, L., Star, J.R., & Witzel, B. (2009). Assisting students struggling with mathematics: Response to intervention (RtI) for elementary and middle schools (NCEE 2009-4060). Washington, D.C.: National Center on Educational Research, Institute of Education Sciences, U.S. Department of Education.,(2009)

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.,(2009)

Star, J.R. & Rittle-Johnson, B. (2008). Flexibility in problem solving: The case of equation solving. Learning and Instruction, 18, 565-579.,(2008)

Star, J.R., & Strickland, S.K. Learning to observe: Using video to improve preservice teachers’ ability to notice. Journal of Mathematics Teacher Education, 11, 107-125.,(2008)

Star, J.R., Smith, J., & Jansen, A. What do students notice as different between reform and traditional mathematics programs? Journal for Research in Mathematics Education, 39(1), 9-32.,(2008)

Star, J.R. Foregrounding procedural knowledge. Journal for Research in Mathematics Education, 38(2), 132-135.,(2007)

Rittle-Johnson, B, & Star, J.R. 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.,(2007)

Smith, J., & Star, J.R. Expanding the notion of impact of Standards-based mathematics curricula. Journal for Research in Mathematics Education, 38(1), 3-34.,(2007)

Halpern, D., Aronson, J., Reimer, N. Simpkins, S., Star, J., & Wentzel, K. Encouraging girls in math and science (NCER 2007-2003). Washington, D.C.: National Center on Educational Research, Institute of Education Sciences, U.S. Department of Education.,(2007)

Star, J.R., & Seifert, C. The development of flexibility in equation solving. Contemporary Educational Psychology, 31, 280-300.,(2006)

Star, J.R. Reconceptualizing procedural knowledge. Journal for Research in Mathematics Education, 36(5), 404-411.,(2005)

Editorial Board, Journal for Research in Mathematics Education,(2016-present)

Editorial Board, Journal of Educational Psychology,(2016-present)

Editorial Board, International Journal of STEM Education,(2013-present)

Co-Editor, Elementary School Journal,(2012-present)

Executive Editor,Editorial Board, Contemporary Educational Psychology,(2006-present)