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Early Algebra Publications

Project Book Chapter | Project Journal Publications | Related Prior Papers | Conference Proceedings | Conference Presentations

Project Book Chapters

Rittle-Johnson, B. & Schneider M. (in press). Developing conceptual and procedural knowledge of mathematics: An updated review. To appear in R. C. Kadosh &  A. Dowker (Eds.) The oxford handbook of numerical cognition. Oxford University Press.

Project Journal Publications

Note: Final journal publication version of the papers are available by request by emailing bethany.rittle-johnson@vanderbilt.edu or the first author of the paper.  Click here for current contact information for the research team.

Rittle-Johnson, B., Loehr, A. M., & Durkin, K. (in press). Promoting self-explanation to improve mathematics learning: A meta-analysis and instructional design principles. ZDM Mathematics Education doi: 10.1007/s11858-017-0834-z

Miller, M., Rittle-Johnson, B., Loehr, A. M., & Fyfe, E. R. (in press). The influence of relational knowledge and executive function on preschoolers’ repeating pattern knowledge. Journal of Cognition and Development.

Rittle-Johnson, B., Fyfe, E. R., Loehr, A. M., & Miller, M. R. (2015). Beyond numeracy in preschool: Adding patterns to the equation. Early Childhood Research Quarterly, 31, 101-112.

Fyfe, E. R., McNeil, N. M., & Rittle‐Johnson, B. (2015). Easy as ABCABC: Abstract Language Facilitates Performance on a Concrete Patterning Task. Child development .

Loehr, A. M., Fyfe, E. R., & Rittle-Johnson, B. (2015). Wait for it… Delaying Instruction improves mathematics problem solving: A classroom study. The Journal of Problem Solving, 7(1), Article 5. Retrieved from http://docs.lib.purdue.edu/jps/vol7/iss1/5

Fyfe, E. R., DeCaro, M. S., & Rittle-Johnson, B. (2014). When feedback is cognitively-demanding: The importance of working memory capacity. Instructional Science. (Early View) doi: 10.1007/s11251-014-9323-8

Fyfe, E. R., DeCaro, M. S., & Rittle-Johnson, B. (2014). An alternative time for telling: When conceptual instruction prior to exploration improves mathematical knowledge. British Journal of Educational Psychology. (Early View) doi: 10.1111/bjep.12035

McEldoon, K. L., Durkin, K. L., & Rittle-Johnson, B. (2013). Is self-explanation worth the time? A comparison to additional practice. British Journal of Educational Psychology. doi:10.1111/j.2044-8279.2012.02083.x

Rittle-Johnson, B., Fyfe, E. R., McLean, L. E., & McEldoon, K. L. (2013). Emerging understanding of patterning in four year olds. Journal of Cognition and Development. doi:10.1080/15248372.2012.689897

Fyfe, E. R., Rittle-Johnson, B., & DeCaro, M. S. (2012). The effects of feedback during exploratory mathematics problem solving: Prior knowledge matters. Journal of Educational Psychology,104, 1094-1108. doi:10.1037/a0028389

Mathews, P. G., Rittle-Johnson, B., McEldoon, K. L., Taylor, R. S. (2012). Measure for measure: What combining diverse measures reveals about children's understanding of the equal sign as an indicator of mathematical equality. Journal for Research in Mathematics Education, 43(3), 316-350.

DeCaro, M. S. & Rittle-Johnson, B. (2012). Exploring mathematics problems prepares children to learn from instruction. Journal of Experimental Child Psychology, 113, 552-568. doi:10.1016/j.jecp.2012.06.009

Rittle-Johnson, B., Mathews, P. G., Taylor, R. & McEldoon, K. (2011). Assessing knowledge of mathematical equivalence: A construct modeling approach. Journal of Educational Psychology, 103, 85-104. doi:10.1037/a0021334

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Related Prior Papers

McNeil, N. M., Rittle-Johnson, B., Hattikudur, S., & Peterson, L. A. (2010). Continuity in representation between children and adults: Arithmetic knowledge hinders undergraduates' algebraic problem solving. Journal of Cognition and Development, 11: 4, 437-457.

Matthews, P. G. & Rittle-Johnson, B. (2009). In pursuit of knowledge: Comparing self-explanations, concepts, and procedures as pedagogical tools. Journal of Experimental Child Psychology, 104, 1-21.

Rittle-Johnson, B., Saylor, M. & Swygart, K. (2008). Learning from explaining: Does it matter if mom is listening? Journal of Experimental Child Psychology, 100(3), 215-224.

Rittle-Johnson, B. (2006). Promoting transfer: Effects of self-explanation and direct instruction. Child Development, 7(1), 1-15.

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.

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Conference Proceedings

DeCaro, D. A., DeCaro, M. S. 1 , & Rittle-Johnson, B. (2013, August). Achievement motivation and strategy selection during exploratory learning. Paper presented at the 35th Annual Conference of the Cognitive Science Society. Berlin, Germany: Cognitive Science Society. (1Joint first author)

Fyfe, E. R., & Rittle-Johnson, B. (2012, August). The effects of feedback during exploration depend on prior knowledge. In N. Miyake, D. Peebles, & R. P. Cooper (Eds.), Proceedings of the 34th Annual Conference of the Cognitive Science Society (pp. 348-354). Sapporo, Japan: Cognitive Science Society.

McEldoon, K., Durkin, K. & Rittle-Johnson, B. (2011, July). The Effects of self-explanation and practice on strategy use [Abstract]. In L. Carlson, C. Hölscher, & T. Shipley (Eds.), Proceedings of the 33rd Annual Conference of the Cognitive Science Society (p. 3258). Boston, MA: Cognitive Science Society. 

McEldoon, K. & Rittle-Johnson, B. (2010, October). Assessing elementary students' functional thinking skills: The case of function tables. In P. Brosnan, D. B. Erchick, & L. Flevares (Eds.) Proceedings of the Thirty Second Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education: Optimizing Student Understanding in Mathematics (p. 202). Columbus, OH: ERIC Clearinghouse for Science, Mathematics, and Environmental Education.

Rittle-Johnson, B., Matthews, P., Taylor, R. & McEldoon, K. (2010, October). Assessing knowledge of mathematical equivalence: A construct modeling approach.  In P. Brosnan, D. B. Erchick, & L. Flevares (Eds.) Proceedings of the Thirty Second Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education: Optimizing Student Understanding in Mathematics (p. 211). Columbus, OH: ERIC Clearinghouse for Science, Mathematics, and Environmental Education.

DeCaro, M. & Rittle-Johnson, B. (2010, August).  The capacity to discover: Working memory and the ability to use self-explanation to discover early algebra concepts. In S. Ohlsson & R. Catrambone (Eds.) Cognition in Flux: Proceedings of the 32nd Annual Meeting of the Cognitive Science Society (p. 536). Austin, TX: Cognitive Science Society. 

McEldoon, K., Cochrane-Braswell, C., & Rittle-Johnson, B. (2010, August). In S. Ohlsson & R. Catrambone (Eds.) Effects of problem context on strategy use within functional thinking. Cognition in Flux: Proceedings of the 32nd Annual Meeting of the Cognitive Science Society (pp. 145-149). Austin, TX: Cognitive Science Society.

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Conference Presentations

Rittle-Johnson, B., Fyfe, E. R., Loehr, A. M., & Miller, M. R. (2015, October). It's a pattern! The importance of pattern knowledge for mathematics. Paper presented at the Cognitive Development Society (CDS), Columbus, OH. 

Loehr, A. M., Rittle-Johnson, B., Fyfe, E. R. (2015, May). It's a pattern! Growth in preschoolers' pattern knowledge. Poster presented at the Math Cognition and Learning Conference, St. Louis, MO. 

Rittle-Johnson, B., Fyfe, E. R., Loehr, A. M. (2015, March). "Just tell me how to solve it." The impact of including procedural instruction in conjunction with conceptual instruction. Poster presented at Society for Research in Child Development (SRCD), Philadelphia, PA.

Fyfe, E. R., Loehr, A. M., Rittle-Johnson, B., Miller, M. R. (2014, April). Enhancing the quality of children’s explanations to promote patterning knowledge. Paper presented at the American Education Research Association Conference (AERA), Philadelphia, PA.

Fyfe, E. R., DeCaro, M. S., & Rittle-Johnson, B. (2014, April). The role of feedback type and working memory capacity during problem solving. Paper presented at the American Education Research Association Conference (AERA), Philadelphia, PA.

Loehr, A. M., Fyfe, E. R., Miller, M. R., & Rittle-Johnson, B. (2014, April). Learning from explanations: Does it matter who provides them? Paper presented at the American Education Research Association Conference (AERA), Philadelphia, PA.

Loehr, A. M., Rittle-Johnson, B., Rajendran, A. (2014, April). Promoting mathematical problem solving and explanation: The effects of extended homework use. Poster presented at the American Education Research Association Conference (AERA), Philadelphia, PA.

Rittle-Johnson, B., Fyfe, E. R., Loehr, A. M., & DeCaro, M. S. (2014, April). Learning from explanation: The timing and source of explanations for learning early algebra. Paper presented at the American Education Research Association Conference (AERA), Philadelphia, PA. 

Miller, M. R., Rittle-Johnson, B., Loehr, A. M., & Fyfe, E. R. (2013, October). Importance of executive function for learning about patterns. Poster presented at the Eighth Biennial Meeting of the Cognitive Development Society, Memphis, TN.

Loehr, A. M., Rittle-Johnson, B., Rajendran, A. (2013, October). Promoting mathematical problem solving and explanation at home. Poster presented at the Eighth Biennial Meeting of the Cognitive Development Society, Memphis, TN. 

Rittle-Johnson, B. (2013, July). The value of problem exploration: When struggling to solve unfamiliar problems prepares children to learn from mathematics instruction. Keynote talk at the 2013 Midwest Meeting on Mathematical Thinking, Minneapolis, MN.

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Loehr, A. M., Miller, M. R., DeCaro, M. S., & Rittle-Johnson, B. (2013, May). Semantic verbal fluency predicts mathematical learning. Poster presented at the Association for Psychological Science 25th Annual Convention, Washington, DC. 

Miller, M. R., Loehr, A. M., Fyfe, E. R., Rittle-Johnson, B., McLean, L. E., & McEldoon, K. L. (2013, May). Preschoolers' knowledge of repeating patterns over time. Poster presented at the Association for Psychological Science 25th Annual Convention, Washington, DC. 

McEldoon, K. L., Liu, R., Rittle-Johnson, B. (2013, April). Verbal imprecision in mathematical explanations as an indicator of learning. Poster presented at The Society for Research in Child Development Conference. Seattle, WA.

McEldoon, K. L., & Rittle-Johnson, B. (2013, April). Self-explanation improves mathematics learning in low prior knowledge students. Poster presented at The Society for Research in Child Development Conference. Seattle, WA.

Fyfe, E. R.,DeCaro, M. S., & Rittle-Johnson, B. (2013, March). An alternative time for telling: When conceptual instruction prior to exploration improves mathematical knowledge. Paper presented at the Society for Research on Educational Effectiveness (SREE), Washington, DC.

McEldoon, K. L., Cho, S. J-., Rittle-Johnson, B. (2012, September). Measuring intervention effectiveness: The benefits of an item response theory approach. Paper presented at the Society for Research in Educational Effectiveness. The Fairmont, Washington, DC.

Rittle-Johnson, B. (2012, August). Overcoming misconceptions: Insights from research on understanding the equal sign. Keynote talk at the International Conference on Conceptual Change, Trier, Germany.

Rittle-Johnson, B., Fyfe, E. R., McLean, L. E., & McEldoon, K. L. (2011, October). Algebra in preschool: Emerging understanding of patterns in four-year-olds. NSF Research and Evaluation on Education in Science and Engineering (REESE) Principle Investigator Meeting, Washington, DC. 

DeCaro, M. & Rittle-Johnson, B. (2011, September). Preparing to learn from math instruction: Mastery-oriented studentsbenefit most from exploratory activities. Paper presented at the Society for Research on Educational Effectiveness (SREE) Fall 2011 Conference, Washington, DC.

Fyfe, E.,Rittle-Johnson, B., & DeCaro, M. (2011, September). The effects of feedback during exploratory math practice. Paper presented at the Society for Research on Educational Effectiveness (SREE) Fall 2011 Conference, Washington, DC.

DeCaro, M. S., & Rittle-Johnson, B. (2011, April). Self-explanation prompts are less beneficial if students know more. Paper presented at the American Education Research Association Conference, New Orleans, LA.

DeCaro, M. S., & Rittle-Johnson, B. (2011, March). Preparing to learn from math instruction by solving problems first. In B. Rittle-Johnson & M. S. DeCaro (chairs), When are times for telling? Preparing students to learn from instruction. Symposium presented atthe  Society for Research in Child Development Conference, Montréal, Canada.

McEldoon, K., Durkin, K., & Rittle-Johnson, B. (2011, March). Making the most of instructional time: The benefit of self-explanation. Paper presented at the Biennial Meeting of the Society for Research in Child Development, Montréal, Canada.

Matthews, P.G., Rittle-Johnson, B., Taylor, R. S., & McEldoon, K. L. (2011, March). Understanding the equals sign as a gateway to algebraic thinking. Poster presented at the Biennial Meeting of the Society for Research in Child Development, Montréal, Canada.

DeCaro, M. S., & Rittle-Johnson, B. (2010, June). Self-explanation as a tool for discovering early algebra procedures: The importance of working memory capacity. Poster presented at the Institute for Education Sciences Research Conference, Washington D.C.

McEldoon, K., Rittle-Johnson, B., DeCaro, M. & Cho, S. J. (2010, June). Measuring multidimensional mathematical equivalence: A construct modeling approach. Poster presented at the Institute for Education Sciences Research Conference, Washington, D.C.

Matthews, P. G., Rittle-Johnson, B., Taylor, R. S., McEldoon, K. (2010, March). Understanding the equals sign as a gateway to algebraic thinking. Paper presented at the 2010 Society for Research on Educational Effectiveness (SREE) conference, Washington DC.

Taylor, R., Rittle-Johnson, B., Matthews, P., & McEldoon, K., (2009, March). Mapping children's understanding of mathematical equivalence. Paper presented at the 2009 Society for Research on Educational Effectiveness conference, Washington DC.

McEldoon, K. L., Cochrane-Braswell, C. & Rittle-Johnson, B. (2009, October). What's the rule? Factors influencing strategy use on functional thinking problems. Poster presented at Cognitive Development Society Conference, El Tropicano Hotel. San Antonio, TX.

McEldoon, K. L. & Rittle-Johnson, B. (2009, June). Mapping functional thinking. Poster presented at Institute of Education Sciences, Marriott Wardman Park Hotel. Washington, DC.

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