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Intervention, Evaluation, and Policy Studies

Learning Algebra by Example in Real-World Classrooms

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REFERENCES

  • Abdal-Haqq, I. (1996). Making time for teacher professional development. In ERIC Digest (#95-4). Washington, DC: ERIC Clearinghouse on Teaching and Teacher Education.
  • Aleven, V., & Koedinger, K.R. (2002). An effective metacognitive strategy: Learning by doing and explaining with a computer-based Cognitive Tutor. Cognitive Science, 26, 147–179.
  • Atkinson, R.K., Renkl, A., & Merrill, M.M. (2003). Transitioning from studying examples to solving problems: Combining fading with prompting fosters learning. Journal of Educational Psychology, 95, 774–783.
  • Barab, S.A., & Squire, K.D. (2004). Design-based research: Putting our stake in the ground. Journal of the Learning Sciences, 13(1), 1–14.
  • Baroody, A., & Ginsburg, H. (1983). The effects of instructions on children's understanding of the equals sign. The Elementary School Journal, 84, 199–212.
  • Bell, B.A., Morgan, G.B., Kromrey, J.D., & Ferron, J.M. (2010). The impact of small cluster size on multilevel models: A Monte Carlo examination of two-level models with binary and continuous predictors. JSM Proceedings, Section on Survey Research Methods (pp. 4057–4067). Vancouver, BC: American Statistical Association.
  • Ben-Zeev, T., & Star, J.R. (2001). Spurious correlations in mathematical thinking. Cognition and Instruction, 19, 253–275.
  • Booth, J.L. (2011). Why can't students get the concept of math? Perspectives on Language and Literacy, Spring, 31–35.
  • Booth, J.L., Barbieri, C., Eyer, F., & Paré-Blagoev, E.J. (2014). Persistent and pernicious misconceptions in algebraic problem solving. Journal of Problem Solving, 7, 10–23.
  • Booth, J.L., Cooper, L., Donovan, M.S., Huyghe, A., Koedinger, K.R., & Paré-Blagoev, E.J. (2015). Design-based research within the constraints of practice: AlgebraByExample. Journal of Education for Students Placed at Risk, 20(1–2), 79–100.
  • Booth, J.L., & Koedinger, K.R. (2008). Key misconceptions in algebraic problem solving. In B.C. Love, K. McRae, & V.M. Sloutsky (Eds.), Proceedings of the 30th Annual Cognitive Science Society (pp. 571–576). Austin, TX: Cognitive Science Society.
  • Booth, J.L., Koedinger, K.R., & Siegler, R.S. (2007). The effect of prior conceptual knowledge on procedural performance and learning in algebra [Abstract]. In D.S. McNamara & J.G. Trafton (Eds.), Proceedings of the 29th Annual Cognitive Science Society (p. 1714). Austin, TX: Cognitive Science Society.
  • Booth, J.L., Lange, K.E., Koedinger, K.R., & Newton, K.J. (2013). Example problems that improve student learning in algebra: Differentiating between correct and incorrect examples. Learning and Instruction, 25, 24–34.
  • Booth, L.R. (1984). Algebra: Children's strategies and errors. Windsor, UK: NFER-Nelson.
  • Brown, A.L. (1992). Design experiments: Theoretical and methodological challenges in creating complex interventions in classroom settings. The Journal of the Learning Sciences, 2(2), 141–178.
  • Carroll, W.M. (1994). Using worked examples as an instructional support in the algebra classroom. Journal of Educational Psychology, 86(3), 360–367.
  • Catrambone, R. (1998). The subgoal learning model: Creating better examples so that students can solve novel problems. Journal of Experimental Psychology: General, 127(4), 355–376.
  • Catrambone, R., & Holyoak, K.J. (1989). Overcoming contextual limitations on problem-solving transfer. Journal of Experimental Psychology: Learning, Memory, and Cognition, 15, 1147–1156.
  • Catrambone, R., & Yuasa, M. (2006). Acquisition of procedures: The effects of example elaborations and active learning exercises. Learning and Instruction, 16, 139–153.
  • Chang, N. (2006). Learning to discriminate and generalize through problem comparisons (Unpublished doctoral dissertation). Carnegie Mellon University, Pittsburgh, PA.
  • Chi, M.T. H. (2000). Self-explaining expository texts: The dual processes of generating inferences and repairing mental models. In R. Glaser (Ed.), Advances in Instructional Psychology (pp 161–238). Hillsdale, NJ: Lawrence Erlbaum Associates.
  • Cooper, G., & Sweller, J. (1987). Effects of schema acquisition and rule automation on mathematical problem-solving transfer. Journal of Educational Psychology, 79(4), 347–362.
  • Davenport, J.L., Klahr, D., & Koedinger, K.R. (2007, August). The influence of diagrams on chemistry learning. Paper presented at the Biennial Conference of the European Association for Research on Learning and Instruction, Hungary, Budapest.
  • Dynarski, M., Agodini, R., Heaviside, S., Novak, T., Carey, N., Campuzano, L., Means, B.,... Sussex, W. (2007). Effectiveness of reading and mathematics software products: Findings from the first student cohort. Washington, DC: U.S. Department of Education, Institute of Education Sciences.
  • Groe, C.S., & Renkl, A. (2007). Finding and fixing errors in worked examples: Can this foster learning outcomes? Learning & Instruction, 17, 617–634.
  • Hausmann, R.G. M., & VanLehn, K. (2007). Explaining self-explaining: A contrast between content and generation. In R. Luckin, K.R. Koedinger, & J. Greer (Eds.), Artificial intelligence in education: Building technology rich learning contexts that work (Vol. 158, pp. 417–424). Amsterdam: IOS Press.
  • Hilbert, T.S., Renkl, A., Kessler, S., & Reiss, K. (2008). Learning to prove in geometry: Learning from heuristic examples and how it can be supported. Learning and Instruction, 18, 54–65.
  • Ingersoll, R.M. (2004). Why do high-poverty schools have difficulty staffing their classrooms with qualified teachers? (Report prepared for Renewing Our Schools, Securing Our Future – A National Task Force on Public Education). Washington, DC: The Center for American Progress and the Institute for America's Future. Retrieved from http://www.americanprogress.org/site/pp.asp?c=biJRJ8OVF&b=252682
  • Kalyuga, S., Chandler, P., & Sweller, J. (2001). Learner experience and efficiency of instructional guidance. Educational Psychology, 21(1), 5–23.
  • Kalyuga, S., Chandler, P., Tuovinen, J., & Sweller, J. (2001). When problem solving is superior to studying worked examples. Journal of Educational Psychology, 93(3), 579–588.
  • Kieran, C. (1981). Concepts associated with the equality symbol. Educational Studies in Mathematics, 12, 317–326.
  • Kim, R., Weitz, R., Heffernan, N., & Krach, N. (2009). Tutored problem solving vs. “pure”: Worked examples. In N.A. Taatgen & H. van Rijn (Eds.), Proceedings of the 31st Annual Conference of the Cognitive Science Society (pp. 3121–3126). Austin, TX: Cognitive Science Society.
  • Knuth, E.J., Stephens, A.C., McNeil, N.M., & Alibali, M.W. (2006). Does understanding the equal sign matter? Evidence from solving equations. Journal for Research in Mathematics Education, 37, 297–312.
  • Koedinger, K.R., Booth, J.L., & Klahr, D. (2013). Instructional complexity and the science to constrain it. Science, 342, 935–937.
  • Küchemann, D. (1978). Children's understanding of numerical variables. Mathematics in School, 7, 23–26.
  • Kulik, J.A. (1994). Meta-analytic studies of findings on computer-based instruction. In E.L.F. Baker and H.F. O’Neil, Jr. (Eds.), Technology assessment in education and training (pp. 9–33). Hillsdale, NJ: Lawrence Erlbaum.
  • Ladson-Billings, G.J. (1995). Toward a theory of culturally relevant pedagogy. American Education Research Journal, 35, 465–491.
  • Maas, C.J. M., & Hox, J.J. (2005). Sufficient sample sizes for multilevel modeling. Methodology, 1(3), 86–92.
  • Mayer, R.E. (1989). Systematic thinking fostered by illustrations in scientific text. Journal of Educational Psychology, 81, 240–246.
  • Mayer, R.E. (2005). Cognitive theory of multimedia learning. In R. Mayer (Ed.), The Cambridge handbook of multimedia learning (pp. 31–48). New York, NY: Cambridge University Press.
  • McLaren, B.M., Lim, S., Gagnon, F., Yaron, D., and Koedinger, K.R. (2006). Studying the effects of personalized language and worked examples in the context of a web-based intelligent tutor. In Proceedings of the 8th International Conference on Intelligent Tutoring Systems (pp. 318–328). New York, NY: Springer.
  • Moreno, R., Reisslein, M., & Ozogul, G. (2009). Optimizing worked-example instruction in electrical engineering: The role of fading and feedback during problem-solving practice. Journal of Engineering Education, 98, 83–92.
  • Murphy, R., Penuel, W., Means, B., Korbak, C., & Whaley, A. (2001). E-DESK: A review of recent evidence on the effectiveness of discrete educational software. Menlo Park, CA: SRI International.
  • National Mathematics Advisory Panel. (2008). Foundations for success: The final report of the National Mathematics Advisory Panel. Washington, DC: U.S. Department of Education.
  • Ohlsson, S. (1996). Learning from error and the design of task environments. International Journal of Educational Research, 25(5), 419–448.
  • Paas, F. (1992). Training strategies for attaining transfer of problem-solving skill in statistics: A cognitive-load approach. Journal of Educational Psychology, 84, 429–434.
  • Paas, F., & Van Merriënboer, J. (1994). Variability of worked examples and transfer of geometrical problem-solving skills: A cognitive-load approach. Journal of Educational Psychology, 86(1), 122–133.
  • Pashler, H., Bain, P., Bottge, B., Graesser, A., Koedinger, K., McDaniel, M., & Metcalfe, J. (2007). Organizing instruction and study to improve student learning (NCER 2007-2004). Washington, DC: National Center for Education Research, Institute of Education Sciences, U.S. Department of Education.
  • Raudenbush, S.W., & Bryk, A.S. (2002). Hierarchical linear models. Applications and data analysis methods (2nd ed.). Thousand Oaks, CA: Sage Publications.
  • Raudenbush, S.W., Bryk, A.S., & Congdon, R. (2004). HLM (Version 6) [Computer software]. Lincolnwood, IL: Scientific Software International.
  • Renkl, A. (1997). Learning from worked-out examples: A study on individual differences. Cognitive Science: A Multidisciplinary Journal, 21(1), 1–29.
  • Renkl, A. (2002). Worked-out examples: Instructional explanations support learning by self-explanations. Learning and Instruction, 12(5), 529–556.
  • Renkl, A., Atkinson, R., Maier, U., & Staley, R. (2002). From example study to problem solving: Smooth transitions help learning. Journal of Experimental Education, 70(4), 293–315.
  • Rittle-Johnson, B. (2006). Promoting transfer: Effects of self-explanation and direct instruction. Child Development, 77, 1–29.
  • Ross, B.H. (1989). Distinguishing types of superficial similarities: Different effects on the access and use of earlier problems. Journal of Experimental Psychology: Learning, Memory, and Cognition, 15, 456–468.
  • Roy, M., & Chi, M.T. H. (2005). Self-explanation in a multi-media context. In R. Mayer (Ed.), The Cambridge handbook of multimedia learning (pp. 271–286). New York, NY: Cambridge University Press.
  • Schorr, T., Gerjets, P., Scheiter, K., & Laouris, Y. (2002). Designing sets of instruction examples to accomplish different goals of instruction. In W.D. Gray & C.D. Schunn (Eds.), Proceedings of the 24th Annual Conference of the Cognitive Science Society (pp. 810–815). Mahwah, NJ: Erlbaum.
  • Schwonke, R., Renkl, A., Krieg, C., Wittwer, J., Aleven, V., & Salden, R.J. C. M. (2009). The worked-example effect: Not an artifact of lousy control conditions. Computers in Human Behavior, 25, 258–266.
  • Siegler, R.S. (2002). Microgenetic studies of self-explanations. In N. Granott & J. Parziale (Eds.), Microdevelopment: Transition processes in development and learning (pp. 31–58). New York, NY: Cambridge University Press.
  • Siegler, R.S., & Chen, Z. (2008). Differentiation and integration: Guiding principles for analyzing cognitive change. Developmental Science, 11, 433–448.
  • Songer, N.B., Lee H., & Kam, R. (2002). Technology-rich inquiry science in urban classrooms: What are the barriers to inquiry pedagogy? Journal of Research in Science Teaching, 39(2), 128–150.
  • Steele, C.M. (1992, April). Race and the schooling of Black Americans. Atlantic Monthly, 68–78.
  • Steele, C.M., & Aronson, J. (1995). Stereotype vulnerability and the intellectual test performance of African Americans. Journal of Personality and Social Psychology, 69, 797–811.
  • Sweller, J. (1999). Instructional design in technical areas. Camberwell, Australia: ACER Press.
  • Sweller, J., & Cooper, G.A. (1985). The use of worked examples as a substitute for problem solving in learning algebra. Cognition and Instruction, 2, 59–89.
  • Tarmizi, R.A., & Sweller, J. (1988). Guidance during mathematical problem solving. Journal of Educational Psychology, 80(4), 424–436.
  • U. S. Department of Education. (1997). Mathematics equals opportunity (White Paper prepared for U.S. Secretary of Education Richard W. Riley). Washington, DC: Author.
  • Vlassis, J. (2004). Making sense of the minus sign or becoming flexible in “negativity.” Learning and Instruction, 14, 469–484.
  • Ward, M., & Sweller, J. (1990). Structuring effective worked examples. Cognition and Instruction, 7(1), 1–39.
  • What Works Clearinghouse. (2014). Procedures and standards handbook, Version 3.0. Retrieved from http://ies.ed.gov/ncee/wwc/DocumentSum.aspx?sid=19
  • Zhu, X., & Simon, H.A. (1987). Learning mathematics from examples and by doing. Cognition and Instruction, 4, 137–166.

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