**Relevant Literature**

**Erroneous Examples - Empirical Studies**

- Booth, J.L., Koedinger, K., & Siegler, R.S. (2007, October). The effect of corrective and typical self-explanation on algebraic problem solving. Poster presented at the Science of Learning Centers Awardee's Meeting in Washington, DC. (See also Pittsburgh Science of Learning Wiki page on Corrective Self-Explanation)
- Durkin, K.L., & Rittle-Johnson, B. (2008). Comparison of incorrect examples in math learning. Poster session presented at the IES annual research conference, Washington, D.C., June 2008.
- Durkin, K., & Rittle-Johnson, B. (2012). The effectiveness of using incorrect examples to support learning about decimal magnitude.
*Learning and Instruction*, 22, 206-214. - Grosse, C.S. & Renkl, A. (2007). Finding and fixing errors in worked examples: Can this foster learning outcomes?
*Learning and Instruction*, 17(6), 612-634. - Huang, T-H., Liu, Y.-C., & Shiu, C.-Y. (2008). Construction of an online learning system for decimal numbers through the use of cognitive conflict strategy.
*Computers & Education*, 50, 61-76. - Kawasaki, M. (2010). Learning to solve mathematics problems: The impact of incorrect solutions in fifth grade peersâ€™ presentations.
*Japanese Journal of Developmental Psychology*, 21 (1), 12-22. - Kopp, V., Stark, R., & Fischer, M. R. (2008). Fostering diagnostic knowledge through computer-supported, case-based worked examples: Effects of erroneous examples and feedback.
*Medical Education*, 42: 823-829. - Siegler, R.S. (2002). Microgenetic studies of self-explanation. In N. Granott and J. Parziale (eds).
*Microdevelopment, Transition Processes in Development and Learning*, (pp. 31-58). Cambridge University Press. - Siegler, R.S., & Chen, Z. (2008). Differentiation and integration: Guiding principles for analyzing cognitive change.
*Developmental Science*, 11, 433-448. - Swan, M. (1983).
*Teaching decimal place value: A comparative study of "conflict"**and "positive only" approaches*. Nottingham: Shell Centre for Mathematical Education. - Tsovaltzi, D., Melis, E., McLaren, B.M., Dietrich, M., Goguadze, G., & Meyer, A-K. (2009). Erroneous examples: A preliminary investigation into learning benefits. In U. Cress, V. Dimitrova, & M. Specht (Eds.),
*Proceedings of the Fourth European Conference on Technology Enhanced Learning, Learning in the Synergy of Multiple Disciplines*(EC-TEL 2009), LNCS 5794, September/October 2009, Nice, France. (pp. 688-693). Springer-Verlag Berlin Heidelberg. - Tsovaltzi, D., Melis, E., McLaren, B.M., Meyer, A-K., Dietrich, M. & Goguadze, G. (2010). Learning from erroneous examples: When and how do students benefit from them? In M. Wolpers, P. A. Kirschner, M. Scheffel, S. Lindstaedt, & V. Dimitrova (Eds.), Proceedings of the
*5th European Conference on Technology Enhanced Learning, Sustaining TEL: From Innovation to Learning and Practice (EC-TEL 2010)*, LNCS 6383, September/October, Barcelona, Spain. (pp. 357-373). Springer-Verlag Berlin Heidelberg.

**Erroneous Examples - Theory and/or Analysis of Possible Effects**

- Borasi, R. (1987). Exploring mathematics through the analysis of errors.
*For the Learning of Mathematics: An International Journal of Mathematics Education*, 7(3), 2-8 - Borasi, R. (1994). Capitalizing on errors as "springboards for inquiry": A teaching experiment.
*Journal for Research in Mathematics Education*, 25(2), 166-208 - Damon, W., & Killen, M. (1982). Peer interaction and the process of change in children's moral reasoning.
*Merrill-palmer Quarterly*, 28, 347-367. - Melis, E. (2005). Design of erroneous examples for ActiveMath. In B. Bredeweg Ch.-K. Looi, G. McCalla and J. Brueker (eds.).
*Artificial Intelligence in Education. Supporting Learning Through Intelligent and Socially Informed Technology. 12th International Conference*(AIED 2005), (pp. 451-458). IOS Press. - Melis, E. (2004). Erroneous examples as a source of learning in mathematics. In P. Isaias Kinshuk, D. G. Sampson (eds).
*Cognition and Exploratory Learning in the Digital Age*(CELDA 2004), (pp. 311-318), Lisbon. - Mischel, T. (1971). Piaget: Cognitive cognitive conflict and the motivation of though. In T. Mischel (Ed.),
*Cognitive development and epistemology*(pp. 311-335). New York: Academic Press. - Ohlsson, S. (1996). Learning from performance errors.
*Psychological Review*, Vol. 103, No. 2, 241-262. - Oser, F. & Spychiger, M. (eds.) (2005).
*Lernen ist schmerzhaft: zur Theorie des Negativen Wissens und zur Praxis der Fehlerkultur*. [English Translation: Learning is painful. On the theory of negative knowledge and the practice of error management.] Weinheim: Beltz (See Kopp et al article for an interpretation of this article.) - Shumway, R. J. (1974). Students Should See "Wrong" Examples: An Idea From Research on Learning.
*Arithmetic Teacher*, 21(4) 344-348 - Tsamir, P. & Tirosh, D. (2003). In-service mathematics teachers' views of errors in the classroom. In
*International Symposium: Elementary Mathematics Teaching*, Prague, August 2003. - Van den Broek, P., & Kendeou, P. (2008). Cognitive processes in comprehension of science texts: The role of co-activation in confronting misconceptions.
*Applied Cognitive Psychology*, 22, 335-351.

**Math Education - Learning of Decimals**

- Bell, A. (1982). Diagnosing students' misconceptions.
*Australian Mathematics Teacher*, 38, 6-10. - Bell, A., Fischbein, E. & Greer, B. (1984) Choice of operation in verbal arithmetic problems: The effects of number size, problem structure and context.
*Educational Studies in Mathematics*, 15 (2), 127-147. - Bell, A. M. Swan, and G. Taylor (1981). Choice of operations in verbal problems with decimal numbers.
*Educational Studies in Mathematics*12: 399-420. - Bell, A., Fischbein, E. & Greer, B. (1984). Choice of operation in verbal arithmetic problems: The effects of number size, problem structure and context.
*Educational Studies in Mathematics*, 15 (2), 127-147. - Bell, A. (1993). Principles for the design of teaching.
*Educational Studies in Mathematics 24*, 5-34. - Brekke, G. (1996). A decimal number is a pair of whole numbers. In L. Puig & A. Gutierrez (Eds.),
*Proceedings of the 20th conference for the International Group for the Psychology of Mathematics Education*(Vol. 2, pp. 137-144). Valencia, Spain: PME. - Brown, M. (1981). Place value and decimals. In K. Hart (Ed.),
*Children's Understanding of Mathematics*, 11-16 (pp. 48-65). London: John Murray. - Brown, M. (1981). 'Is it an 'add', Miss?'
*Mathematics in School*10:1, 26-28. - Brueckner, L.J. (1928). Analysis of difficulties in decimals.
*Elementary School Journal*, 29, 32-41. - Fischbein, E., M. Deri, M. Nello, & M. Marino (1985). The role of implicit models in solving verbal problems in multiplication and division.
*Journal of Research in Mathematics Education*, 16: 3-17. - Fuglestad, A. B. (1998). Computer support for diagnostic teaching. A case of decimal numbers.
*Nordic Studies in Mathematics Education (Nordisk Matematikk**Didaktikk), 6*(3-4), 25-50. - Greer, B. (1987). Nonconservation of multiplication and division involving decimals.
*Journal for Research in Mathematics Education*, 18(1), 37-45. - Graeber, A. & Tirosh, D. (1988). Multiplication and division involving decimals: Preservice elementary teachers' performance and beliefs.
*Journal of Mathematics Behavior*, 7, 263-280. - Graeber, A., Tirosh, D. & Glover, R. (1986). Preservice teachers' beliefs and performance on measurement and partitive division problems. In: G. Lappen & R. Even (Eds.)
*Proceedings of the Eighth Annual Psychology of Mathematics Education North America Conference*. East Lansing, MI. - Grossnickle, Foster E. (1941). Types of errors in division of decimals.
*The Elementary School Journal*, 42(3), 184-194 - Harel, G., Behr, M., Post, T., & Lesh, R. (1994). The impact of number type on the solution of multiplication and division problems: Further considerations. In G. Harel & J. Confrey (Eds.),
*The development of multiplicative reasoning in the learning of mathematics*(pp. 365-388). Albany, NY: SUNY Press. - Hayes, R. L. (1998).
*Teaching Negative Number Operations*. Doctor of Education Thesis, University of Melbourne. - Hiebert, J. & Tonnessen, L.H. (1978). Development of the fraction concept in two physical contexts: An exploratory investigation.
*Journal for Research in Mathematics Education*, 9, 374-378. (Cataloging of decimal misconceptions) - Hiebert, J. (1992). Mathematical, cognitive, and instructional analyses of decimal fractions. Chapter 5 in
*Analysis of arithmetic for mathematics teaching*. Lawrence Erlbaum. 283-322. - Hiebert, J., & Wearne, D. (1985). Procedures over concepts: The acquisition of decimal number knowledge. In J. Hiebert (Ed.),
*Conceptual and procedural knowledge: the case of mathematics*(pp. 199-223). Hillsdale, NJ: Erlbaum. - Hiebert, J., & Wearne, D. (1986). Procedures over concepts: The acquisition of decimal number knowledge. In J. Hiebert (Ed.),
*Conceptual and Procedural Knowledge: The Case of Mathematics*(pp. 199-223). Hillsdale, New Jersey: Lawrence Erlbaum. - Hiebert, J., Wearne, D., & Taber, S. (1991). Fourth graders' gradual construction of decimal fractions during instruction using different physical representations.
*The Elementary School Journal*, 91(4), 321-341. - Irwin, K.C. (2001). Using everyday knowledge of decimals to enhance understanding.
*Journal for Research in Mathematics Education*, 32(4), 399-420. - Isotani, S., McLaren, B.M., & Altman, M. (2010). Towards intelligent tutoring with erroneous examples: A taxonomy of decimal misconceptions. In V. Aleven, J. Kay, J. Mostow (Eds.),
*Proceedings of the 10th International Conference on Intelligent Tutoring Systems (ITS-2010)*. Lecture Notes in Computer Science, 6094 (pp. 346-348). Berlin: Springer. []**pdf** - Liu, Man-Li (2003). Study of students' decimal concepts from decimal symbol issues.
*Pingdong Normal College Journal*(18), 459-494. - Owens, D., & Super, D. (1993). Teaching and learning decimal fractions. In D. Owens (Ed.),
*Research Ideas for the Classroom: Middle Grade Mathematics*(pp. 137-158). New York, NY: Macmillan Publishing Co. - Prediger, S. (2008). The relevance of didactic categories for analysing obstacles in conceptual change: Revisiting the case of multiplication of fractions.
*Learning and Instruction*, 18(1), 1-15. - Putt, I. J. (1995). Preservice teachers ordering of decimal numbers: When more is smaller and less is larger! Focus on Learning Problems in Mathematics, 17(3), 1-15.
- Resnick, L. B., Nesher, P., Leonard, F., Magone, M., Omanson, S., & Peled, I. (1989). Conceptual bases of arithmetic errors: The case of decimal fractions.
*Journal for Research in Mathematics Education*, 20(1), 8-27. - Rittle-Johnson, B. & Koedinger, K. R. (2002). Comparing instructional strategies for integrating conceptual and procedural knowledge.
*Proceedings of the Annual Meeting [of the] North American Chapter of the International Group for the Psychology of Mathematics Education*, 969-978. - Sackur-Grisvard, C., & Leonard, F. (1985). Intermediate cognitive organizations in the process of learning a mathematical concept: The order of positive decimal numbers.
*Cognition and Instruction*, 2, 157-174. - Stacey, K., & Steinle, V. (1999). A Longitudinal study of children's thinking about decimals: A preliminary analysis. Paper presented at the
*23rd Conference of the International Group for the Psychology of Mathematics Education*, Haifa, Israel. - Stacey, K. & Steinle, V. (1998). Refining the classification of students' interpretations of decimal notation.
*Hiroshima Journal of Mathematics Education*, 6, 49-69. - Stacey, K., Helme, S., & Steinle, V. (2001). Confusions between decimals, fractions and negative numbers: A consequence of the mirror as a conceptual metaphor in three different ways. In M. v. d. Heuvel-Panhuizen (Ed.),
*Proceedings of the 25th Conference of the International Group for the Psychology of Mathematics Education*(Vol. 4, pp. 217-224). Utrecht: PME. - Stacey, K., Helme, S., Steinle, V., Baturo, A., Irwin, K., & Bana, J. (2001). Preservice teachers' knowledge of difficulties in decimal numeration.
*Journal of Mathematics Teacher Education*, 4(3),205-25. - Standiford, S. N., Klein, M. F., & Tatsuoka, K. K. (1982). Decimal fraction arithmetic: Logical Error Analysis and Its validation.
*Research report - University of Illinois at Urbana-Champaign*. - Steinle, V., & Stacey, K. (1998a). Students and decimal notation: Do they see what we see?
*Paper presented at the Thirty-fifth Annual Conference of the Mathematical Association of Victoria*. The Mathematical Association of Victoria, Brunswick, Vic. - Steinle, V. & Stacey, K. (1998). The incidence of misconceptions of decimal notation amongst students in grades 5 to 10. In C. Kanes, M. Goos and E. Warren (Eds), Teaching Mathematics in New Times.
*Proceedings of the 21st Annual Conference of MERGA*, (2) 548-555. Brisbane: MERGA. - Steinle, V. (2004). Detection and remediation of decimal misconceptions. In B. Tadich, S. Tobias, C. Brew, B. Beatty, & P. Sullivan (Eds.),
*Towards Excellence in Mathematics*(pp. 460-478). Brunswick: The Mathematical Association of Victoria. - Swan, M. (1983).
*Teaching decimal place value: A comparative study of "conflict"**and "positive only" approaches*. Nottingham: Shell Centre for Mathematical Education. - Thipkong, S. & Davis, E.J. (1991). Preservice teacher's misconceptions in interpreting and applying decimals.
*School Science and Mathematics*, 9, 93-99. (Considerable difficult that both adults and children have difficulty with decimals; A catalog of decimal misconceptions) - Woodward, J., Baxter, J., & Robinson, R. (1999). Rules and reasons: Decimal Instruction for academically low achieving students.
*Learning Disabilities Research & Practice*, 14(1), 15-24

**Math Education - Relevant General Work about Mathematics Learning**

- Brown, J.S. & Burton, R.R. (1978). Diagnostic models for procedural bugs in basic mathematical skills.
*Cognitive Science*, 2, 155-192. - Brown, J.S. & VanLehn, K. (1980). Repair Theory: A generative theory of bugs in Procedural Skills.
*Cognitive Science*, 4, 379-426. - Brown, J.S. & VanLehn, K. (1982). Towards a generative theory of "bugs." In T.P. Carpenter, J.M. Moser, & T.A. Romberg (Eds.),
*Addition and Subtraction: A Cognitive Perspective*(pp. 117-135). Hillsdale, NJ: Lawrence Erlbaum Associates, Inc. - Curtis, D.A., Heller, J.I., Clarke, C., Rabe-Hesketh, S., & Ramirez, A. (2009). The impact of math pathways and pitfalls on students' mathematics achievement.
*Paper presented at the Annual Meeting of the American Educational Research Association*(AERA) - Eryilmaz, A. (2002). Effects of conceptual assignments and conceptual change discussions on students' misconceptions and achievement regarding force and motion.
*Journal of Research in Science Teaching*39(10), 1001-10015. - Greeno, J.G. (1980). Analysis of understanding in problem solving. In R.H. Kluwe & H. Spada (Eds.),
*Developmental Models of Thinking*(pp. 199-212). New York: Academic Press. - 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(2), 346-362. - Silver, E.A. (1986). Using conceptual and procedural knowledge: A focus on relationships. In J. Hiebert (Ed.),
*Conceptual and Procedural Knowledge: The Case of Mathematics*(pp. 181-198). Hillsdale, NJ: Erlbaum.

**Correct Worked Examples**

- 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. - Catrambone, R. (1994). Improving examples to improve transfer to novel problems.
*Memory & Cognition*, 22, 606-615. - Catrambone, R. (1998). The subgoal learning model: Creating better examples so that students can solve novel problems.
*Journal of Experimental Psychology*: General 1998, Vol. 127, No. 4, 355-376. - Chi, M.T.H., Bassok, M., Lewis, M.W., Reimann, P., & Glaser, R. (1989). Self explanations: How students study and use examples in learning to solve problems.
*Cognitive Science*, 13, 145-182. - Kalyuga, S., Chandler, P., Tuovinen, J., & Sweller, J. (2001). When problem solving is superior to studying worked examples.
*Journal of Educational Psychology*, 93, 579-588. - Kalyuga, S. & Sweller, J. (2004). Measuring Knowledge to Optimize Cognitive Load Factors During Instruction.
*Journal of Educational Psychology*, Vol. 96, No. 3, 558 -568 - McLaren, B.M., Lim, S., & Koedinger, K.R. (2008). When and how often should worked examples be given to students? New results and a summary of the current state of research. In B. C. Love, K. McRae, & V. M. Sloutsky (Eds.),
*Proceedings of the 30th Annual Conference of the Cognitive Science Society*(pp. 2176-2181). Austin, TX: Cognitive Science Society. - McLaren, B.M., Lim, S., Gagnon, F., Yaron, D., & Koedinger, K.R. (2006). Studying the effects of personalized language and worked examples in the context of a web-based intelligent tutor; In the
*Proceedings of the 8th International Conference on Intelligent Tutoring Systems*(ITS-2006). Jhongli, Taiwan, June 26-30. (p. 318-328). - Paas, F. & Van Merrienboer, J.J.G. (1994). Variability of worked examples and transfer of geometrical problem-solving skills: A cognitive-load approach.
*Journal of Educational Psychology*, 86(1), 122-133. - Renkl, A. (1997). Learning from worked-out examples: A study on individual differences.
*Cognitive Science*, 21, 1-29. - Schwonke, R., Wittwer, J., Aleven, V., Salden, R.J.C.M., Krieg, C., & Renkl, A. (2007). Can tutored problem solving benefit from faded worked-out examples?
*Proceedings of the 2nd European Cognitive Science Conference*(pp. 59-64). - Schworm, S. & Renkl, A. (2002). Learning by solved example problems: Instructional explanations reduce self-explanation activity. In W. D. Gray and C. D. Schunn, editors,
*24th Annual Conference of the Cognitive Science Society*, pages 816-821. Mahwah, NJ: Erlbaum. - Sweller, J. and Cooper, G.A. (1985). The use of worked examples as a substitute for problem solving in learning algebra.
*Cognition and Instruction*, 2, 59-89. - Trafton, J.G. & Reiser, B.J. (1993). The contributions of studying examples and solving problems to skill acquisition.
*Proceedings of the 15th Conference of the Cognitive Science Society*(pp. 1017-1022). - van Gog, T., Kester, L. & Paas, F. (submitted). Effectiveness of different example-based learning strategies: Should worked examples be alternated with problems and how? Submitted for publication.
- Zhu, X., and H.A. Simon (1987). Learning mathematics from examples and by doing.
*Cognition and Instruction*4 (3): 137-66.

**Adaptation in Tutoring or Learning Systems**

- Boneh, T. Nicholson, A., Sonenberg, L., Stacey, K., & Steinle, V. (2003). Decsys: An intelligent tutoring system for decimal numeration.
*Technical Report 134*, School of CSSE, Monash University, Australia. - Evangelos, T., Andreas, P., & Stavros, D. (2003). The design and the formative evaluation of an adaptive educational system based on
cognitive styles.
*Computers & Education*, 41(1), 87-103. - Huang, T-H., Liu, Y.-C., & Shiu, C.-Y. (2008). Construction of an online learning system for decimal numbers through the use of cognitive conflict strategy.
*Computers & Education*, 50, 61-76. - Kalyuga, S. (2009). Managing cognitive load in adaptive multimedia learning, Hershey, PA: Information Science Reference.
- Melis, E., Budenbender, J., Andres, E., Frischauf, A., Goguadze, G., Libbrecht, P., Pollet, M. & Ullrich, C. (2001). ActiveMath: A generic and adaptive web-based learning environment.
*International Journal of Artificial Intelligence and Education*, 12(4): 385-407. - Monthienvichienchai, R. & Melis, E. (2005). Implementing Courseware to Support Learning Through Real-World Erroneous Examples: Student's Perceptions of Tertiary Courseware and Obstacles to Implementing Effective Delivery Through VLE, In D. Remenyi (ed).
*Proceedings of European Conference on eLearning*(ECEL-2005), (pp. 281-289). Academic Conferences International. - Stacey, K., Sonenberg, E., Nicholson, A., Boneh, T., & Steinle, V. (2003), A teacher model exploiting cognitive conflict driven by a bayesian network. In Peter Brusilovsky, Albert T. Corbett, Fiorella De Rosis (Eds),
*User Modeling 2003: Proceedings of the Ninth International Conference*. (pp. 352-362) New York: Springer-Verlag (ISBN 3540403817). - Stacey, K. & Flynn, J. (2003) Evaluating an adaptive computer system for teaching about decimals: Two case studies. In V. Aleven, U. Hoppe, J. Kay, R. Mizoguchi, H.Pain, F. Verdejo, K. Yacef (Eds) AI-ED2003
*Supplementary Proceedings of the 11th International Conference on Artificial Intelligence in Education*. (pp 454-460), Sydney: University of Sydney.

**Games for Learning Decimals**

- Boneh, T. Nicholson, A., Sonenberg, L., Stacey, K., & Steinle, V. (2003). Decsys: An intelligent tutoring system for decimal numeration.
*Technical Report 134*, School of CSSE, Monash University, Australia. - Klawe, M. (1998). When does the use of computer games and other interactive multimedia software help students learn mathematics? In:
*NCTM Standards 2000 Technology Conference.* - McIntosh, J., Stacey, K., Tromp, C., & Lightfoot, D. (2000). Designing constructivist computer games for teaching about decimal numbers. In Bana, J., Chapman, A. (eds) Mathematics Education Beyond 2000.
*Proceedings of the 23rd Annual Conference of the Mathematics Research Group of Australasia*, Freemantle (2000). 409-416. - Stacey, K. & Flynn, J. (2003) Evaluating an adaptive computer system for teaching about decimals: Two case studies. In V. Aleven, U. Hoppe, J. Kay, R. Mizoguchi, H.Pain, F. Verdejo, K. Yacef (Eds) AI-ED2003
*Supplementary Proceedings of the 11th International Conference on Artificial Intelligence in Education*. (pp 454-460), Sydney: University of Sydney.

**Erroneous Examples in Science Learning**

- Alvermann, D. E., & Hague, S. A. (1989). Comprehension of counterintuitive science text: Effects of prior knowledge and text structure.
*Journal of Educational Research*, 82, 197-202. (See Siegler and Durkin/Rittle-Johnson papers for relevance) - Eryilmaz, A. (2002). Effects of Conceptual Assignments and Conceptual Change Discussions on Students' Misconceptions and Achievement Regarding Force and Motion.
*Journal of Research in Science Teaching*39(10), 1001-10015. (See Siegler and Durkin/Rittle-Johnson papers for relevance) - Hagen, R. & Sonenberg, E.A. (1993). Automated classification of student misconceptions in physics. In C. Rowles, H. Liu, and N. Foo (eds.),
*Proceedings of the 1993 Australian Joint Conference on Artificial Intelligence*, AI'93, pp 153-159. World Scientific, 1993. - Sleeman, D. (1984). Mis-generalisation: An explanation of observed mal-rules. In
*Proceedings of the 6th Annual Conference of the Cognitive Science Society*, pp. 51-56. - Van den Broek, P., & Kendeou, P. (2008). Cognitive processes in comprehension of science texts: The role of co-activation in confronting misconceptions.
*Applied Cognitive Psychology*, 22, 335-351. (See Siegler and Durkin/Rittle-Johnson papers for relevance)

**(Possibly) Relevant Collaborative Learning Literature**

- Schwarz, B.B., Neuman, Y., Biezuner, S. (2000). Two wrongs may make a right ... if they argue together!
*Cognition and Instruction.*18, 461-494. - Schwarz, B.B. & Linchevski, L. (2007). The role of task design and argumentation in cognitive development during peer interaction: The case of proportional reasoning.
*Learning and Instruction.*17, 510-531. - Ellis, S., Klahr, D., & Siegler, R.S. (1993). Effects of feedback and collaboration on changes in children's use of mathematical rules. Paper presented at the meetings of the Society for Research in Child Development, New Orleans, March, 1993.
- Light, P. & Glachan, M. (1985). Facilitation of individual problem solving through peer interaction.
*Educational Psychology*5, 217-225. - Walker, E., Rummel, N., & Koedinger, K. R. (2009). CTRL: A research framework for providing adaptive collaborative learning support.
*User Modeling and User-Adapted Interaction, 19*(5), 387-431. (Some evidence of Tutor learning from the Tutee's errors.)

**Open Repositories - the PSLC DataShop**

- Koedinger, K.R., Baker, R.S.J.d., Cunningham, K., Skogsholm, A., Leber, B., Stamper, J. (2010) A Data Repository for the EDM community: The PSLC DataShop. In Romero, C., Ventura, S., Pechenizkiy, M., Baker, R.S.J.d. (Eds.)
*Handbook of Educational Data Mining*. Boca Raton, FL: CRC Press.