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University of Groningen

The effectiveness of hints during computer supported word problem solving

de Kock, Willem Daniel

IMPORTANT NOTE: You are advised to consult the publisher's version (publisher's PDF) if you wish to cite from it. Please check the document version below.

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Publication date: 2016

Link to publication in University of Groningen/UMCG research database

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de Kock, W. D. (2016). The effectiveness of hints during computer supported word problem solving. Rijksuniversiteit Groningen.

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Baker, R. S., Corbett, A. T., & Koedinger, K. R. (2004). Detecting student misuse of intelligent tutoring systems. In J. C. Lester, R. M. Vicario, & F. Paraguaçu (Eds.), Proceedings of seventh international conference on intelligent tutoring systems, ITS 2004 (pp. 531–540). Berlin: Springer Verlag.

Baker, R. S., Walonoski, J., Heffernan, N., Roll, I., Corbett, A., & Koedinger, K. R. (2008). Why students engage in "gaming the system" behavior in interactive learning environments. Journal of Interactive Learning Research, 19 (2), 185–224. doi:10.1.1.297.2912

Bannert, M., Hildebrand, M., & Mengelkamp, C. (2009). Effects of a metacognitive support device in learning environments. Computers in Human Behavior, 25 (4), 829–835. doi:10.1016/ j.chb.2008.07.002.

Bannert, M., Sonnenberg, C., Mengelkamp, C., & Pieger, E. (2015). Short and long term effects of students’ selfdirected metacognitive prompts on navigation behavior and learning performance. Computers in Human Behavior, 52, 293306. doi: 10.1016/j.chb.2015.05.038

Barron, B. (2000). Achieving Coordination in Collaborative ProblemSolving Groups. Journal of Learning Sciences, 9 (4), 403–436.

Berthold, K., Nückles, M., & Renkl, A. (2007). Do learning protocols support learning strategies and outcomes? The role of cognitive and metacognitive prompts. Learning and Instruction, 17, 564–577.

Bollen, L., Gijlers, H., & Van Joolingen, W. (2012). Computersupported collaborative drawing in primary school education – Technical realization and empirical findings. In V. Herskovic, H. U. Hoppe, M. Jansen & J. Ziegler (Eds.), Collaboration and technology (pp. 1–16). Berlin Heidelberg: Springer.

Boonen, A.J.H., Van Wesel, F., Jolles, J. & Van der Schoot, M. (2014). The role of visual representation type, spatial ability and reading comprehension in word problem solving: An itemlevel analysis in primary school children. International Journal of Educational Research, 68, 15–26.

Briggs, R. O., De Vreede, G. J. , Nunamaker, J. F. Jr. , & Tobey, D. (2001). ThinkLets: Achieving Predictable, Repeatable Patterns of Group Interaction with Group Support Systems (GSS). Proceedings of the Hawaii International Conference on System Sciences, Los Alamitos, IEEE Computer Society Press.

Bruun, F. (2013). Elementary Teachers’ Perspectives of Mathematics Problem Solving Strategies. The Mathematics Educator. 23 (1), 45–59.

Bulu, S. T. & Pedersen, S. (2010). Scaffolding middle school students' content knowledge and illstructured problem solving in a problembased hypermedia learning environment. Educational Technology Research and Development, 58(5), 507–529.

Capraro, R. M., Capraro, M. M., & Rupley, W. H. (2012). Reading  enhanced word problem solving: A theoretical model. European Journal of Psychology of Education, 27 (1) , 91  114. doi:10.1007/s10212  011  0068  3

Capuano, N., D’Aniello, G., Gaeta, A., & Miranda, S. (2015). A personality based adaptive approach for information systems. Computers in Human Behavior, 44, 156–165. doi:10.1016/j.chb.2014.10.058

Chang, K., Sung, Y., & Lin, S. (2006). Computerassisted learning for mathematical problem solving. Computers & Education, 46, 140–151. doi:10.1016/j.compedu.2004.08.002

Cheng, X., Li, Y., Sun, J., & Huang, J. (2015). Application of a novel collaboration engineering method for learning design: A case study. British Journal of Educational Technology, 47 (4), 803818.

Chung, K. K. H., & Tam, Y. H. (2005). Effects of cognitivebased instruction on mathematical problem solving by learners with mild intellectual disabilities. Journal of Intellectual and Developmental Disability, 30, 207–216. doi:10.1080/13668250500349409

CITO. (2002). RekenenWiskunde 2002. Opgavenboekje M7[Mathematics work book M7]. Arnhem, The Netherlands: Citogroep.

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Clarebout, G., Elen, J., Johnson, W. L., & Shaw, E. (2002). Animated pedagogical agents: An opportunity to be grasped? Journal of Educational Multimedia and Hypermedia, 11, 267–286.

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Clark, R. C., & Mayer, R. E. (2011). Elearning and the science of instruction. (3rd ed.). San Francisco: John Wiley & Sons, Inc.

Cohen, D., & Hill, H. (2000). Instructional policy and classroom performance: The mathematics reform in California. Teachers College Record, 102, 294–343. Cohen, J (1988). Statistical Power Analysis for the Behavioral Sciences (second

ed.). Lawrence Erlbaum Associates.

Cooper, B., & Harries, T. (2005). Making sense of realistic word problems: Portraying working class “failure” on a division with remainder problem. International Journal of Research & Method in Education, 28, 147–169 Corbalan, G., Kester, L., & Van Merriënboer, J. J. G. (2008). Selecting learning

tasks: Effects of adaptation and shared control on efficiency and task involvement. Contemporary Educational Psychology, 33, 733–756.

Corter, J. E. & Zahner, D. (2007). Use of external visual representations in probability problem solving. Statistics Education Research Journal, 6 (1), 2250.

Crippen, K. J., & Earl, B. L. (2007). The impact of Webbased worked examples and selfexplanation on performance, problem solving, and selfefficacy. Computers & Education, 49 (3), 809–821. doi:10.1016/j.compedu.2005.11.018

DarlingHammond, L., Wei, R. C., & Johnson, C. M. (2009). Teacher preparation and teacher learning: A changing policy landscape. In G. Sykes, B. L. Schneider, & D. N. Plank (Eds.), Handbook of education policy research (pp. 613–636). New York, NY: Routledge.

De Boer, H., Donker, A. S., & Van der Werf, M. P. C. (2014). Effects of the attributes of educational interventions on students’ academic performance: a meta analysis. Review of Educational Research, 84 (4), 509  545.

De Jong, T. (2005). The Guided Discovery Principle in Multimedia learning. In R. Mayer (Ed.), The Cambridge Handbook of Multimedia Learning (pp. 507– 523). New York, NY: Cambridge University Press.

De Kock, W. D., & Harskamp, E. G. (2014). Can Teachers in Primary Education Implement a Metacognitive Computer Programme for Word Problem Solving in their Mathematics Classes? Educational Research and Evaluation, 20 (3), 231–250. doi:10.1080/13803611.2014.901921

Demetriadis, S.N., Papadopoulos, P.M., Stamelos, J.G., & Fischer, F. (2008). The effect of scaffolding students’ contextgenerating cognitive activity in technologyenhanced casebased learning. Computers and Education, 51 (2), 939–954.

Desoete, A., Roeyers, H., & De Clercq, A. (2003). Can offline metacognition enhance mathematical problem solving? Journal of Educational Psychology, 95, 188–200.doi:10.1037/00220663.95.1.188

Devolder, A., Van Braak, J., & Tondeur, J. (2012). Supporting selfregulated learning in computerbased learning environments: Systematic review of effects of scaffolding in the domain of science education. Journal of Computer Assisted Learning, 28, 557–573.

De Vreede, G. J., Kolfschoten, G. L., & Briggs, R. O. (2006). ThinkLets: a collaboration engineering pattern language. International Journal of Computer Applications in Technology, 25 (2), 140154.

Dignath, C., & Büttner, G. (2008). Components of fostering selfregulated learning among students. A metaanalysis on intervention studies at primary and secondary school level. Metacognition and Learning, 3, 231– 264.doi:10.1007/s114090089029x

Dillenbourg, P., & Tchounikine, P. (2007). Flexibility in macro CSCL scripts. Journal of Computer Assisted Learning, 23 (1), 113.

Ding, N. (2009). Computersupported collaborative learning and gender (Doctoral dissertation). Groningen: University of Groningen.

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Clarebout, G., Elen, J., Johnson, W. L., & Shaw, E. (2002). Animated pedagogical agents: An opportunity to be grasped? Journal of Educational Multimedia and Hypermedia, 11, 267–286.

Clark, H., & Brennan, S. (1991). Grounding in communication. In L. B. Resnick, J. Levine, & S. D. Teasley (Eds.), Perspectives on socially shared cognition (pp. 127–149). Washington, DC: APA.

Clark, R. C., & Mayer, R. E. (2011). Elearning and the science of instruction. (3rd ed.). San Francisco: John Wiley & Sons, Inc.

Cohen, D., & Hill, H. (2000). Instructional policy and classroom performance: The mathematics reform in California. Teachers College Record, 102, 294–343. Cohen, J (1988). Statistical Power Analysis for the Behavioral Sciences (second

ed.). Lawrence Erlbaum Associates.

Cooper, B., & Harries, T. (2005). Making sense of realistic word problems: Portraying working class “failure” on a division with remainder problem. International Journal of Research & Method in Education, 28, 147–169 Corbalan, G., Kester, L., & Van Merriënboer, J. J. G. (2008). Selecting learning

tasks: Effects of adaptation and shared control on efficiency and task involvement. Contemporary Educational Psychology, 33, 733–756.

Corter, J. E. & Zahner, D. (2007). Use of external visual representations in probability problem solving. Statistics Education Research Journal, 6 (1), 2250.

Crippen, K. J., & Earl, B. L. (2007). The impact of Webbased worked examples and selfexplanation on performance, problem solving, and selfefficacy. Computers & Education, 49 (3), 809–821. doi:10.1016/j.compedu.2005.11.018

DarlingHammond, L., Wei, R. C., & Johnson, C. M. (2009). Teacher preparation and teacher learning: A changing policy landscape. In G. Sykes, B. L. Schneider, & D. N. Plank (Eds.), Handbook of education policy research (pp. 613–636). New York, NY: Routledge.

De Boer, H., Donker, A. S., & Van der Werf, M. P. C. (2014). Effects of the attributes of educational interventions on students’ academic performance: a meta analysis. Review of Educational Research, 84 (4), 509  545.

De Jong, T. (2005). The Guided Discovery Principle in Multimedia learning. In R. Mayer (Ed.), The Cambridge Handbook of Multimedia Learning (pp. 507– 523). New York, NY: Cambridge University Press.

De Kock, W. D., & Harskamp, E. G. (2014). Can Teachers in Primary Education Implement a Metacognitive Computer Programme for Word Problem Solving in their Mathematics Classes? Educational Research and Evaluation, 20 (3), 231–250. doi:10.1080/13803611.2014.901921

Demetriadis, S.N., Papadopoulos, P.M., Stamelos, J.G., & Fischer, F. (2008). The effect of scaffolding students’ contextgenerating cognitive activity in technologyenhanced casebased learning. Computers and Education, 51 (2), 939–954.

Desoete, A., Roeyers, H., & De Clercq, A. (2003). Can offline metacognition enhance mathematical problem solving? Journal of Educational Psychology, 95, 188–200.doi:10.1037/00220663.95.1.188

Devolder, A., Van Braak, J., & Tondeur, J. (2012). Supporting selfregulated learning in computerbased learning environments: Systematic review of effects of scaffolding in the domain of science education. Journal of Computer Assisted Learning, 28, 557–573.

De Vreede, G. J., Kolfschoten, G. L., & Briggs, R. O. (2006). ThinkLets: a collaboration engineering pattern language. International Journal of Computer Applications in Technology, 25 (2), 140154.

Dignath, C., & Büttner, G. (2008). Components of fostering selfregulated learning among students. A metaanalysis on intervention studies at primary and secondary school level. Metacognition and Learning, 3, 231– 264.doi:10.1007/s114090089029x

Dillenbourg, P., & Tchounikine, P. (2007). Flexibility in macro CSCL scripts. Journal of Computer Assisted Learning, 23 (1), 113.

Ding, N. (2009). Computersupported collaborative learning and gender (Doctoral dissertation). Groningen: University of Groningen.

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Donker, A. S., De Boer, H., Kostons, D., DignathVan Ewijk, C. C., & Van der Werf, M. P. (2014). Effectiveness of learning strategy instruction on academic performance: a metaanalysis. Educational Research Review, 11, 1–26. Dreyfus, T. & Eisenberg, T. (1996). On different factes of mathematical thinking. in

R. Sternberg & BenZeev (Eds). The Nature of Mathematical Thinking. Hillsdale, NY: Lawrence Erlbaum Associates.

Dufresne, R. J. & Gerace, W. J. & Leonard, W. J. (1997). Solving physics problems with multiple representations. The Physics Teacher, 35 (5), 270275.

Edens, K. & Potter, E. (2008). How Students "Unpack" the Structure of a Word Problem: Graphic Representations and Problem Solving. Science and School Mathematics Journal, 108 (5), 184–193.

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for collaborative and argumentative writing. In E. de Corte (Ed.), Powerful learning environments (pp. 159–177). Amsterdam: Pergamon.

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Fuchs, L. S., Zumeta, R. O., Schumacher, R. F., Powell, S. R., Seethaler, P. M., Hamlett, C. L., & Fuchs, D. (2010b). The effects of schemabroadening instruction on second graders’ wordproblem performance and their ability to represent word problems with algebraic equations: A randomized control study. The Elementary School Journal, 110, 440–463. doi:10.1086/651191 Ginns, P. (2005). Metaanalysis of the modality effect. Learning and Instruction,

15, 313–331. doi:10.1016/j.learninstruc.2005.07.001.

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R. Sternberg & BenZeev (Eds). The Nature of Mathematical Thinking. Hillsdale, NY: Lawrence Erlbaum Associates.

Dufresne, R. J. & Gerace, W. J. & Leonard, W. J. (1997). Solving physics problems with multiple representations. The Physics Teacher, 35 (5), 270275.

Edens, K. & Potter, E. (2008). How Students "Unpack" the Structure of a Word Problem: Graphic Representations and Problem Solving. Science and School Mathematics Journal, 108 (5), 184–193.

Efklides, A. (2006). Metacognition and affect: What can metacognitive experiences tell us about the learning process? Educational Research Review, 1, 314. Erkens, G., Kanselaar, G., Prangsma, M., & Jaspers, J. (2003). Computer support

for collaborative and argumentative writing. In E. de Corte (Ed.), Powerful learning environments (pp. 159–177). Amsterdam: Pergamon.

Fischer, F., & Mandl, H. (2002). Facilitating knowledge convergence in videoconferencing environments: The role of external representation tools. Paper presented at the Computer Support for Collaborative Learning: Foundations for a CSCL Community Conference, Boulder, CO., University of Munrich, Germany

Foshay, R., & Kirkley, J. (2003). Principles for teaching problem solving (Technical Paper No. 4). Retrieved from PLATO Learning website:http://www.learningace.com/doc/2440565/e094c08dc4a564128df 491521b5d4ef8/2003_foshay_platolearninginc_techpaper4_principles forteachingproblemsolving

Fuchs, L. S., Fuchs, D., Stuebing, K., Fletcher, J. M., Hamlett, C. L., & Lambert, W. (2008). Problem solving and computational skill: Are they shared or distinct aspects of mathematical cognition? Journal of Educational Psychology, 100, 30–47. doi:10.1037/00220663.100.1.30

Fuchs, L. S., Powell, S. R., Seethaler, P. M., Cirino, P. T., Fletcher, J. M., Fuchs, D., & Hamlett, C. L. (2010a). The effects of strategic counting instruction, with and without deliberate practice, on number combination skill among students with mathematics difficulties. Learning and Individual Differences, 20, 89–100. doi:10.1016/j.lindif.2009.09.003

Fuchs, L. S., Powell, S. R., Seethaler, P. M., Cirino, P. T., Fletcher, J. M., Fuchs, D.,…Zumeta, R. O. (2009). Remediating number combination and word problem deficits among students with mathematics difficulties: A randomized control trial. Journal of Educational Psychology, 101, 561–576. doi:10.1037/a0014701

Fuchs, L. S., Zumeta, R. O., Schumacher, R. F., Powell, S. R., Seethaler, P. M., Hamlett, C. L., & Fuchs, D. (2010b). The effects of schemabroadening instruction on second graders’ wordproblem performance and their ability to represent word problems with algebraic equations: A randomized control study. The Elementary School Journal, 110, 440–463. doi:10.1086/651191 Ginns, P. (2005). Metaanalysis of the modality effect. Learning and Instruction,

15, 313–331. doi:10.1016/j.learninstruc.2005.07.001.

Ginns, P., Martin, A., & Marsh, H. (2013). Designing instructional text in a conversational style: a metaanalysis. Educational Psychology Review, 25 (4), 1–28. doi:10.1007/s1064801392280.

Ginsburg, H. P. (1983). The Development of Mathematical Thinking. Orlando (FL): Academic Press, Inc.

Goos, M. (2002). Understanding metacognitive failure. Journal of Mathematical Behavior, 21, 283–302.

Gräsel, C., Fischer, F., & Mandl, H. (2000). The use of additional information in problemoriented learning environments. Learning Environment Research, 3, 287–325. doi:10.1023/A:1011421732004.

Groff, J. & Mouza, C. (2008). A framework for addressing challenges to classroom technology use. AACE Journal, 16, 2146.

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Harskamp, E. G., Mayer, R. E., & Suhre, C. (2007). Does the modality principle for multimedia learning apply to science classrooms? Learning and Instruction, 17 (5), 465–477. doi:10.1016/j.learninstruc.2007.09.010.

Heidig, S., & Clarebout, G. (2011). Do pedagogical agents make a difference to student motivation and learning? Educational Research Review, 6, 27–54. doi:10.1016/j.edurev.2010.07.004.

Hegarty, M & Kozhevnikov, M. (1999). Types of visual–spatial representations and mathematical problem solving. Journal of Educational Psychology, 91 (4), 684–689. doi:10.1037/00220663.91.4.684

Hegarty, M., Mayer, R. E., & Monk, C. A. (1995). Comprehension of

arithmetic word problems: A comparison of successful and

unsuccessful problem solvers. Journal of Educational Psychology,

87, 1832.

Hill, J. R. & Hannafin, M. J. (2001). Teaching and learning in digital environments: the resurgence of resourcebased learning. Educational Technology Research and Development, 49 (3), 37–52.

HmeloSilver, C. E., Chinn, C.A., Chan, C. K. & O’Donnell, A. (2013). The International Handbook of Collaborative Learning. Routledge, New York. Hodgen, J., & Marks, R. (2013). The Employment Equation: Why our young

people need more maths for today’s jobs. London.

Hohn, R. L., & Frey, B. (2002). Heuristic training and performance in elementary mathematical problem solving. The Journal of Educational Research, 95, 374–380. doi:10.1080/00220670209596612

Hurme, T. R., & Järvelä, S. (2005). Student’s activity in computersupported collaborative problem solving in mathematics. International Journal of Computers for Mathematical Learning, 10, 49–73. doi: 10.1007/s10758005 45793

Inspectie van het Onderwijs. (2008). Basisvaardigheden rekenenwiskunde in het basisonderwijs [Basic math skills in elementary education]. Utrecht, The Netherlands: Author.

Jacobs, V. R., Franke, M. L., Carpenter, T. P., Levi, L., & Battey, D. (2007). Professional development focused on children’s algebraic reasoning in elementary schools. Journal for Research in Mathematics Education , 38 (3), 258288.

Jacobse, A. E. (2012). Can we improve children’s thinking? (Doctoral dissertation). Groningen, The Netherlands: University of Groningen.

Jacobse, A. E., & Harskamp, E. G. (2009). Studentcontrolled metacognitive training for solving word problems in primary school mathematics. Educational Research and Evaluation, 15, 447–463. doi:10.1080/13803610903444519

Janssen, J. (2014). Opening the black box of collaborative learning: A meta analysis investigating the antecedents and consequences of collaborative interaction. Report no. 41111632 commissioned by NWOPROO and NRO. University of Utrecht, Utrecht (2014)

Janssen, J., Erkens, G., & Kirschner, P. A. (2011). Group awareness tools: It’s what you do with it that matters. Computers in Human Behavior, 27, 1046–1058. doi:10.1016/j.chb.2010.06.002

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Gutwin, C., & Greenberg, S. (2004) The Importance of Awareness for Team Cognition in Distributed Collaboration. In E. Salas and S. M. Fiore (Editors) Team Cognition: Understanding the Factors that Drive Process and Performance (pp. 177201), Washington: APA Press.

Harskamp, E. G., & Ding, N. (2006). Structured Collaboration versus Individual Learning in Solving Physics Problems. International Journal of Science Education, 28 (14), 1669–1688.

Harskamp, E. G., Mayer, R. E., & Suhre, C. (2007). Does the modality principle for multimedia learning apply to science classrooms? Learning and Instruction, 17 (5), 465–477. doi:10.1016/j.learninstruc.2007.09.010.

Heidig, S., & Clarebout, G. (2011). Do pedagogical agents make a difference to student motivation and learning? Educational Research Review, 6, 27–54. doi:10.1016/j.edurev.2010.07.004.

Hegarty, M & Kozhevnikov, M. (1999). Types of visual–spatial representations and mathematical problem solving. Journal of Educational Psychology, 91 (4), 684–689. doi:10.1037/00220663.91.4.684

Hegarty, M., Mayer, R. E., & Monk, C. A. (1995). Comprehension of

arithmetic word problems: A comparison of successful and

unsuccessful problem solvers. Journal of Educational Psychology,

87, 1832.

Hill, J. R. & Hannafin, M. J. (2001). Teaching and learning in digital environments: the resurgence of resourcebased learning. Educational Technology Research and Development, 49 (3), 37–52.

HmeloSilver, C. E., Chinn, C.A., Chan, C. K. & O’Donnell, A. (2013). The International Handbook of Collaborative Learning. Routledge, New York. Hodgen, J., & Marks, R. (2013). The Employment Equation: Why our young

people need more maths for today’s jobs. London.

Hohn, R. L., & Frey, B. (2002). Heuristic training and performance in elementary mathematical problem solving. The Journal of Educational Research, 95, 374–380. doi:10.1080/00220670209596612

Hurme, T. R., & Järvelä, S. (2005). Student’s activity in computersupported collaborative problem solving in mathematics. International Journal of Computers for Mathematical Learning, 10, 49–73. doi: 10.1007/s10758005 45793

Inspectie van het Onderwijs. (2008). Basisvaardigheden rekenenwiskunde in het basisonderwijs [Basic math skills in elementary education]. Utrecht, The Netherlands: Author.

Jacobs, V. R., Franke, M. L., Carpenter, T. P., Levi, L., & Battey, D. (2007). Professional development focused on children’s algebraic reasoning in elementary schools. Journal for Research in Mathematics Education , 38 (3), 258288.

Jacobse, A. E. (2012). Can we improve children’s thinking? (Doctoral dissertation). Groningen, The Netherlands: University of Groningen.

Jacobse, A. E., & Harskamp, E. G. (2009). Studentcontrolled metacognitive training for solving word problems in primary school mathematics. Educational Research and Evaluation, 15, 447–463. doi:10.1080/13803610903444519

Janssen, J. (2014). Opening the black box of collaborative learning: A meta analysis investigating the antecedents and consequences of collaborative interaction. Report no. 41111632 commissioned by NWOPROO and NRO. University of Utrecht, Utrecht (2014)

Janssen, J., Erkens, G., & Kirschner, P. A. (2011). Group awareness tools: It’s what you do with it that matters. Computers in Human Behavior, 27, 1046–1058. doi:10.1016/j.chb.2010.06.002

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Jitendra, A. K., PetersonBrown, S., Lein, A., Zaslofsky, A., Kunkel, A., Jung, PG., & Egan, A. (2015). Teaching mathematical word problem solving: The quality of evidence for strategy instruction priming the problem structure. Journal of Learning Disabilities, 48 (1), 51–72.

Jitendra, A. K., Rodriguez, M., Kanive, R. G., Huang, JP., Church, C., Corroy, K. C., & Zaslofsky, A. F. (2013). The impact of smallgroup tutoring interventions on the mathematical problem solving and achievement of third grade students with mathematics difficulties. Learning Disability Quarterly, 36, 21–35.

Jitendra, A. K., Star, J., Starosta, K., Leh, J., Sood, S., Caskie, G., & Mack, T. (2009). Improving students’ learning of ratio and proportion problem solving: The role of schemabased instruction. Contemporary Educational Psychology, 34 (3), 250–264.

Johnson, D. W., & Johnson, R. T. (1999). Making cooperative learning work. Theory into Practice, 38 (2), 67–73.

Johnson, D. W. & Johnson R. T. (2009). An Educational Psychology Success Story: Social Interdependence Theory and Cooperative Learning. Educational Researcher, 38, 365 – 379.

Jonassen, D. H. (2000). Toward a design theory of problem solving. Educational Technology Research and Development, 48 (4), 6385.

Jonassen, D. H. (2003). Using cognitive tools to represent problems. Journal of Research on Technology in Education, 35 (3), 362381.

Jonassen, D. H. (2010). Learning to solve problems: A handbook. New York: Routledge.

Kirschner, F., Paas, F., & Kirschner, P. A. (2009). A cognitive load approach to collaborative learning: United brains for complex tasks. Educational Psychological Review, 21, 31–42. doi:10.1007/s1064800890952

Koedinger, K. R., & Aleven, V. (2007). Exploring the assistance dilemma in experiments with cognitive tutors. Educational Psychology Review, 19, 239– 264. doi:10.1007/s1064800790490.

Koedinger, K. R., & Nathan, M. J. (2004). The real story behind story problems: Effects of representations on quantitative reasoning. Journal of the Learning Sciences, 13, 129–164.

Kolfschoten, G. L., Vreede, G. J. de, Briggs, R. O., & Sol, H. G. (2010). Collaboration ‘Engineerability’. Group Decision & Negotiation, 19 (3), 301  312.

Kollar I., Fischer F., & Hesse F. W. (2006). Collaboration scripts—A conceptual analysis. Educational Psychology Review, 18, 159–185. doi:10.1007/s10648 00690072.

Kollar, I., Ufer, S., Reichersdorfer, E., Vogel, F., Fischer, F., & Reiss, K. (2014). Effects of Collaboration Scripts and Heuristic Worked Examples on the Acquisition of Mathematical Argumentation Skills of Teacher Students with Different Levels of Prior Achievement. Learning and Instruction, 32, 2236. Kramarski, B., & Friedman, S. (2014). Solicited versus Unsolicited Metacognitive

Prompts for Fostering Mathematical ProblemSolving Using Multimedia. Journal of Educational Computing Research, 50 (3), 285–314.

Kramarski, B., & Gutman, M. (2006). How can selfregulated learning be supported in mathematical Elearning environments? Journal of Computer Assisted Learning, 22, 24–33. doi:10.1111/j.13652729.2006.00157.x

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Ku, H., Harter, C., Liu, P., Thompson, L., & Cheng, Y. (2007). The effects of individually personalized computerbased instructional program on solving mathematics problems. Computers in Human Behavior, 23 (3), 1195–1210. Kyndt, E., Raes, E., Lismont, B., Timmers, F., Cascallar, E., & Dochy, F. (2013). A

metaanalysis of the effects of facetoface cooperative learning. Do recent studies falsify or verify earlier findings? Educational Research Review, 10(0), 133149. doi:10.1016/j.edurev.2013.02.002

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Jitendra, A. K., PetersonBrown, S., Lein, A., Zaslofsky, A., Kunkel, A., Jung, PG., & Egan, A. (2015). Teaching mathematical word problem solving: The quality of evidence for strategy instruction priming the problem structure. Journal of Learning Disabilities, 48 (1), 51–72.

Jitendra, A. K., Rodriguez, M., Kanive, R. G., Huang, JP., Church, C., Corroy, K. C., & Zaslofsky, A. F. (2013). The impact of smallgroup tutoring interventions on the mathematical problem solving and achievement of third grade students with mathematics difficulties. Learning Disability Quarterly, 36, 21–35.

Jitendra, A. K., Star, J., Starosta, K., Leh, J., Sood, S., Caskie, G., & Mack, T. (2009). Improving students’ learning of ratio and proportion problem solving: The role of schemabased instruction. Contemporary Educational Psychology, 34 (3), 250–264.

Johnson, D. W., & Johnson, R. T. (1999). Making cooperative learning work. Theory into Practice, 38 (2), 67–73.

Johnson, D. W. & Johnson R. T. (2009). An Educational Psychology Success Story: Social Interdependence Theory and Cooperative Learning. Educational Researcher, 38, 365 – 379.

Jonassen, D. H. (2000). Toward a design theory of problem solving. Educational Technology Research and Development, 48 (4), 6385.

Jonassen, D. H. (2003). Using cognitive tools to represent problems. Journal of Research on Technology in Education, 35 (3), 362381.

Jonassen, D. H. (2010). Learning to solve problems: A handbook. New York: Routledge.

Kirschner, F., Paas, F., & Kirschner, P. A. (2009). A cognitive load approach to collaborative learning: United brains for complex tasks. Educational Psychological Review, 21, 31–42. doi:10.1007/s1064800890952

Koedinger, K. R., & Aleven, V. (2007). Exploring the assistance dilemma in experiments with cognitive tutors. Educational Psychology Review, 19, 239– 264. doi:10.1007/s1064800790490.

Koedinger, K. R., & Nathan, M. J. (2004). The real story behind story problems: Effects of representations on quantitative reasoning. Journal of the Learning Sciences, 13, 129–164.

Kolfschoten, G. L., Vreede, G. J. de, Briggs, R. O., & Sol, H. G. (2010). Collaboration ‘Engineerability’. Group Decision & Negotiation, 19 (3), 301  312.

Kollar I., Fischer F., & Hesse F. W. (2006). Collaboration scripts—A conceptual analysis. Educational Psychology Review, 18, 159–185. doi:10.1007/s10648 00690072.

Kollar, I., Ufer, S., Reichersdorfer, E., Vogel, F., Fischer, F., & Reiss, K. (2014). Effects of Collaboration Scripts and Heuristic Worked Examples on the Acquisition of Mathematical Argumentation Skills of Teacher Students with Different Levels of Prior Achievement. Learning and Instruction, 32, 2236. Kramarski, B., & Friedman, S. (2014). Solicited versus Unsolicited Metacognitive

Prompts for Fostering Mathematical ProblemSolving Using Multimedia. Journal of Educational Computing Research, 50 (3), 285–314.

Kramarski, B., & Gutman, M. (2006). How can selfregulated learning be supported in mathematical Elearning environments? Journal of Computer Assisted Learning, 22, 24–33. doi:10.1111/j.13652729.2006.00157.x

Kroesbergen, E. H., & Van Luit, J. E. H. (2002). Teaching multiplication to low math performers: Guided versus structured instruction. Instructional Science, 30, 361–378. doi:10.1023/A:1019880913714

Ku, H., Harter, C., Liu, P., Thompson, L., & Cheng, Y. (2007). The effects of individually personalized computerbased instructional program on solving mathematics problems. Computers in Human Behavior, 23 (3), 1195–1210. Kyndt, E., Raes, E., Lismont, B., Timmers, F., Cascallar, E., & Dochy, F. (2013). A

metaanalysis of the effects of facetoface cooperative learning. Do recent studies falsify or verify earlier findings? Educational Research Review, 10(0), 133149. doi:10.1016/j.edurev.2013.02.002

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Lesh, R., & Doerr, H. (2000). Symbolizing, communicating and mathematizing: Key components of models and modeling. In P. Cobb, E. Yackel, & K. McClain (Eds.), Symbolizing and communicating in mathematics classrooms (pp. 361–383). Mahwah, NJ: Lawrence Erlbaum.

Li, Q., & Ma, X. (2010). A metaanalysis of the effects of computer technology on school students’ mathematics learning. Educational Psychology Review, 22, 215–243. doi:10.1007/s1064801091258

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Liu, M., Bera, S., Corliss, S. B., Svinicki, M. D., & Beth, A. D. (2004). Understanding the Connection Between Cognitive Tool Use and Cognitive Processes as used by Sixth Graders in a ProblemBased Hypermedia Learning Environment. Journal of Educational Computing Research, 31 (3), 309–334.

Low, R., & Over, R. (1989). Detection of missing irrelevant information within algebraic story problems. Britisch Journal of Educational Psychology, 59 (3), 296–305.

Low, R., & Over, R. (1990). Text editing of algebraic word problems. Australian Journal of Psychology, 42 (1), 63–73.

Lu, J., Lajoie, S. P., & Wiseman, J. (2010). Scaffolding problembased learning with tools. International Journal of ComputerSupported Collaborative Learning, 5 (3), 283–298. doi:10.1007/s1141201090926

Makel, M. C., & Plucker, J. A. (2014). Facts are more important than novelty: Replication in the education sciences. Educational Researcher, 43, 304–316. doi:10.3102/0013189x14545513

Martin, M.O. & Mullis, I.V.S. (Eds.). (2013). TIMSS and PIRLS 2011: Relationships Among Reading, Mathematics, and Science Achievement at the Fourth Grade—Implications for Early Learning. Chestnut Hill, MA: TIMSS & PIRLS International Study Center, Boston College.

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Mayer, R. E., Dow, G., & Mayer, S. (2003). Multimedia learning in an interactive selfexplaining environment: what works in the design of agentbased microworlds? Journal of Educational Psychology, 95, 806–813.

Mayer, R. E., & Hegarty, M. (1996). The process of understanding mathematical problem solving. In: Sternberg, R. J. and BenZeev T., (Eds.), The nature of mathematical thinking (pp. 29–54).Mahwah, NJ: Erlbaum.

Mayer, R. E., Mathias, A., & Wetzell, K. (2002). Fostering understanding of multimedia messages through pretraining: Evidence for a twostage theory of mental model construction. Journal of Experimental Psychology: Applied, 8,147–154. doi:10.1037/1076898X.8.3.147

McLaren, B.M., van Gog, T., Ganoe, C., Karabinos, M., & Yaron, D. (2016). The efficiency of worked examples compared to erroneous examples, tutored problem solving, and problem solving in classroom experiments. Computers in Human Behavior, 55, 8799. doi:10.1016/j.chb.2015.08.038

Meijer, J., & Riemersma, F. (2002). Teaching and testing mathematical problem solving by offering optional assistance. Instructional Science, 30, 187–220. Mevarech, Z. R., & Kramarski, B. (1997). IMPROVE: A multidimensional method

for teaching mathematics in heterogeneous classrooms. American Educational Research Journal 34 (2), 365–394.

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Lee, H., Lim, K., & Grabowski, B. L. (2010). Improving selfregulation, learning strategy use, and achievement with metacognitive feedback. Educational Technology Research and Development, 58 (6), 629–648.

Lesh, R., & Doerr, H. (2000). Symbolizing, communicating and mathematizing: Key components of models and modeling. In P. Cobb, E. Yackel, & K. McClain (Eds.), Symbolizing and communicating in mathematics classrooms (pp. 361–383). Mahwah, NJ: Lawrence Erlbaum.

Li, Q., & Ma, X. (2010). A metaanalysis of the effects of computer technology on school students’ mathematics learning. Educational Psychology Review, 22, 215–243. doi:10.1007/s1064801091258

Lipponen, L., Rahikainen, M., Lallimo, J., & Hakkarainen, K. (2001). Analyzing patterns of participation and discourse in elementary students’ online science discussion. In P. Dillenbourg, A. Eurelings., & K. Hakkarainen (Eds.), European Perspectives on ComputerSupported Collaborative Learning. Proceedings of the First European Conference on CSCL (pp. 421428). Maastricht, the Netherlands: Maastricht McLuhan Institute.

Liu, M., Bera, S., Corliss, S. B., Svinicki, M. D., & Beth, A. D. (2004). Understanding the Connection Between Cognitive Tool Use and Cognitive Processes as used by Sixth Graders in a ProblemBased Hypermedia Learning Environment. Journal of Educational Computing Research, 31 (3), 309–334.

Low, R., & Over, R. (1989). Detection of missing irrelevant information within algebraic story problems. Britisch Journal of Educational Psychology, 59 (3), 296–305.

Low, R., & Over, R. (1990). Text editing of algebraic word problems. Australian Journal of Psychology, 42 (1), 63–73.

Lu, J., Lajoie, S. P., & Wiseman, J. (2010). Scaffolding problembased learning with tools. International Journal of ComputerSupported Collaborative Learning, 5 (3), 283–298. doi:10.1007/s1141201090926

Makel, M. C., & Plucker, J. A. (2014). Facts are more important than novelty: Replication in the education sciences. Educational Researcher, 43, 304–316. doi:10.3102/0013189x14545513

Martin, M.O. & Mullis, I.V.S. (Eds.). (2013). TIMSS and PIRLS 2011: Relationships Among Reading, Mathematics, and Science Achievement at the Fourth Grade—Implications for Early Learning. Chestnut Hill, MA: TIMSS & PIRLS International Study Center, Boston College.

Mayer, R. E. (1992) Thinking, problem solving, cognition (2nd Ed.). New York: W. H. Freeman.

Mayer, R. E., Dow, G., & Mayer, S. (2003). Multimedia learning in an interactive selfexplaining environment: what works in the design of agentbased microworlds? Journal of Educational Psychology, 95, 806–813.

Mayer, R. E., & Hegarty, M. (1996). The process of understanding mathematical problem solving. In: Sternberg, R. J. and BenZeev T., (Eds.), The nature of mathematical thinking (pp. 29–54).Mahwah, NJ: Erlbaum.

Mayer, R. E., Mathias, A., & Wetzell, K. (2002). Fostering understanding of multimedia messages through pretraining: Evidence for a twostage theory of mental model construction. Journal of Experimental Psychology: Applied, 8,147–154. doi:10.1037/1076898X.8.3.147

McLaren, B.M., van Gog, T., Ganoe, C., Karabinos, M., & Yaron, D. (2016). The efficiency of worked examples compared to erroneous examples, tutored problem solving, and problem solving in classroom experiments. Computers in Human Behavior, 55, 8799. doi:10.1016/j.chb.2015.08.038

Meijer, J., & Riemersma, F. (2002). Teaching and testing mathematical problem solving by offering optional assistance. Instructional Science, 30, 187–220. Mevarech, Z. R., & Kramarski, B. (1997). IMPROVE: A multidimensional method

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Pfannenstiel, K. H., Bryant, D. P., Bryant, B.R., & Porterfield, J. A. (2015). Cognitive strategy instruction for teaching word problems to primarylevel struggling students. Intervention in School and Clinic, 50 (5), 291–296. doi: 10.1177/1053451214560890

Pfister, H. R. (2005). How to support synchronous netbased learning discourses: Principles and perspectives. In R. Bromme, F. Hesse & H. Spada (Eds.). Barriers and biases in computermediated knowledge communication (pp. 39–57). New York: Springer.

Powell, S. R. (2011). Solving word problems using schemas: A review of the literature. Learning Disabilities Research & Practice, 26 (2), 94–108. Prinsen, F. R., Volman, M. L. L., & Terwel, J. (2006). The influence of learner

characteristics on degree and type of participation in a CSCL environment. British Journal of Educational Technology, 38 (6), 10371055. doi:10.1111/j.14678535.2006.00692.x

Rasbash, J., Steele, F., Browne, W. J., & Goldstein, H. (2012). A user’s guide to MLwiN, v2.26. Bristol: Centre for Multilevel Modelling, University of Bristol.

Rau, W. & Heyl, B. S. (1990). Humanizing the college classroom: Collaborative learning and social organization among students. Teaching Sociology, 18, 141–155.

Reinwein, J. (2012). Does the modality effect exist? And if so, which modality effect? Journal of Psycholinguistic Research, 41, 1–32. doi:10.1007/s10936 01191804.

Renkl, A. (2011). Instruction based on examples. In R. E. Mayer & P. A. Alexander (Eds.), Handbook of research on learning and instruction (pp. 272295). New York: Routledge.

Ritter, S., Anderson, J. R., Koedinger, K. R., & Corbett, A. (2007). Cognitive tutor: applied research in mathematics education. Psychonomic Bulletin & Review, 14 (2), 249–255.

RittleJohnson, B., & Koedinger, K. R. (2005). Designing knowledge scaffolds to support mathematical problem solving. Cognition and Instruction, 23 (3), 313–349. doi:10.1207/s1532690xci2303_1

Roll, I., Aleven, V., McLaren, B. M., & Koedinger, K. R. (2007). Designing for metacognition—applying cognitive tutor principles to the tutoring of help seeking. Metacognition and Learning, 2 (23), 125–140.

Roll, I., Aleven, V., McLaren, B. M., & Koedinger, K. R. (2011). Improving students’ helpseeking skills using metacognitive feedback in an intelligent tutoring system. Learning and Instruction, 21, 267–280.

Rummel, N., Mullins, D., & Spada, H. (2012). Scripted collaborative learning with the cognitive tutor algebra. International Journal of Computer Supported Collaborative Learning, 7 (2), 307339. doi:10.1007/s114120129146z. Salomon, G., & Globerson, T. (1989). When teams don’t function the way they

ought to. International Journal of Educational Research, 13, 89–100. Schoenfeld, A. H. (1992). Learning to think mathematically: Problem solving,

metacognition, and sense making in mathematics. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching (pp. 334–370). New York, NY: Macmillan.

Schoenfeld, A. H. (2002). Research methods in (Mathematics) Education. In L. English (Ed.), Handbook of International Research in Mathematics Education (pp. 435–488). Mahwah, NJ: Erlbaum.

Schoenfeld, A. H. (2013). Reflections on problem solving theory and practice. The Mathematics Enthusiast, 10 (12), 9–34.

Schraw, G. (2009). Measuring metacognitive judgments. In D. Hacker, J. Dunlosky, & A. Greasser (Eds.), Handbook of metacognition in education (pp. 415–429). New York, NY: Routledge.

Sfard, A., & Kieran, C. (2001). Cognition as communication: Rethinking learning by talking through multifaceted analysis of students’ mathematical interactions. Mind, Culture, and Activity, 8 (1), 42–76.

Sfard, A., Nesher, P., Streefland, L., Cobb, P., & Mason, J. (1998). Learning mathematics through conversation: Is it as good as they say? A debate. For the Learning of Mathematics, 18 (1), 41–51.

References

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