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New research directions in learning and cognition

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Abstract

Research in learning and cognition continues to extend the boundaries of possibilities for theoretical frameworks, research designs, and questions interrogated. This overview captures a snapshot of recent research for the purpose of drawing attention to new directions. It includes: types of theoretical frameworks employed to study student learning, the reciprocity of teaching and learning, and identifying underpinning conceptual understanding that can contribute to curriculum development, including a discussion paper on possible roles of algorithms. Future directions for research are then discussed. The papers in this special issue are briefly introduced in relevant sections. This paper draws attention to the increased use of multi-theoretical perspectives and what they have enabled us to learn about the complexities of teaching and learning in classrooms. It also draws attention to some of the innovative research designs and analysis techniques that have been employed to enable the answering of various research questions.

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Notes

  1. Extended papers from Topic Study Group 22 (TSG22): Learning and Cognition, at the 12th International Congress on Mathematics Education (ICME-12) in Korea in 2012.

  2. http://www.mathunion.org/icmi/news/details/?tx_ttnews[tt_news]=801&cHash=9f09d8ef9ae6d4393f2ffb6efdea781b.

References

  • Alibali, M., Nathan, M., Church, R. B., Wolfgram, M., Kim, S., & Knuth, E. (2013). Teachers’ gestures and speech in mathematics lessons: forging common ground by resolving trouble spots. ZDM—The International Journal on Mathematics Education, 45(3), 425–440. doi:10.1007/s11858-012-0476-0.

    Article  Google Scholar 

  • Antonietti, A., Ignazi, S., & Perego, P. (2000). Metacognitive knowledge about problem-solving methods. British Journal of Educational Psychology, 70, 1–16.

    Article  Google Scholar 

  • Artigue, M., & Blomhøj, M. (2013). Conceptualizing inquiry-based education in mathematics. ZDM—The International Journal on Mathematics Education, 45(6), 797–810. doi:10.1007/s11858-013-0506-6.

    Article  Google Scholar 

  • Attard, C. (2013). “If I had to pick any subject, it wouldn’t be maths”: Foundations for engagement with mathematics during the middle years. Mathematics Education Research Journal, 25(4), 569–587. doi:10.1007/s13394-013-0081-8.

    Article  Google Scholar 

  • Cai, J., Moyer, J., Wang, N., Hwang, S., Nie, B., & Garber, T. (2013). Mathematical problem posing as a measure of curricular effect on students’ learning. Educational Studies in Mathematics, 83(1), 57–69. doi:10.1007/s10649-012-9429-3.

    Article  Google Scholar 

  • Cai, J., Perry, B., Wong, N.-Y., & Wong, T. (2009). What is effective teaching? A study of experienced mathematics teachers from Australia, the Mainland China, and Hong Kong-China, and the United States. In J. Cai, G. Kaier, B. Perry, & N.-Y. Wong (Eds.), Effective mathematics teaching from teachers’ perspectives: National and cross-national studies (pp. 1–36). Rotterdam: Sense Publishers.

    Google Scholar 

  • Campione, J. C., Brown, A. L., & Connell, M. L. (1989). Metacognition: On the importance of understanding what you are doing. In R. I. Charles, & E. A. Silver (Eds.), The teaching and assessing of mathematical probelm solving: research agenda for mathematics education (Vol. 3, pp. 93–114). Hillsdale, NJ: Erlbaum.

  • Chen, C.-L., & Herbst, P. (2013). The interplay among gestures, discourse, and diagrams in students’ geometrical reasoning. Educational Studies in Mathematics, 83(2), 285–307. doi:10.2307/23434221.

    Article  Google Scholar 

  • Choi, K., Choi, T., & McAninch, M. (2012). A comparative investigation of the presence of psychological conditions in high achieving eighth graders from TIMSS 2007 Mathematics. ZDM-The International Journal on Mathematics Education, 44(2), 189–199. doi:10.1007/s11858-012-0401-6.

    Article  Google Scholar 

  • Cobb, P., Wood, T., Yackel, E., & McNeal, B. (1992). Characteristics of classroom mathematics traditions: An interaction analysis. American Educational Research Journal, 29(3), 573–604.

    Article  Google Scholar 

  • Cobb, P., Yackel, E., & Wood, T. (2011). Young children’s emotional acts while engaged in mathematical problem solving. In A. Sfard, K. Gravemeijer, & E. Yackel (Eds.), A Journey in Mathematics Education Research (Vol. 48, pp. 41–71). Netherlands: Springer.

    Google Scholar 

  • Cole, M., & Wertsch, J. (1994). Beyond the individual-social antimony in discussions of Piaget and Vygotsky. http://www.massey.ac.nz/~alock/virtual/colevyg.htm. Accessed 29 April 2014.

  • David, M., & Tomaz, V. (2012). The role of visual representations for structuring classroom mathematical activity. Educational Studies in Mathematics, 80(3), 413–431. doi:10.1007/s10649-011-9358-6.

    Article  Google Scholar 

  • De Smedt, B., Verschaffel, L., & Ghesquière, P. (2009). The predictive value of numerical magnitude comparison for individual differences in mathematics achievement. Journal of Experimental Child Psychology, 103, 469–479. doi:10.1016/j.jecp.2009.01.010.

    Article  Google Scholar 

  • Dreyfus, T., Hershkowitz, R., & Schwarz, B. (2001). Abstraction in context II: The case of peer interaction. Cognitive Science Quarterly, 1(3), 307–368.

    Google Scholar 

  • Dweck, C. S. (2012). Mindset: How you can fulfill your potential, Constable and Robinson.

  • Fan, L., & Bokhove, C. (2014, this issue). Rethinking the role of algorithms in school mathematics: a conceptual model with focus on cognitive development. ZDM—The International Journal on Mathematics Education,. doi:10.1007/s11858-014-0590-2.

    Google Scholar 

  • Francisco, J. (2013). Learning in collaborative settings: Students building on each other, Äôs ideas to promote their mathematical understanding. Educational Studies in Mathematics, 82(3), 417–438. doi:10.1007/s10649-012-9437-3.

    Article  Google Scholar 

  • Freitas, E. D., & Sinclair, N. (2013). New materialist ontologies in mathematics education: the body in/of mathematics. Educational Studies in Mathematics, 83(3), 453–470. doi:10.2307/23434902.

  • Funahashi, Y., & Hino, K. (2014, this issue). The teacher’s role in guiding children’s mathematical ideas toward meeting lesson objectives. ZDM—The International Journal on Mathematics Education.,. doi:10.1007/s11858-014-0592-0.

    Google Scholar 

  • Galbraith, P., Stillman, G., & Brown, J. (2010). Turning ideas into modeling problems. In R. Lesh, P. Galbraith, C. Haines, & A. Hurford (Eds.), Modeling students’ mathematical modeling competencies ICTMA 13 (pp. 243–283). New York: Springer.

    Google Scholar 

  • Givvin, K. B., Jacobs, J., Hollingsworth, H., & Hiebert, J. (2009). What is effective mathematics teaching? International educators’ judgment of mathematics lessons from the TIMSS 1999 video study. In J. Cai, G. Kaiser, B. Perry, & N.-Y. Wong (Eds.), Effective mathematics teaching from teachers’ perspectives: National and cross-national studies (pp. 37–69). The Netherlands: Sense Publishers.

    Google Scholar 

  • Glover, S., Burns, J., Butler, H., & Patton, G. (1998). Social environments and the emotional well-being of young people. Family Matters, 49, 11–16.

    Google Scholar 

  • Goos, M., & Williams, J. (2013). Modelling with mathematics and technology. In K. Clements, A. Bishop, J. Kilpatrick, F. Leung, & C. Keitel (Eds.), Third international handbook in mathematics education (pp. 549–569). New York: Springer.

    Google Scholar 

  • Hannula, M. (2005). Shared cognitive intimacy and self-defence: Two socioemotional processes in problem solving. Nordic Studies in Mathematics Education, 10(1), 25–41.

    Google Scholar 

  • Hannula, M. (2012). Looking at the third wave from the West: Framing values within a broader scope of affective traits. ZDM—The International Journal on Mathematics Education, 44(1), 83–90. doi:10.1007/s11858-012-0410-5.

    Article  Google Scholar 

  • Harpen, X., & Sriraman, B. (2013). Creativity and mathematical problem posing: An analysis of high school students’ mathematical problem posing in China and the USA. Educational Studies in Mathematics, 82(2), 201–221. doi:10.1007/s10649-012-9419-5.

    Article  Google Scholar 

  • Hennessey, M. N., Higley, K., & Chesnut, S. R. (2012). Persuasive Pedagogy: A new paradigm for mathematics education. Educational Psychology Review, 24(2), 187–204. doi:http://dx.doi.org/10.1007/s10648-011-9190-7.

  • Hernandez-Martinez, P., & Williams, J. (2013). Against the odds: Resilience in mathematics students in transition. British Educational Research Journal, 39(1), 45–49.

    Google Scholar 

  • Hershkowitz, R., Tabach, M., Rasmussen, C., & Dreyfus, T. (2014). Knowledge shifts in a probability classroom—A case study coordinating two methodologies. ZDM—The International Journal on Mathematics Education,. doi:10.1007/s11858-014-0576-0. (this issue).

    Google Scholar 

  • Huang, H.-M. E. (2014, this issue). Third to fourth-grade students’ conceptions of multiplication and area measurement. ZDM—The International Journal on Mathematics Education,. doi:10.1007/s11858-014-0603-1

  • Huang, H.-M. E., & Witz, K. G. (2011). Developing children’s conceptual understanding of area measurement: A curriculum and teaching experiment. Learning and Instruction, 21(1), 1–13. doi:10.1016/j.learninstruc.2009.09.002.

    Article  Google Scholar 

  • Huang, H.-M. E., & Witz, K. G. (2013). Children’s conceptions of area measurement and their strategies for solving area measurement problems. Journal of Curriculum and Teaching, 2(1), 10–26. doi:10.5430/jct.v2n1p10.

    Google Scholar 

  • Kattou, M., Kontoyianni, K., Pitta-Pantazi, D., & Christou, C. (2013). Connecting mathematical creativity to mathematical ability. ZDM—The International Journal on Mathematics Education, 45(2), 167–181. doi:10.1007/s11858-012-0467-1.

    Article  Google Scholar 

  • Kensington-Miller, B., Yoon, C., Sneddon, J., & Stewart, S. (2013). Changing beliefs about teaching in large undergraduate mathematics classes. Mathematics Teacher Educational Development, 15(2), 52–69.

    Google Scholar 

  • Kim, D., & Ju, M. K. (2012). A changing trajectory of proof learning in the geometry inquiry classroom. ZDM—The International Journal on Mathematics Education, 44, 149–160.

    Article  Google Scholar 

  • Kim, Y. R., Park, M. S., Moore, T. J., & Varma, S. (2013). Multiple levels of metacognition and their elicitation through complex problem-solving tasks. The Journal of Mathematical Behavior, 32(3), 377–396. doi:http://dx.doi.org/10.1016/j.jmathb.2013.04.002.

  • Kroesbergen, E. H., Van Luit, J. E. H., & Aunio, P. (2012). Editorial: Mathematical and cognitive predictors of the development of mathematics. British Journal of Educational Psychology, 82, 24–27. doi:10.1111/j.2044-8279.2012.02065.x.

    Article  Google Scholar 

  • Kwon, O. N., & Cho, S. J. (2012). Balance between foundations and creativity: Features of Korean mathematics education. ZDM—The International Journal on Mathematics Education., 44, 105–108.

    Article  Google Scholar 

  • Langrall, C. W. (2014). Linking research and practice: Another call to action? Journal for Research in Mathematics Education, 45(2), 154–156. doi:10.5951/jresematheduc.45.2.0154.

    Article  Google Scholar 

  • Lee, N. H., Yeo, J. S. D., & Hong, S. E. (2014, this issue). A metacognitive-based instruction for primary four students to approach non-routine mathematical word problems. ZDMThe International Journal on Mathematics Education. doi:10.1007/s11858-014-0599-6.

  • Leikin, R., & Lev, M. (2013). Mathematical creativity in generally gifted and mathematically excelling adolescents: What makes the difference? ZDM—The International Journal on Mathematics Education, 45(2), 183–197. doi:10.1007/s11858-012-0460-8.

    Article  Google Scholar 

  • Leikin, R., & Pitta-Pantazi, D. (2013). Creativity and mathematics education: The state of the art. ZDM—The International Journal on Mathematics Education, 45(2), 159–166. doi:10.1007/s11858-012-0459-1.

    Article  Google Scholar 

  • Lerman, S. (1996). Intersubjectivity in mathematics learning: A challenge to the radical constructivist paradigm? Journal for Research in Mathematics Education, 27(2), 133–150. doi:10.2307/749597.

    Article  Google Scholar 

  • Lerman, S. (2013). Theories in practice: Mathematics teaching and mathematics teacher education. ZDM—The International Journal on Mathematics Education, 45(4), 623–631. doi:10.1007/s11858-013-0510-x.

    Article  Google Scholar 

  • Lew, H.-C., Cho, W.-Y., Koh, Y., Koh, H., & Paek, J. (2012). New challenges in the 2011 revised middle school curriculum of South Korea: Mathematical process and mathematical attitude. ZDM—The International Journal on Mathematics Education, 44(2), 109–119. doi:10.1007/s11858-012-0392-3.

    Article  Google Scholar 

  • Lewis, K. E. (2014). Difference not deficit: Reconceptualizing mathematical learning disabilities. Journal for Research in Mathematics Education, 45(3), 351–396. doi:10.5951/jresematheduc.45.3.0351.

    Article  Google Scholar 

  • Liljedahl, P. (2013). Illumination: An affective experience? ZDM—The International Journal on Mathematics Education., 45(2), 253–265. doi:10.1007/s11858-012-0473-3.

    Article  Google Scholar 

  • Martin, A., Anderson, J., Bobis, J., Way, J., & Vellar, R. (2012). Switching on and switching off in mathematics: An ecology study of future intent and disengagement among middle school students. Journal of Educational Psychology, 104, 1–18.

    Article  Google Scholar 

  • Mayer, R. E. (2008). Learning and instruction. Upper Saddle River, NJ: Pearson Education.

  • Meira, & Lerman, S. (2009). Zones of proximal development as fields for communication and dialogue. In C. Lightfoot & M. C. D. P. Lyra (Eds.), Challenges and strategies to study human development in cultural contexts (pp. 199–220): Firera & Liuzzo Group. http://www.educazione.it/public/Challenges%20and%20Strategies_2.pdf#page=199. Accessed 4 May 2014.

  • NCTM Research Committee. (2014). The NCTM research presession: A brief history and reflection. Journal for Research in Mathematics Education, 45(2), 157–172. doi:10.5951/jresematheduc.45.2.0157.

    Article  Google Scholar 

  • Nunes, T., Bryant, P., Barros, R., & Sylva, K. (2012). The relative importance of two different mathematical abilities to mathematical achievement. British Journal of Educational Psychology, 82, 136–156.

    Article  Google Scholar 

  • Nunes, T., Bryant, P., Evans, D., Gottardis, L., & Terleksti, M.-E. (2014, this issue). The cognitive demands of understanding the sample space. ZDMThe International Journal on Mathematics Education. doi:10.1007/s11858-014-0581-3.

  • Passolunghi, M. C., & Lanfranchi, S. (2012). Domain-specific and domain-general precursors of mathematical achievement: A longitudinal study from kindergarten to first grade. British Journal of Educational Psychology, 82, 42–63. doi:10.1111/j.2044-8279.2011.02039.x.

    Article  Google Scholar 

  • Pitta-Pantazi, D., Sophocleous, P., & Christou, C. (2013). Spatial visualizers, object visualizers and verbalizers: Their mathematical creative abilities. ZDM—The International Journal on Mathematics Education, 45(2), 199–213. doi:10.1007/s11858-012-0475-1.

    Article  Google Scholar 

  • Radford, L. (2009). Why do gestures matter? Sensuous cognition and the palpability of mathematical meanings. Educational Studies in Mathematics, 70(2), 111–126. doi:10.2307/40284564.

    Article  Google Scholar 

  • Radford, L. (2013). Perceiving with the eyes and with the hands. Journal for Research in Mathematics Education. 3(1)

  • Radford, L. (2014, this issue). Towards an embodied, cultural, and material conception of mathematics cognition. ZDMThe International Journal on Mathematics Education. doi:10.1007/s11858-014-0591-1.

  • Rasmussen, C., & Stephan, M. (2008). A methodology for documenting collective activity. In A. E. Kelly, R. A. Lesh, & J. Y. Baek (Eds.), Handbook of innovative design research in science, technology, engineering, mathematics (STEM) education (pp. 195–215). New York: Taylor and Francis.

    Google Scholar 

  • Remillard, K. S. (2014). Identifying discursive entry points in paired-novice discourse as a first step in penetrating the paradox of learning mathematical proof. The Journal of Mathematical Behavior, 34(0), 99–113. doi:http://dx.doi.org/10.1016/j.jmathb.2014.02.002.

  • Resnick, L. B. (2010). 2009 Wallace Foundation distinguished lecture: nested learning systems for the thinking curriculum. Educational Researcher, 39(3), 183–197. doi:10.2307/27764582.

    Article  Google Scholar 

  • Roth, W.-M. (2013). Contradictions and uncertainty in scientists’ mathematical modeling and interpretation of data. The Journal of Mathematical Behavior, 32(3), 593–612. doi:http://dx.doi.org/10.1016/j.jmathb.2013.07.001.

  • Ryve, A., Nilsson, P., & Pettersson, K. (2013). Analyzing effective communication in mathematics group work: The role of visual mediators and technical terms. Educational Studies in Mathematics82(3), 497–514. doi:10.2307/23434475.

  • Sarrazy, B., & Novotná, J. (2013). Didactical contract and responsiveness to didactical contract: A theoretical framework for enquiry into students’ creativity in mathematics. ZDM—The International Journal of Mathematics Education, 45(2), 281–293. doi:10.1007/s11858-013-0496-4.

    Article  Google Scholar 

  • Schifter, D., & Szymaszek, J. (2003). Structuring a rectangle: Teachers write to learn about their students’ thinking. In D. H. Clements, & G. Bright (Eds.), Learning and teaching measurement. 2003 year book (pp. 143–156). Reston: National Council of Teachers of Mathematics.

  • Schoenfeld, A. (1985). Mathematical problem solving. New York: Academic Press.

    Google Scholar 

  • Schoenfeld, A. (2013). Classroom observations in theory and practice. ZDM—The International Journal on Mathematics Education, 45(4), 607–621. doi:10.1007/s11858-012-0483-1.

    Article  Google Scholar 

  • Schwarz, B., Dreyfus, T., & Hershkowitz, R. (2009). The nested epistemic actions model for abstraction in context. In B. Schwarz, T. Dreyfus, & R. Hershkowitz (Eds.), Transformation of knowledge through classroom interaction (pp. 11–41). NY: Routledge.

    Google Scholar 

  • Seligman, M. (with Reivich, K., Jaycox, L., Gillham, J.). (1995). The Optimistic Child. Adelaide: Griffin Press.

  • Shimizu, Y. (2010). A task-specific analysis of explicit linking in lesson sequences in three Japanese mathematics classrooms. In Y. Shimizu, B. Kaur, R. Huang, & D. J. Clarke (Eds.), Mathematical tasks in classrooms around the world (pp. 87–102). The Netherlands: Sense Publications.

    Google Scholar 

  • Shimizu, Y., & Williams, G. (2013). Studying learners in intercultural contexts. In K. Clements, A. Bishop, J. Kilpatrick, F. Leung, & C. Keitel (Eds.), Third international handbook in mathematics education (pp. 145–168). New York: Springer.

    Google Scholar 

  • Silver, E. A. (1997). Fostering creativity through instruction rich in mathematical problem solving and problem posing. ZDM-Zentrallblatt fur Didaktik der Mathematik (International reviews on mathematics education), 97, 75–80.

    Article  Google Scholar 

  • Silver, E. (2013). Problem-posing research in mathematics education: Looking back, looking around, and looking ahead. Educational Studies in Mathematics, 83(1), 157–162. doi:10.1007/s10649-013-9477-3.

    Article  Google Scholar 

  • Simon, M. (2013). Promoting fundamental change in mathematics teaching: A theoretical, methodological, and empirical approach to the problem. ZDM—The International Journal of Mathematics Education, 45(4), 573–582. doi:10.1007/s11858-013-0486-6.

    Article  Google Scholar 

  • Skemp, R. (1976). Instrumental understanding and relational understanding. Mathematics Teaching, 77, 20–26.

    Google Scholar 

  • Stacey, K. (2010). Mathematics teaching and learning to reach beyond the basics. Paper presented at the Australian Research Council Conference, 15–17 August, 2010. http://research.acer.edu.au/research_conference/RC2010/17august/1/. Retrieved 3 June 2014.

  • Staples, M. E., Bartlo, J., & Thanheiser, E. (2012). Justification as a teaching and learning practice: Its (potential) multifacted role in middle grades mathematics classrooms. The Journal of Mathematical Behavior, 31(4), 447–462. doi:http://dx.doi.org/10.1016/j.jmathb.2012.07.001.

  • Stillman, G., Cheung, K., Mason, R., Sheffield, L., Bharatah, S., & Ueno, K. (2009). Challenging mathematics: Classroom practices. In E. J. Barbeau & P. Taylor, J (Eds.), Challenging mathematics in and beyond the classroom. New ICMI Study Series 12 (pp. 243–283). New York: Springer.

  • Sullivan, P., Clarke, D., Clarke, D., Farrell, L., & Gerrard, J. (2013). Processes and priorities in planning mathematics teaching. Mathematics Education Research Journal, 25(4), 457–480. doi:10.1007/s13394-012-0066-z.

    Article  Google Scholar 

  • Szilágyi, J., Clements, D. H., & Sarama, J. (2013). Young children's understandings of length measurement: Evaluating a learning trajectory. Journal for Research in Mathematics Education, 44(3), 581–620. doi:10.5951/jresematheduc.44.3.0581.

  • Tabach, M., & Friedlander, A. (2013). School mathematics and creativity at the elementary and middle-grade levels: How are they related? ZDM—The International Journal on Mathematics Education, 45(2), 227–238. doi:10.1007/s11858-012-0471-5.

    Article  Google Scholar 

  • Thomas, M. J., & Klymchuk, S. (2012). The school–tertiary interface in mathematics: Teaching style and assessment practice. Mathematics Education Research Journal, 24(3), 283–300. doi:10.1007/s13394-012-0051-6.

    Article  Google Scholar 

  • Tomasello, M., Carpenter, M., Call, J., Behne, T., & Moll, H. (2005). Understanding and sharing intentions: The origins of cultural cognition. Behavioral and Brain Sciences, 28, 1–17.

    Google Scholar 

  • Tzur, R., & Lambert, M. A. (2011). Intermediate participatory stages as zone of proximal development correlate in constructing counting-on: a plausible conceptual source for children’s transitory “Regress” to counting-all. Journal for Research in Mathematics Education, 42(5), 418–450. doi:10.5951/jresematheduc.42.5.0418.

    Google Scholar 

  • Usher, E. L., & Pajares, F. (2009). Sources of self-efficacy in mathematics: A validation study. Contemporary Educational Psychology, 34(1), 89–101. doi:http://dx.doi.org/10.1016/j.cedpsych.2008.09.002.

  • Voica, C., & Singer, F. (2013). Problem modification as a tool for detecting cognitive flexibility in school children. ZDM—The International Journal of Mathematics Education, 45(2), 267–279. doi:10.1007/s11858-013-0492-8.

    Article  Google Scholar 

  • Vygotsky, L. S. (1978). Mind and society: The development of higher psychological processes. M. Cole, V. John-Steiner, S. Scribner, & E. Souberman, (Eds.), (J. Teller, Trans.). Cambridge: Harvard University Press.

  • Wawro, M. (2014, this issue). Student reasoning about the Invertible Matrix Theorem in linear algebra. ZDM—The International Journal on Mathematics Education. doi:10.1007/s11858-014-0579-x.

  • Weber, K., Maher, C., Powell, A., & Lee, H. S. (2008). Learning opportunities from group discussions: Warrants become the objects of debate. Educational Studies in Mathematics, 68(3), 247–261. doi:10.2307/40284524.

    Article  Google Scholar 

  • Wei, W., Yuan, H., Chan, C., & Zhou, X. (2012). Cognitive correlates of performance in advanced mathematics. British Journal of Educational Psychology, 82, 157–181. doi:10.1111/j.2044-8279.2011.02049.x.

    Article  Google Scholar 

  • Williams, G. (2005). Improving intellectual and affective quality in mathematics lessons: How autonomy and spontaneity enable creative and insightful thinking. Unpublished doctoral dissertation, University of Melbourne, Melbourne, Australia. http://repository.unimelb.edu.au/10187/2380. Accessed 10 November 2005.

  • Williams, G. (2006). Autonomous looking-into support creative mathematical thinking: Capitalising on activity in Australian LPS classrooms. In D. Clarke, C. Kietel, & Y. Shimizu (Eds.), Mathematics classrooms in twelve countries: The insider’s perspective (pp. 221–236). The Netherlands: Sense Publications.

    Google Scholar 

  • Williams, G. (2010). Symbiosis between creative mathematical thinking accompanied by high positive affect, and optimism. In M. Pinto & T. Kawasaki (Eds.), Proceedings of 34th conference of the International Group for the Psychology of Mathematics Education (Vol. 5, pp. 297–304). Belo Horizonte: PME.

    Google Scholar 

  • Williams, G. (2011). Building optimism in prospective mathematics teachers: Psychological characteristics enabling flexible pedagogy. In O. Zaslavsky & P. Sullivan (Eds.), Constructing knowledge for teaching secondary mathematics, Mathematics Teacher Education (Vol. 6, pp. 307–323). NY: Springer.

    Chapter  Google Scholar 

  • Williams, G. (2014, this issue). Optimistic problem-solving activity: Enacting confidence, persistence, and perseverance. ZDM—The International Journal on Mathematics Education. doi:10.1007/s11858-014-0586-y.

  • Winsløw, C., Matheron, Y., & Mercier, A. (2013). Study and research courses as an epistemological model for didactics. Educational Studies in Mathematics, 83(2), 267–284. doi:10.2307/23434220.

    Article  Google Scholar 

  • Wood, M. B. (2013). Mathematical micro-identities: Moment-to-moment positioning and learning in a fourth-grade classroom. Journal for Research in Mathematics Education, 44(5), 775–808. doi:10.5951/jresematheduc.44.5.0775.

    Article  Google Scholar 

  • Wood, T., Hjalmarson, M., & Williams, G. (2008). Learning to design in small group mathematical modelling. In J. S. Zawojewski, H. Diefes-Dux, & K. Bowman (Eds.), Models and modeling in engineering education: Designing experiences for all students (pp. 187–212). Rotterdam: Sense Publications.

    Google Scholar 

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Williams, G., Huang, HM.E. New research directions in learning and cognition. ZDM Mathematics Education 46, 335–347 (2014). https://doi.org/10.1007/s11858-014-0602-2

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