Science Technology Engineering Mathematics and Environmental Education Research Group

Re-imagining futures in STEME

The role of optimism in collaborative problem solving in mathematics: building problem solving capacity

Lack of persistence creates substantial barriers to mathematical problem solving. Successful problem solving that can raise mathematical performance is predicated on a suite of affective characteristics involving optimism (e.g., academic resilience, confidence, risk-taking). Dr Gaye Williams’ award winning study (Chancellor’s Prize, University of Melbourne) linked optimism and individual problem solving and raised questions about optimism influencing group activity. Video-stimulated student interviews in a pilot study using Gaye’s Engaged to Learn pedagogy (developed as a teacher and refined through her PhD) elicited frequent creative group thinking through optimistic interactions. This new angle to examining reasons for disparate group performances on challenging tasks should increase mathematics achievement.

Team member: Dr. Gaye Williams

Funding body: ARC Discovery Project with Australian Postdoctoral Fellowship


  • Williams, G. (2014). Optimistic problem-solving activity: Enacting confidence, persistence, and perseverance. ZDM—The International Journal on Mathematics Education, 46(3): 407-422. doi:10.1007/s11858-014-0586-y.
  • Williams, G. (2013). Associations between the ontogenesis of confidence and inclination to explore unfamiliar mathematical problems. In A. Lindmeier and A. Heinze (Eds.). Proceedings of the 37th Conference of the International Group for the Psychology of Mathematics Education: Mathematics across the lifespan, (Vol. 4, pp. 393-400), Kiel, Germany: PME.
  • Williams, G. (2013). High performance, confidence, and disinclination to explore: A case study. In V. Steinle, L. Ball, & C. Bardina (Eds.). Mathematics Education Yesterday and Today: Proceedings of the 36th annual conference of the Mathematics Education Research Group of Australasia, (Vol. 2, pp. 658-665), Melbourne, Australia: MERGA.
  • Williams, G. (2013). Grouping: Successes, surprises, and catastrophes. In Andrea McDonough, Anne Downton, and Leicha Bragg (Eds.). Mathematics of the Planet Earth (pp. 76-84), Brunswick, Victoria: The Mathematics Association of Victoria. [Keynote Address MAV Conference]
  • Williams, G. (2011). Relationships between cognitive, social, and optimistic mathematical problem solving activity. In B. Ubuz (Ed.). Proceedings of the 35th Conference of the International Group for the Psychology of Mathematics Education, (Vol. 4, pp. 345-352), Ankara, Turkey: PME.
  • Williams, G. (2011). Queries without hints, affirming, or ‘telling’, that sustained spontaneous problem solving activity. In J. Clark, B. Kissane, J. Mousley, T. Spencer, & S. Thornton (Eds.). Mathematics: Traditions and [new] practices, (Vol. 2, pp. 795-803). Adelaide: Australian Association of Mathematics Teachers & Mathematics Education Research Group of Australasia.
  • Williams, G. (2010). Symbiosis between creative mathematical thinking accompanied by high positive affect, and optimism. In Pinto, M., & Kawasaki, T. (Eds.). Proceedings of 34th conference of the International Group for the Psychology of Mathematics Education, (Vol. 5, pp. 297-304). Belo Horizonte, Brazil: PME.
  • Williams, G. (2010). Student-created tasks inform conceptual task design. In Y. Shimizu, B. Kaur, R. Huang & D. J. Clarke (Eds.), Mathematical tasks in classrooms around the world. (pp. 165-184). Sense Publications: The Netherlands.
  • Williams, G. (2009). Engaged to learn pedagogy: Theoretically identified optimism-building situations. In R. Hunter, B. Bicknell, & T. Burgess. Crossing Divides: Mathematics Education Research Group of Australasia 32 Conference Proceedings, (Vol. 2. 595-602). Wellington, NZ: MERGA.
  • Williams, G. (2009). Spontaneous student questions: informing pedagogy to promote creative mathematical thinking. In Tzekaki, M., Kaldrimidou, M., & Sakonidis, H. (Eds.). Proceedings of 33rd conference of the International Group for the Psychology of Mathematics Education, (Vol. 5, pp. 345-352). Thessaloniki, Greece: PME.
  • Williams, G. (2007). Abstracting in the context of spontaneous learning. (Abstraction, Special Edition) Mathematics Education Research Journal, 19(2), 69–88.