Problem solving

      In a nutshell

      • Mathematical problem-solving requires the ability to apply a range of different solution strategies and representations.
      • Problem-solving involves several steps that progress from identifying a problem to evaluating the solution.
      • Problem-solving skills are crucial for young children as they become independent in their real and academic lives.

      Problem‑solving skill refers to the ability to handle non‑routine problems for which no ready‑made solution strategy is available, requiring the learner to adapt or invent new strategies to reach a solution (Doorman et al., 2007). Mathematical problem-solving requires the ability to apply a range of different solution strategies and representations. It is common for students to perform well on routine exercises they have practiced before but struggle when faced with problems that differ from previously encountered ones.

      Schoenfeld (1992) asserted that problem-solving skills are frequently emphasized in mathematics syllabi worldwide to enhance children’s ability to solve real-life problems. In many countries, problem-solving in mathematics is taught as an isolated skill. Cai (2010) highlighted the importance of incorporating problem-solving skills into the teaching and learning of mathematics to create children who are problem-solvers. Problem-solving in maths involves possibility thinking, which involves finding relevant alternatives to tackle puzzles or word problems (Craft, 2002). Problem-solving activities also aid learners in learning significant mathematical concepts (Lesh & Zawojewski, 2007; van Bommel & Palmér, 2016).

      Problem-solving typically involves the following steps:

      • Recognizing that a problem exists and deciding to address it
      • Describing and understanding the problem
      • Gathering relevant information
      • Selecting information that is useful
      • Generating possible solutions
      • Evaluating these options and choosing the best one
      • Trying out the chosen solution
      • Reviewing how well the solution worked

      Research briefs

      References

      Cai, J. (2010). Commentary on problem solving heuristics, affect, and discrete mathematics: A representational discussion. In B. Sriraman, & L. English (Eds.), Theories of mathematics education: Seeking new frontiers. Springer. https://doi.org/10.1007/978-3-642-00742-2_25

      Craft, A. (2002). Creativity and early years education. Continuum.

      Doorman, M., Drijvers, P., Dekker, T. et al. (2007). Problem solving as a challenge for mathematics education in The Netherlands. ZDM Mathematics Education, 39, 405–418. https://doi.org/10.1007/s11858-007-0043-2

      English, L., & Sriraman, B. (2010). Problem solving for the 21st century. In B. Sriraman & L. English (Eds.), Theories of mathematics education: Seeking new frontiers. Springer. https://doi.org/10.1007/978-3-642-00742-2_27

      Lesh, R. & Zawojewski, J. (2007). Problem solving and modeling. In F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 763-804). Charlotte: Information Age.

      Schoenfeld, A. H. (1992). Learning to think mathematically: Problem solving, metacognition, and sense-making in mathematics. In D. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 334–370).

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      Learning mathematical skills

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