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Empirical research on problem solving and problem posing: a look at the state of the art

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Abstract

Problem solving and problem posing have long been of interest to the mathematics education community. In this survey paper we first look at some of the seminal moments in the history of research on the important topics. We then use this history to position the state-of-the-art research being done in both problem solving and problem posing, before introducing the presented state-of-the-art developments in problem solving and problem posing. We then use this work as a backdrop against which to introduce the 16 empirical papers that make up this special issue. Together these 16 papers add nuance to what is already known about problem solving and problem posing; this nuance is the result of attending to very specific contexts and purposes in which these activities are embedded. We end the paper by discussing the future directions these fields can take.

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Notes

  1. It is with great sadness that, as we write this historical survey on the emergence of problem solving and problem posing in mathematics education, we learn that Marion Walter passed away at the age of 92. Her contributions to mathematics education in general and problem posing in particular are significant, valuable, and much appreciated.

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Authors and Affiliations

  1. Simon Fraser University, Burnaby, BC, Canada

    Peter Liljedahl

  2. University of Delaware, Newark, DE, USA

    Jinfa Cai

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  1. Peter Liljedahl
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  2. Jinfa Cai
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Correspondence to Peter Liljedahl.

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Liljedahl, P., Cai, J. Empirical research on problem solving and problem posing: a look at the state of the art. ZDM Mathematics Education 53, 723–735 (2021). https://doi.org/10.1007/s11858-021-01291-w

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