Multiple Approaches to Problem Posing - Theoretical Considerations Regarding its Definition, Conceptualisation, and Implementation

Oct 15, 2026

Multiple Approaches to Problem Posing presents theoretical considerations on the definition, conceptualisation, and implementation of mathematical problem posing. The paper organizes existing meanings across three levels: comparing definitions, relating problem posing to other constructs such as problem solving, mathematical creativity, and modelling, and synthesizing how it is implemented in research and teaching settings. The analysis yields five categories, showing no consensus on conceptualisations and motivating arguments about whether shared agreement on an accepted concept is needed.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages22

Reading Time55 min

AccessFree to download

Introduction

Problem posing as a research focus

Educational potential for student learning

Importance for teachers

Diversity of approaches in the literature

doi: 10.26529/cepsj.878 Multiple Approaches to Problem Posing: Theoretical Considerations Regarding its Definition, Conceptualisation, and Implementation Ioannis Papadopoulos*1, Nafsika Patsiala2, Lukas Baumanns3 and Benjamin Rott3 • The importance of mathematical problem posing has been acknowledged by many researchers. In this theoretical paper, we want to capture different meanings and aspects of problem posing by approaching it from three different levels: (1) by comparing definitions,(2) by relating it to other constructs, and (3) by referring to research and teaching settings. The first level is an attempt to organise existing definitions of problem posing. The result of this analysis are five categories, which shows that there is no consensus regarding the conceptualisations of problem posing. In the second level, we examine how problem posing is conceived by the research community compared to other mathematical constructs, such as problem solving, mathematical creativity, or modelling. Finally, in the third level, we summarise possible ways of implementing problem posing in research and teaching settings as they are depicted in the relevant literature. Given this broad variance regarding the conceptualisations of problem posing, we attempt to provide some arguments as to whether there is a need for consensus on a commonly accepted concept of problem posing. Keywords: problem posing, definition, conceptualisation, implementation 1 *Corresponding Author. Faculty of Elementary Education, Aristotle University of Thessaloniki, Greece; [ypapadop@eled.auth.gr](ypapadop@eled.auth.gr). 2 Faculty of Elementary Education, Aristotle University of Tessaloniki, Greece. 3 University of Cologne, Germany. Večdimenzionalni pristop k zastavljanju problemov: teoretični premisleki glede njegove opredelitve, konceptualizacije in izvedbe Ioannis Papadopoulos, Nafsika Patsiala, Lukas Baumanns in Benjamin Rott • Pomen zastavljanja matematičnih problemov je obravnavalo že več raziskovalcev. V tem teoretičnem prispevku želimo zajeti različne opredelitve in vidike zastavljanja problemov, h katerim smo pristopili na trehrazličnih ravneh: 1) primerjava opredelitev; 2) povezave z drugimi konstrukti; 3) izvedene raziskave in poučevalne prakse. Na prvi ravni smo želeli organizirati različne obstoječe opredelitve zastavljanja problemov. Rezultate te analize smo uvrstili v pet kategorij, s čimer pokažemo, da nikonsenza glede opredelitve zastavljanja problemov. Na drugi ravni povzamemo, kako je zastavljanje problemov sprejeto v skupnosti raziskovalcev in kako se ta povezuje z drugimi konstrukti, kot na primer z reševanjem problemov, s kreativnostjo, z modeliranjem. Nazadnje, na tretji ravni, iz relevantnih raziskav povzamemo mogoče načine raziskovanja zastavljanja problemov in implementiranja v poučevanje. Upoštevajoč precejšnja odstopanja glede konceptualizacije zastavljanja problemov, poskušamo navesti nekaj argumentov za potrebo po soglasju o splošnosprejetem konceptu zastavljanja problemov. Ključne besede: zastavljanje problemov, opredelitev, konceptualizacija, implementacija Introduction Problem posing is considered an important topic that, from time to time, attracts the attention of the research community (Cai & Hwang, 2020; Stanic & Kilpatrick, 1988) . For example, Einstein and Infeld (1938) emphasise the importance of problem posing by claiming that ‘the formulation of a problem is often more essential than its solution’ (p. 95) . The potential of problem posing to enhance students’ learning in mathematics has been acknowledged by many researchers, thus confirming its importance (English, 1998; Silver, 1994) . They attribute this potential to the fact that problem-posing activities are cognitively demanding tasks (Cai & Hwang, 2002), which require students to expand their thinking beyond already known procedures to improve their understanding by reflecting on the structure of the given problem. In this sense, proble

FAQs

What are the three analytical levels used to examine problem posing?

The paper examines problem posing (1) by comparing definitions, (2) by relating it to other mathematical constructs, and (3) by referring to research and teaching settings for implementation.

What does the analysis of existing definitions produce?

It organizes existing definitions into five categories, indicating that there is no consensus regarding how problem posing is conceptualised.

Why does the paper discuss the need for consensus on the concept of problem posing?

Because the conceptualisations vary widely across the literature, the paper provides arguments about whether a commonly accepted concept is necessary.

Oct 15, 2026

Uploaded by Mafia Boss