Problem Posing: understandings

Possamai, Janaína Poffo; Allevato, Norma Suely Gomes

doi:10.1590/1980-4415v38a2300422

Abstract

The problem posing has gained prominence in curriculum documents and current research, in which many questions are still open, and are not manifested clearly and coherently in school practices. This article aims to identify and establish understandings for the terms formulation, elaboration, creation, and problem posing to support the context of Brazilian research and practice in the field of Mathematics Education. To this end, a literature review is presented, resuming historical aspects and constituting a theoretical reference about the implications on the context of mathematics learning and students' comprehensive education. Then, based on the results obtained from a systematic study review and moving forward in the constitution of a theoretical body knowledge, we present the meanings attributed to these expressions in several Brazilian and international studies and then present the definitions we assume: we understand that problem creation involves the processes of problem formulation and elaboration and it is inserted in the problem posing which advances to present the created problem to a potential solver. The relevance of these definitions covers both contexts of educational practices that contemplate the association with problem solving and research in Mathematics Education, with conditions and reflections on the collection and analysis of data, in order to deepen the understanding of specific aspects related to problem posing to be considered in future studies.

Keywords
Elaboration/Formulation of problems; Problem solving; Mathematics Teaching

Problem-posing categories:	Problem-posing situations:
Free	Problems written for a friend; Problems from data; Problems I like; Problems which involve the use of a specific concept or mathematical method, etc.
Semi-structured	Problem posing situations based on a specific problem structure: Problems which fit given computations; Problems which are similar to a previously solved problem; Open-ended problems; Mathematical investigations, etc. Problem posing situations based on a specific solution structure: Problem posing which involves the use of a specific mathematical method within a given problem structure, etc
Structure	Problem-posing situations based on a specific problem: Problem variations; Reformulations, etc. Problem-posing situations based on a specific solution: Restating a problem on the basis of its solution, etc

Author	Definition
Bonotto (2013BONOTTO, C. Artifacts as sources for problem-posing activities. Educational Studies in Mathematics, Dordrecht, v. 83, n. 1, p. 37-55, 2013., p. 39)	The term problem posing has been used to refer both to the generation of new problems and to the reformulation of given problems
Cai e Hwang (2020CAI, J.; HWANG, S. Learning to teach through mathematical problem posing: theoretical considerations, methodology, and directions for future research. International Journal of Educational Research, [s. L.], v. 102, [s. n.], p. 1-8, 2020., p. 3)	(a) Students pose mathematical problems based on given problem situations which may include mathematical expressions or diagrams, and (b) students pose problems by changing (i.e., reformulating) existing problems.
Chen e Cai (2020)CHEN, T.; CAI, J. An elementary mathematics teacher learning to teach using problem posing: A case of the distributive property of multiplication over addition, International Journal of Educational Research, v. 102, p. 1-11; 2020. DOI: https://doi.org/10.1016/j.ijer.2019.03.004. Disponível em: https://www.sciencedirect.com/science/article/abs/pii/S0883035518320299?via%3Dihub. Acesso em: 06 abr. 2024 https://doi.org/10.1016/j.ijer.2019.03.0...	Teachers ask students to pose mathematical problems based on a given numerical expression.
Elgrably e Leikin (2021ELGRABLY, H.; LEIKIN, R. Creativity as a Function of Problem-Solving Expertise: Posing New Problems Through Investigations. ZDM - Mathematics Education, Berlim, v. 53, [s. n.], p. 891-904, 2021. DOI: https://doi.org/10.1007/s11858-021-01228-3 Disponível em: https://link.springer.com/article/10.1007/s11858-021-01228-3. Acesso em: 06 abr. 2024. https://doi.org/10.1007/s11858-021-01228... , p. 894)	Problem posing is a broad concept, usually related to the creation of a new problem in response to a requirement to create a problem or a set of problems.
Singer e Voica (2013SINGER, F. M.; VOICA, C. A Problem-Solving Conceptual Framework and its Implications in designing Problem-Posing tasks. Educational Studies in Mathematic s, Dordrecht, v. 83, [s. n.], p. 9-26, 2013. DOI: 10.1007/s10649-012-9422-x. Disponível em: https://link.springer.com/article/10.1007/s10649-012-9422-x. Acesso em: 04 abr. 2024 https://link.springer.com/article/10.100... , p. 10)	[...] PP involves extracting/identifying a (new) problem from the multitude of data or information available to the proposer.
Stoyanova e Ellerton (1996STOYANOVA, E.; ELLERTON, N. F. A framework for research into students' problem posing in school mathematics. In: CLARKSON, P. C. (Ed.). Technology in mathematics education. Melbourne: Mathematics Education Research Group of Australasia, 1996. p. 518-525., p. 518)	Problem posing will be defined as the process by which, on the basis of mathematical experience, students construct personal interpretations of concrete situations and formulate them as meaningful mathematical problems.
Xu et al. (2020)	Problem posing refers to both the creation of new problems and the reformulation of certain problems.
Cai (2022, p. 37)	Problem posing is defined as the following specific intellectual activities: (1) Students pose mathematical problems based on given problem situations which may include mathematical expressions or diagrams; (2) students pose problems by changing (i.e., reformulating) existing problems; (3) teachers generate mathematical problem-posing situations for students to pose problems; and (4) teachers predict the kinds of problems that students can pose based on given problem situations.

Brasil

Brasil

Problem Posing: understandings

Abstract