Problem Posing and Solving with Mathematical Modeling

English, Lyn D.; Fox, Jillian L.; Watters, James J.

doi:10.5951/tcm.12.3.0156

Cited by 46 publications

(15 citation statements)

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“…In our study, we focused on the generation of problems before problem solving in semi-structured situations with given descriptions of real-world situations. Giving students a rich situation, such as a real-world situation, provides students multiple opportunities for learning (English et al 2005;Bonotto 2013).…”

Section: Problem Posingmentioning

confidence: 99%

Create your own problem! When given descriptions of real-world situations, do students pose and solve modelling problems?

Hartmann

Krawitz

Schukajlow

2021

ZDM Mathematics Education

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As problem posing has been shown to foster students’ problem-solving abilities, problem posing might serve as an innovative teaching approach for improving students’ modelling performance. However, there is little research on problem posing regarding real-world situations. The present paper addresses this research gap by using a modelling perspective to examine (1) what types of problems students pose (e.g., modelling vs. word problems) and (2) how students solve different types of self-generated problems. To answer these questions, we recruited 82 ninth- and tenth-graders from German high schools and middle schools to participate in this study. We presented students with different real-world situations. Then we asked them to pose problems that referred to these situations and to solve the problems they posed. We analyzed students’ self-generated problems and their solutions using criteria from research on modelling. Our analysis revealed that students posed problems that were related to reality and required the application of mathematical methods. Therefore, problem posing with respect to given real-world situations can be a beneficial approach for fostering modelling abilities. However, students showed a strong tendency to generate word problems for which important modelling activities (e.g., making assumptions) are not needed. Of the students who generated modelling problems, a few either neglected to make assumptions or made assumptions but were not able to integrate them adequately into their mathematical models, and therefore failed to solve those problems. We conclude that students should be taught to pose problems, in order to benefit more from this powerful teaching approach in the area of modelling.

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Section: Problem Posingmentioning

confidence: 99%

Create your own problem! When given descriptions of real-world situations, do students pose and solve modelling problems?

Hartmann

Krawitz

Schukajlow

2021

ZDM Mathematics Education

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“…( 3) Despite some research papers in which problem posing is defined as an act of modelling, other researchers view both as two closely interlinked concepts. For example, English, Fox, and Watters (2005) state that in mathematical modelling as a rich problem situation, the generation of problems and questions, as well as solving those, occur naturally. When students attempt to make sense of incomplete, ambiguous, or undefined information as in a modelling situation, numerous questions naturally arise for the children as they try to make sense of this information, elicit and work with the embedded mathematical ideas, and modify and refine their model.…”

Section: (2)mentioning

confidence: 99%

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

Papadopoulos

Patsiala

Baumanns

et al. 2021

CEPSj

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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.

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“…Problem posing is one strategy that can both improve students' problem-solving skills, deepen students' conceptual understanding (Cifarelli & Cai, 2005;Silver, 1994), and provide opportunities for students to engage in mathematically creative thinking (English et al, 2005;Mann, 2006;Silver et al, 1990). For example, when teachers encourage students to problem pose it can lead students to share original ideas about what they notice or wonder (English, 1997a;Mann, 2006;Silver, 1997;Silver & Cai, 2005) or provide students the opportunity to discover something (Amabile, 2013).…”

Section: Introductionmentioning

confidence: 99%

“…By engaging students in problem posing, teachers can learn more about what students know and can do in mathematics (Barlow & Cates, 2006). Problem posing promotes genuine formative assessment between gifted students and their teachers (English et al, 2005). The use of problem posing during mathematics instruction will address NAGC's call for educators to encourage students to identify their preferred approaches to learning and to facilitate learning that will allow students to expand upon them (NAGC, 2019).…”

Section: Introductionmentioning

confidence: 99%

Fostering Mathematical Creativity Through Problem Posing and Three-Act Tasks

Lewis

Colonnese

2021

Gifted Child Today

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The National Association for Gifted Children and The National Council of Teachers of Mathematics both call for problem posing. This article illustrates the strategies used during a series of three Three-Act Tasks to foster second grade students’ abilities to problem pose. The students’ problem posing improved across the three Three-Act Tasks and revealed mathematically creative thinking. To support and encourage the students to problem pose, the teacher asked generative questions, modeled various problems, provided concrete manipulatives, and had the students create their own sequel to the Three-Act Tasks.

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Problem Posing and Solving with Mathematical Modeling

Abstract: In recent years, we have introduced elementary school children to the powerful world of mathematical modeling. Models are used to interpret real-world situations in a mathematical format. For example, graphs and tables model complex relationships among various phenomena.

Cited by 46 publications

References 0 publications

Create your own problem! When given descriptions of real-world situations, do students pose and solve modelling problems?

Create your own problem! When given descriptions of real-world situations, do students pose and solve modelling problems?

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

Fostering Mathematical Creativity Through Problem Posing and Three-Act Tasks

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