An exploratory framework for handling the complexity of mathematical problem posing in small groups

Kontorovich, Igor’; Koichu, Boris; Лейкин, Роза; Berman, Abraham

doi:10.1016/j.jmathb.2011.11.002

Cited by 73 publications

(32 citation statements)

References 19 publications

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“…Looking more specifi cally at the collective activities of students in classrooms, Kontorovich, Koichu, Leikin, and Berman ( 2012 ) have proposed a theoretical framework to help researchers handle the complexity of students' mathematical problem posing in small groups. This framework integrates fi ve facets: task organization, students' knowledge base, problem-posing heuristics and schemes, group dynamics and interactions, and individual considerations of aptness.…”

Section: What Does a Classroom Look Like When Students Engage In Probmentioning

confidence: 99%

Problem-Posing Research in Mathematics Education: Some Answered and Unanswered Questions

Cai

Hwang

Jiang³

et al. 2015

Mathematical Problem Posing

142

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This chapter synthesizes the current state of knowledge in problemposing research and suggests questions and directions for future study. We discuss ten questions representing rich areas for problem-posing research: (a) Why is problem posing important in school mathematics? (b) Are teachers and students capable of posing important mathematical problems? (c) Can students and teachers be effectively trained to pose high-quality problems? (d) What do we know about the cognitive processes of problem posing? (e) How are problem-posing skills related to problem-solving skills? (f) Is it feasible to use problem posing as a measure of creativity and mathematical learning outcomes? (g) How are problem-posing activities included in mathematics curricula? (h) What does a classroom look like when students engage in problem-posing activities? (i) How can technology be used in problem-posing activities? (j) What do we know about the impact of engaging in problem-posing activities on student outcomes?

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Section: What Does a Classroom Look Like When Students Engage In Probmentioning

confidence: 99%

Problem-Posing Research in Mathematics Education: Some Answered and Unanswered Questions

Cai

Hwang

Jiang³

et al. 2015

Mathematical Problem Posing

142

View full text Add to dashboard Cite

show abstract

“…Much work has been done to understand how different factors influence the effectiveness of collaborative learning. These factors include students’ participation and social behavior when they learn together (e.g., Abdu et al, 2019 ; Barron, 2003 ; Dillenbourg, 1999 ; Kontorovich et al, 2012 ; Webb et al, 2014 ), effects of teacher support (Dekker & Elshout-Mohr, 2004 ; van Leeuwen & Janssen, 2019 ; Webb, 2009 ), and, specifically for the current article, the effects of different group formations on the effectiveness of learning (e.g., Lou et al, 1996 ; Pearlstein, 2021 ). Educators can use learning analytics systems to support collaborative learning (Wise & Schwarz, 2017 ): For example, by presenting data about the indicators of collaborative learning situations (D’Angelo et al, 2015 ; Schwarz et al, 2018 ; Wise & Schwarz, 2017 ), supporting teachers’ decision-making in regard to collaborative learning (Martinez-Maldonado, 2019 ; van Leeuwen, 2015 ), supporting co-reflection on the collaborative learning process (Schwarz et al, 2015 ) and, specifically to this current article, group formation (see Borges et al, 2018 ; Maqtary et al, 2019 ).…”

Section: Theoretical Backgroundmentioning

confidence: 99%

Pedagogical Considerations for Designing Automated Grouping Systems: the Case of the Parabola

Abdu

Olsher

Yerushalmy

2021

Digit Exp Math Educ

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This article queries how learning analytics systems can support content-specific group formation to develop students’ thinking about a specific mathematical concept. Automated group formation requires identifying personal characteristics, designing tasks to probe students’ perceptions, and grouping them to increase individual learning chances. Designers of automated group formation recommendation modules (GFRMs) rarely consider content-specific objectives. We draw on theories on conceptual learning in mathematics and dialogic thinking to emphasize the role of a dialogic gap between students’ voices to enhance individual learning. In an experiment, fifty 8th and 9th grade students solved three mathematical tasks in a pre-intervention-post-set-up: individually, then in dyads, and then individually again. We used a learning analytics system to collect fine-grained content-specific data on students’ responses based on four pre-defined aspects of the parabola concept. We compared students’ answers with those of their peers in order to identify interpersonal relations. The experiment results indicate that students’ thinking about the parabola concept was the most successfully developed when every group member had a different perception of this concept. We illustrate the learning trajectories of four students and elaborate on the learning sequence of one of these students in particular. This article suggests that the centrality of a dialogic gap in developing personal learning is probably content independent. We thus call for software engineers to think about GFRMs that can support content-specific learning and instruction.

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“…Furthermore, they will think that only the numerators are used and denominators stay the same in the addition of fractions (Siegler & Pyke, 2013). At this point, problem posing activities may help teachers gain insight into their students' understanding and misconceptions of the addition of fractions (Kontorovich, Koichu, Leikin, & Berman, 2012). To be able to determine what the students know and what kind of errors made in their posed problems, teachers need to pose correct problems themselves.…”

Section: Fractionsmentioning

confidence: 99%

The Analysis of the Problems Posed by Pre-service Elementary Teachers for the Addition of Fractions

Coşkun¹

2019

INT J INSTRUCTION

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The purpose of this study is to analyze pre-service elementary teachers' problems in terms of the different meanings of the addition of fractions and to determine the types of errors made in these problems. Data were collected from 83 pre-service elementary teachers in the spring semester of the 2016-2017 academic year by means of a problem posing test related to the addition of fractions. The problem posing test consisted of four questions asking pre-service elementary teachers to pose a problem corresponding to fractions given in a symbolic form. After the problems posed by pre-service elementary teachers were categorized as a problem, not-a-problem, or unable to pose a problem via content analysis method, the meanings, part-part-whole and joining, incorporated into these problems were analyzed. Finally, the types of errors made in these problems were classified. The analysis of the posed problems indicated that although most of the pre-service elementary teachers were able to pose problems, less than one-fourth of these problems were appropriate for the given symbolic form of the addition of fractions. The subsequent meaning analysis of the problems revealed that pre-service elementary teachers were more successful in posing part-part-whole problems than in posing join problems. In terms of error types, the majority of pre-service elementary teachers made the error of failure in establishing part-whole relationship.

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An exploratory framework for handling the complexity of mathematical problem posing in small groups

Cited by 73 publications

References 19 publications

Problem-Posing Research in Mathematics Education: Some Answered and Unanswered Questions

Problem-Posing Research in Mathematics Education: Some Answered and Unanswered Questions

Pedagogical Considerations for Designing Automated Grouping Systems: the Case of the Parabola

The Analysis of the Problems Posed by Pre-service Elementary Teachers for the Addition of Fractions

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