Mathematical Problem Posing

Singer, Florence Mihaela; Ellerton, Nerida F.; Cai, Jinfa

doi:10.1007/978-1-4614-6258-3

Cited by 62 publications

(11 citation statements)

References 129 publications

(227 reference statements)

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“…Our illustrative example shows in detail what kinds of information such a task can provide, and how can it inform us about respondent's reasoning and pedagogical content knowledge. The results again confirmed the importance of problem posing in future teachers' education (Hošpesová and Tichá, 2015). We are aware that the weak point of our study consists in size of the sample, and that the results cannot be generalized.…”

Section: Discussionsupporting

confidence: 73%

“…(Littler and Tylor-Basil, 1999: 76) The inability to identify the whole often causes misconceptions also during problem posing; typical examples of such misconceptions were presented e.g. by Hošpesová and Tichá (2015) who asked in-service and pre-service teachers to pose several word problems including fractions 1/2 and 3/4, and, among others, received the following responses:…”

Section: Fractions In the Primary School Classroommentioning

confidence: 99%

“…Another instrument used in this study is problem posing. We have been using it in future teachers' education for more than 10 years, as an educational, motivational and diagnostic tool (Tichá and Hošpesová, 2013;Hošpesová and Tichá, 2015), and we are convinced that it can lead future teachers to deeper understanding of mathematical topics as well as to enhancement of their pedagogical content knowledge. Recently, we have often combined Concept Cartoons and problem posing together, to get another perspective on future teachers' reasoning and pedagogical content knowledge: by combining the two instruments we already observed future teachers' open approach to mathematics (Samková and Tichá, 2016c), and reasoning during pattern generalization (Samková and Tichá, 2017a).…”

Section: Diagnostic Instrumentmentioning

confidence: 99%

“…For the purpose of the research on the second research question we shall ask future primary school teachers to pose tasks in the form of Concept Cartoons, and observe how they reason when posing the task. The topic of fractions belongs to the most difficult ones, both in primary and secondary school context; many empirical researchers point out that (future) teachers tend to have only limited knowledge about this topic (Cramer and Lesh, 1988;Ma, 1999;Tirosh, 2000;Depaepe et al, 2015;Singer, Ellerton and Cai, 2015). The limitations refer to content knowledge as well as pedagogical content knowledge, so that our contribution addresses both these aspects.…”

Section: Introductionmentioning

confidence: 99%

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On the Way to Observe How Future Primary School Teachers Reason About Fractions

Samková

Tichá

2017

ERIES Journal

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In our contribution we focus on the possibility to use an educational tool called Concept Cartoons in future primary school teachers' education, as an instrument for observing how future primary school teachers reason about fractions. In the introduction section we present Concept Cartoons, and also the primary school level of the fractions topic. In the first part of the research we analyse data obtained when future primary school teachers were solving a problem in the Concept Cartoon form. The task which we adapted to this form belongs to primary school mathematics, it focuses on the concept of a fraction per se (on the parts-and-whole decision and on comparison of two pre-partitioned models with diverse wholes). Using Concept Cartoons, we can observe which statements about the issue our respondents consider as correct, and which kinds of reasoning they use in their justifications. In the second part of the research we analyse problems that the respondents themselves posed in the Concept Cartoon form, with particular focus on tasks devoted to fractions.

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Section: Discussionsupporting

confidence: 73%

Section: Fractions In the Primary School Classroommentioning

confidence: 99%

Section: Diagnostic Instrumentmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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On the Way to Observe How Future Primary School Teachers Reason About Fractions

Samková

Tichá

2017

ERIES Journal

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“…This support for incorporating problem posing in classrooms is centered on the documented constructive consequences of developing these skills. Findings from prior research have indicated that as students' problem-posing skills evolve, positive outcomes can be noticed in their creativity, understanding, problem solving, and critical thinking (Singer et al, 2015;Van Harpen and Presmeg, 2013). Moreover, problem posing can assist teachers in identifying mathematical misunderstandings (Koichu et al, 2013).…”

Section: Introductionmentioning

confidence: 99%

Portrait of a Second-Grade Problem Poser

Kopparla

Capraro

2018

European Journal of STEM Education

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Although some students might struggle with problem posing, the positive effects on student learning and abilities may be far reaching for those who engage in this activity. Problem posing requires students to create their own problems rather than to solve problems posed by others. Problem posing is not regularly taught; however, reform proponent groups recognize problem posing as a strategy that should be integrated more routinely into mathematics classrooms. A single case study was conducted in conjunction with a larger quasiexperimental study in which mathematics education researchers worked with groups of 2 nd -5 th grade students twice a week over the course of a semester. For the single case study, two of the researchers randomly selected one second-grade student and examined the student's progress as she engaged in problem-posing activities during the semester. Based on the student's work, some possible elements of the lesson that impacted her engagement and performance were identified. Results from this case study indicate that problem posing for this student was an effective tool with which to evaluate misconceptions and to explore her informal mathematics understanding.

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Improving mathematical learning in Scotland's Curriculum for Excellence through problem posing: an integrative review

McDonald

Smith

2019

The Curriculum Journal

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The purpose of this paper is to explore the importance of problem posing in learning mathematics at the compulsory education level. Despite acknowledging that children have a natural disposition to pose questions, no curricular provision currently exists for the conceptualisation and operationalisation of mathematical problem posing within Scotland's Curriculum for Excellence. In order to provide evidence to support any curricular change, integrative systematic review and narrative synthesis of quantitative and qualitative studies was conducted. Results suggest that problem posing can offer an array of valuable didactic benefits for pupils such as deeper conceptual knowledge, enhanced problem-solving skills and an increase in the enjoyment of mathematics. Evidence from the qualitative synthesis provides some tentative guidance on considerations regarding the integration of problem posing to the curriculum. This study argues that in order to improve future learning experiences, mathematical problem posing should be embedded in all Scottish classrooms. Furthermore, problem posing is determined to be effective in the pedagogical development of prospective primary and secondary mathematics practitioners.

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Mathematical Problem Posing

Cited by 62 publications

References 129 publications

On the Way to Observe How Future Primary School Teachers Reason About Fractions

On the Way to Observe How Future Primary School Teachers Reason About Fractions

Portrait of a Second-Grade Problem Poser

Improving mathematical learning in Scotland's Curriculum for Excellence through problem posing: an integrative review

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