Dissecting success stories on mathematical problem posing: a case of the Billiard Task

Koichu, Boris; Kontorovich, Igor’

doi:10.1007/s10649-012-9431-9

Cited by 58 publications

(27 citation statements)

References 21 publications

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“…Crespo and Sinclair ( 2008 ) suggested that without the opportunity to explore the limits of the mathematical situation in which students are working, the students are limited in the types of problems they can pose. Similarly, Koichu and Kontorovich ( 2013 ) found that the successful prospective teachers in their study posed the most interesting problems when blending exploration and problem solving with their problem posing. It would appear that students are able to improve the breadth and level of challenge of the problems they pose when they have experience solving such problems, and are prompted by informal contexts such as pictures, which may leave more room for exploration, instead of formal symbolic contexts (Crespo, 2003 ;English, 1998 ).…”

Section: Can Students and Teachers Be Effectively Trainedmentioning

confidence: 91%

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

Cai

Hwang

Jiang³

et al. 2015

Mathematical Problem Posing

143

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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: Can Students and Teachers Be Effectively Trainedmentioning

confidence: 91%

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

Cai

Hwang

Jiang³

et al. 2015

Mathematical Problem Posing

143

View full text Add to dashboard Cite

show abstract

“…suggested that without the opportunity to explore the limits of the mathematical situation in which students are working, the students are limited in the types of problems they can pose. Similarly, Koichu and Kontorovich ( 2013 ) found that the successful prospective teachers in their study posed the most interesting problems when blending exploration and problem solving with their problem posing. It would appear that students are able to improve the breadth and level of challenge of the problems they pose when they have experience solving such problems, and are prompted by informal contexts such as pictures, which may leave more room for exploration, instead of formal symbolic contexts .…”

Section: Can Students and Teachers Be Effectively Trained To Pose Higmentioning

confidence: 91%

“…considered situations in which students pose problems and defi ned problem posing 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" (p. 518). The subjective nature of this defi nition-one should decide in which meaning the problem is meaningful and for whom-is apparent (see Koichu & Kontorovich, 2013 , for an elaborated discussion about this issue). referred to problem posing either as generating new problems and questions for exploring a given situation or reformulating a given problem during the process of solving it.…”

Section: Theoretical Backgroundmentioning

confidence: 99%

Mathematical Problem Posing

Singer¹,

Ellerton²,

Cai³

2015

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“…However, research suggests that the ability to pose suitable tasks is correlated with problem-solving competence in practitioners (e.g. Crespo, 2003;Koichu & Kontorovich, 2013). Moreover, workload pressures inhibit teachers from producing resources.…”

Section: The Role Of Problem Posing In Mathematicsmentioning

confidence: 99%

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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Dissecting success stories on mathematical problem posing: a case of the Billiard Task

Cited by 58 publications

References 21 publications

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

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

Mathematical Problem Posing

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

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