Generalized and generative thinking in US and Chinese students’ mathematical problem solving and problem posing

Cai, Jinfa; Hwang, Stephen

doi:10.1016/s0732-3123(02)00142-6

Cited by 235 publications

(197 citation statements)

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“…So, one important line of research in problem posing has been to explore what problems teachers and students are able to pose (Cai, 1998;Cai & Hwang, 2002;English, 1997aEnglish, , 1997bSilver & Cai, 1996;Silver, Mamona-Downs, Leung, & Kenney, 1996;Stoyanova & Ellerton, 1996). In this line of inquiry, researchers usually design a problem situation and ask subjects to pose problems that can be solved using the information given in the situation.…”

Section: Students' Problem Posing and Problem Solvingmentioning

confidence: 99%

“…A second important direction for investigation has been probing the links between problem posing and problem solving (e.g., Cai, 1998;Cai & Hwang, 2002;Ellerton, 1986;Kilpatrick, 1987;Silver & Cai, 1996). Kilpatrick (1987) provided a theoretical argument that the quality of the problems subjects pose might serve as an index of how well they can solve problems.…”

Section: Students' Problem Posing and Problem Solvingmentioning

confidence: 99%

“…For example, Cai and his associates (Cai, 1998;Cai & Hwang, 2002) used problem-posing and problem-solving tasks that were closely related to one another in order to examine Chinese and US students' solving and posing performances. Cai and Hwang (2002) found differential relationships between posing and solving for US and Chinese students. That is, there was a stronger link between problem solving and problem posing for the Chinese sample, whereas the link was much weaker for the US sample.…”

Section: Students' Problem Posing and Problem Solvingmentioning

confidence: 99%

“…Thus, the ability to pose complex problems should allow for more robust problemsolving abilities (e.g., Cai & Hwang, 2002). Encouraging students to generate problems is therefore not only likely to foster student understanding of problem situations, but also to nurture the development of more advanced problem-solving strategies.…”

Section: Problem Posing In the Curriculummentioning

confidence: 99%

“…In contrast, problem-posing research is relatively new (Cai & Hwang, 2002;Kilpatrick, 1987;Silver, 1994;Silver & Cai 1996). Nevertheless, there have been efforts around the world to incorporate problem posing into school mathematics at different educational levels (e.g., Brink, 1987;Chinese National Ministry of Education, 1986;Hashimoto, 1987;Healy, 1993;Keil, 1964Keil, /1967).…”

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Mathematical problem posing as a measure of curricular effect on students' learning

et al. 2012

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In this study, we used problem posing as a measure of the effect of middle-school curriculum on students' learning in high school. Students using a Standards-based curriculum in middle school performed equally well or better than students who used more traditional curricula in high school. The findings from this study not only show evidence of strengths one might expect of students who used the Standards-based reform curriculum, but also bolster the feasibility and validity of problem posing as a measure of curriculum effect on student learning. In addition, the findings of this study demonstrate the usefulness of employing a qualitative rubric to assess different characteristics of students' responses to the posing tasks. Instructional and methodological implications of this study, as well as future directions for research are discussed.

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Section: Students' Problem Posing and Problem Solvingmentioning

confidence: 99%

Section: Students' Problem Posing and Problem Solvingmentioning

confidence: 99%

Section: Students' Problem Posing and Problem Solvingmentioning

confidence: 99%

Section: Problem Posing In the Curriculummentioning

confidence: 99%

mentioning

confidence: 99%

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Mathematical problem posing as a measure of curricular effect on students' learning

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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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Improving Chinese junior high school students’ ability to ask critical questions

Huang

Lederman

Cai³

2017

J Res Sci Teach

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The present study explores ways to enhance students’ question‐asking ability (i.e., the ability to ask critical questions), which is the premise of scientific inquiry and a precondition for effective science teaching. A survey of junior high school students in Zhejiang province in China showed that students’ questioning behavior was not well developed and that their ability and willingness to question authority were weak. These results are consistent with an educational culture that dictates that textbooks and science teachers are always correct and cannot be questioned. The intervention involved several designed cases that included the explicit teaching of questioning strategies and ample opportunities to ask questions for inquiry and question card use. After the intervention, a dependent t‐test of several dimensions was conducted, the students’ question‐asking consciousness and question quality were compared, and the frequency distribution of different levels of questions was analyzed and compared. The development of question‐asking ability was further identified in the interviews. The efficacy and implications of the treatment for enhancing the critical question‐asking ability of middle‐school students in Chinese science classrooms are discussed. © 2017 Wiley Periodicals, Inc. J Res Sci Teach 9999:963–987, 2017

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Generalized and generative thinking in US and Chinese students’ mathematical problem solving and problem posing

Cited by 235 publications

References 7 publications

Mathematical problem posing as a measure of curricular effect on students' learning

Mathematical problem posing as a measure of curricular effect on students' learning

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

Improving Chinese junior high school students’ ability to ask critical questions

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