An investigation of relationships between students’ mathematical problem-posing abilities and their mathematical content knowledge

Harpen, Xianwei Y. Van; Presmeg, Norma

doi:10.1007/s10649-012-9456-0

Cited by 84 publications

(61 citation statements)

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“…Van-Harpen and Presmeg (2013) found a relationship between students' mathematical knowledge and their problem-posing abilities. Posing problems benefits students, pre-service teachers, and teachers in multiple ways.…”

Section: Benefits Of Problem Posingmentioning

confidence: 90%

A New Problem-Posing Approach Based on Problem-Solving Strategy: Analyzing Pre-service Primary School Teachers’ Performance

2017

EDUC SCI-THEOR PRACT

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Citation: Kılıç, Ç. (2017). A new problem-posing approach based on problem-solving strategy: Analyzing pre-service primary school teachers' performance. AbstractThis study examined pre-service primary school teachers' performance in posing problems that require knowledge of problem-solving strategies. Quantitative and qualitative methods were combined. The 120 participants were asked to pose a problem that could be solved by using the find-a-pattern a particular problem-solving strategy. After that, task-based interviews were conducted with 5 of the 120 participants who had answered in different ways. The data obtained were analyzed using semantic, descriptive, and content analysis methods. It was determined that 55% of the participants could pose a word problem that can

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Section: Benefits Of Problem Posingmentioning

confidence: 90%

A New Problem-Posing Approach Based on Problem-Solving Strategy: Analyzing Pre-service Primary School Teachers’ Performance

2017

EDUC SCI-THEOR PRACT

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“…We found 11 studies of problem posing, 9 of which were included in a special issue of Educational Studies in Mathematics, a leading mathematics education journal. In that issue, problem posing was defined as a process in which students used their experiences to "construct personal interpretations of concrete situations and from these situations formulate meaningful (i.e., non-trivial) mathematical problems" [62] (p. 119). All of the problem posing articles in our sample that could be coded for methodology (n = 7) were coded as qualitative.…”

Section: Word Problems and Problem Posingmentioning

confidence: 99%

Conceptualizations of Students With and Without Disabilities in Educational Research in Mathematics; A Critical Review

Lambert¹,

Tan²

2017

Preprint

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Students with disabilities are often framed as "the problem" and have limited opportunities to engage in standards based mathematics leading to persistent underachievement. In this paper, we investigate a research divide between mathematics educational research for students with and without disabilities, a divide with significant differences in the theoretical orientations and research methodologies used to understand learners. Based on an analysis of 149 mathematics educational research articles published between 2013 and 2015, we found significant differences between articles focused on learners with and without disabilities. For those with disabilities, mathematical problem solving was understood primarily from behavioral and information processing theoretical perspectives, while for those without disabilities, problem solving was understood primarily through constructivist and sociocultural perspectives. While 86% of research on problem-solving including students with disabilities was quantitative, only 35% of research on students without disabilities was quantitative. 50% of problem-solving research on students without disabilities was qualitative, compared to only 6% of research on students with disabilities. Problem solving, then, is studied in very different ways for learners with and without disabilities. Students without disabilities are studied through close analysis of learning, often individual. Students with disabilities are most often studied quantitatively, in groups, with no analysis of individual thinking. By offering only a limited range of methods and theoretical orientations, this research divide reifies deficit constructions of students with disabilities.

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“…Many researchers argue that problem posing activities make a contribution to students' problem solving skills and mathematical thinking (Silver, 1994;Stoyanova, 2003), which makes it essential for problem posing to have a larger role in classroom learning activities (Akay, 2006;Van Harpen & Presmeg, 2013;Knott, 2010). Although problem posing is becoming more and more important, there are not many studies that specifically focus on the quality of problems posed by students and the ways of reasoning they use when posing problems.…”

Section: Introductionmentioning

confidence: 99%

Generalizability Theory Research On Developing a Scoring Rubric to Assess Primary School Students' Problem Posing Skills

Cankoy¹,

Özder²

2017

EURASIA J MATH SCI T

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The aim of this study is to develop a scoring rubric to assess primary school students' problem posing skills. The rubric including five dimensions namely solvability, reasonability, mathematical structure, context and language was used. The raters scored the students' problem posing skills both with and without the scoring rubric to test the reliability of the rubric. The study used generalizability theory to test the reliability of the scores obtained with and without the use of the rubric. More reliable scoring was obtained using the scoring rubric. The G and phi coefficients rose somewhat after increasing the number of items and raters in both scoring methods. However, increasing the number of items affected these coefficients slightly more than increasing the number of the raters.

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An investigation of relationships between students’ mathematical problem-posing abilities and their mathematical content knowledge

Cited by 84 publications

References 10 publications

A New Problem-Posing Approach Based on Problem-Solving Strategy: Analyzing Pre-service Primary School Teachers’ Performance

A New Problem-Posing Approach Based on Problem-Solving Strategy: Analyzing Pre-service Primary School Teachers’ Performance

Conceptualizations of Students With and Without Disabilities in Educational Research in Mathematics; A Critical Review

Generalizability Theory Research On Developing a Scoring Rubric to Assess Primary School Students' Problem Posing Skills

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