A problem-solving conceptual framework and its implications in designing problem-posing tasks

Singer, Florence Mihaela; Voica, Cristian

doi:10.1007/s10649-012-9422-x

Cited by 90 publications

(60 citation statements)

References 13 publications

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“…Therefore, we prepared the problem-posing task as a multiple-choice test. We preferred to use distracters in options, as did Singer and Voica (2012). Hence, we did not establish any evaluation criterion; we only assessed the correctness of problems posed by students.…”

Section: Discussionmentioning

confidence: 99%

Investigation of Problem-Solving and Problem-Posing Abilities of Seventh-Grade Students

2015

EDUC SCI-THEOR PRACT

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This study aims to examine the effect of multiple problem-solving skills on the problem-posing abilities of gifted and non-gifted students and to assess whether the possession of such skills can predict giftedness or affect problem-posing abilities. Participants' metaphorical images of problem posing were also explored. Participants were 20 gifted and 85 non-gifted seventh graders, and quantitative and qualitative research methods were used for data collection and analysis. The relationship between multiple problem-solving skills and giftedness was investigated, and a strong corre lation between problem solving in multiple ways and problem-posing abilities was observed in both the gifted and non-gifted students. Moreover, problem solving in multiple ways was observed in both the gifted and non-gifted students. Metaphorical images were based on the participants' experiences with problem posing, and they associated their positive or negative metaphors depending on their problem-posing performance. u c a t i o n a l S c i e n c e s : T h e o r y & P r a c t i c e 1404Problem solving and problem posing are accepted essential components of mathematics education worldwide. Many studies related to the two concepts have been conducted (Brown & Walter, 1999;Cankoy & Darbaz, 2010;Dede & Yaman, 2005a, 2005bLeung, 1996;Silver & Cai, 1996;Schoenfeld, 1992), and research in this area continues to expand rapidly because of its importance to world governments. While problem solving is defined as the heart of mathematics education (Cockcraft, 1982;Dede & Yaman, 2005a, 2005b, problem posing can be identified as one of the coronary vessels. The National Council of Teachers of Mathematics (NCTM) (1980) emphasized that students should solve mathematics problems in different ways and generate their own problems in given situations.If a problem is considered as difficult (Kilpatrick, 1987), problem solving refers to overcoming the difficulty. Problem solving is accepted as a central activity in education programs in many countries such as Australia, Japan, Korea, Singapore, and China, which were top performers in PISA 2012 (OECD, 2013). Most commonly known problem-solving steps were introduced by Polya (1957), who cited four steps to solve a mathematical problem: understanding the problem (can you state the problem in your own words?); devising a plan (look for a pattern or equation or examine related problems); executing the plan (implementing a strategy and checking operations and links); and looking back (checking the results). Many researchers (e.g., Abu-Elwan, 2002) include problem posing or creating a new problem after final steps. Furthermore, problem posing is incorporated as a feature of mathematics teaching in many countries (e.g., Japan) that employ it as a means of analyzing problems and enhancing students' problem-solving competence (Silver, 1994).Problem posing in education was introduced by Freire (1970) for the first time as an alternative to banking education. Problem posing entails the generation of a new...

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Section: Discussionmentioning

confidence: 99%

Investigation of Problem-Solving and Problem-Posing Abilities of Seventh-Grade Students

2015

EDUC SCI-THEOR PRACT

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“…Barton (2003) studied how Pascal's Triangle can provide another opportunity to connect young children to deeper mathematical truth; the numeric form of Pascal's Triangle is filled with hidden relationships and connections to deeper mathematics concepts. Singer and Voica (2013) applied fractals in their study to develop a reference framework for designing problem-posing tasks. On the college level, Ding and Li (2009) studied the dimension of Sierpiński pedal triangle, which could be used by college students for practicing calculus knowledge.…”

Section: Research On Fractal Teaching Practicementioning

confidence: 99%

Assessing United States and Chinese Secondary Mathematics Teachers’ Interest in Fractal Geometry

2018

JME

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“…Generally, when problems are presented in multiple formats, students are better able to acquire deeper understandings (Cai et al, 2013;Singer and Voica, 2012). When students can revise the problem itself, or design an analogous one, their understanding of the subtleties of the problem increases (Priest, 2009).…”

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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A problem-solving conceptual framework and its implications in designing problem-posing tasks

Cited by 90 publications

References 13 publications

Investigation of Problem-Solving and Problem-Posing Abilities of Seventh-Grade Students

Investigation of Problem-Solving and Problem-Posing Abilities of Seventh-Grade Students

Assessing United States and Chinese Secondary Mathematics Teachers’ Interest in Fractal Geometry

Portrait of a Second-Grade Problem Poser

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