The relation between the problem posing and problem solving skills of prospective elementary mathematics teachers

Kar, Tuğrul; Özdemir, Ercan; İpek, Ali Sabri; Albayrak, Mustafa

doi:10.1016/j.sbspro.2010.03.239

Cited by 44 publications

(35 citation statements)

References 8 publications

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“…During the intervention focused on problem posing, Paula displayed marginal improvements in her problemsolving skills as was substantiated by prior researchers (Cai et al, 2013;Kar et al, 2010). More importantly, Paula's problem-posing responses were helpful in informally assessing her thought processes, understandings, and performance.…”

Section: Discussionmentioning

confidence: 61%

“…Problem posing shifts the emphasis from attempting to uncover appropriate methods and derive correct answers in problem solving, to imaginatively posing a problem and then discovering the appropriate solution from a wide range of possibilities (Brown and Walter, 2005). An improvement in problem-solving skills is often observed as an outcome of engaging in problem-posing activities (Kar et al, 2010). Problem posing and solving can be two sides of the same coin -both pedagogies helping students develop mathematical understanding.…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Discussionmentioning

confidence: 61%

Section: Introductionmentioning

confidence: 99%

Portrait of a Second-Grade Problem Poser

Kopparla

Capraro

2018

European Journal of STEM Education

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“…Look back (Senemo lu, 2011). Kar et al (2010) found that there is a significant relation between problem posing and problem solving skills of prospective elementary mathematics teachers. With respect to problem solving, it was seen that prospective teachers posing two or more problems had higher level compared to those that pose two or less problems.…”

Section: Introductionmentioning

confidence: 95%

Problem Solving and Problem Posing Skills of Prospective Mathematics Teachers About the ‘Sets’ Subject

Şengül

Katrancı

2012

Procedia - Social and Behavioral Sciences

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Problem is a topic, event or activity, which no memorized or specified rules are known regarding its solution. Problem posing is a crucial component for mathematics discipline and problem solving is the situation of elimination of confusion in human mind. In this sense, the problem sentence of the study was determined as; 'What are Problem Solving and Posing Behaviours of Prospective Primary Mathematics Teachers about the 'Sets' Subject and Their Experiences and Difficulties Encountered During this Process?'. The purpose of this study is to analyze problem solving and posing behaviours of prospective primary mathematics teachers about the sets subject and to determine the experiences and difficulties that can be seen during these processes. The study was carried out with 56 sophomore students who study at Kocaeli University, Department of Teaching Primary Mathematics. The data was obtained using a data collection form which was prepared by the researchers. The data were analyzed and interpreted in three steps using the content analysis method including i) free problem posing and solving, ii) the experiences that can be seen during problem solving and posing processes, iii) solution recommendations relating to the difficulties (if any) that can be experienced during problem posing and solving processes. It was determined that 53 students could pose problems about the Sets subject suitable to Primary Second Grade level and also they were able to solve these problems. It was seen that 41 students had difficulties in adjusting the degree of difficulty of the problem, not being able to have the full subject knowledge and matching the primary school level during problem posing process. And it was determined that 12 students expressed that they did not experience any difficulties and did not make any solution recommendations. Based on the findings, it was concluded that students could display free problem posing skills but they could not solve the problems according to problem solving steps. This situation can be explained with the fact that the students have not studied problem posing and solving before. It was determined that students had difficulties in matching the primary school level and in adjusting the degree of difficulty of the problem and they believed that they could overcome these difficulties by gaining experience in time. This situation can explained with the fact that since students are sophomore, they do not perceive themselves as real teachers.

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“…Other studies underline the need to incorporate problem-posing activities into mathematics classrooms to determine prospective teachers' problem-posing skills appropriate to selecting, translating, comprehending, and editing models and the possible difficulties they could encounter during the process in fraction problems (Işık et al 2011), to explore students' creativity in mathematics by analyzing their problem-posing abilities in geometric scenarios (Van Harpen and Sriraman 2013) and to examine the knowledge influences of learners' abilities in posing combinatorial problems (Melušová and Šunderlík 2014). Furthermore, some studies provide evidence that problem posing has a positive influence on students' abilities in problem solving (e.g., Kar et al 2010;Şengül and Katranci 2012). Kar et al (2010) asserted that the positive relation between posing and solving problems is an indicator of the acceptance of problem-posing skills as a phase in the development of problem-solving skills.…”

Section: Related Workmentioning

confidence: 99%

“…Furthermore, some studies provide evidence that problem posing has a positive influence on students' abilities in problem solving (e.g., Kar et al 2010;Şengül and Katranci 2012). Kar et al (2010) asserted that the positive relation between posing and solving problems is an indicator of the acceptance of problem-posing skills as a phase in the development of problem-solving skills. In the analysis of the posed problems, the participants map the level of their own notions and concepts, understanding, and various interpretations and realize possible misconceptions and erroneous reasoning (Tichá and Hošpesová 2009).…”

Section: Related Workmentioning

confidence: 99%

Model-based analysis of thinking in problem posing as sentence integration focused on violation of the constraints

Supianto

Hayashi

Hirashima

2017

RPTEL

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The advancement of computer and communication technologies has enabled researchers to conduct and analyze the learning process of posing problems. This study investigates what learners think while posing problems as sentence integration in terms of intermediate products as well as the posed problems as the resultant product. Problem posing as sentence integration defines the arithmetic word problem structure, and posing a problem is a task to satisfy all the constraints and requirements to build a valid structure. A previous study shows that, in problem posing as sentence integration for arithmetic word problems, learners try to satisfy a relatively large number of constraints in the posed problems. In contrast, this study focuses on the violation of constraints in the intermediate products while posing problems. The result shows that learners were inclined to avoid as many violated constraints as possible throughout the problem-posing process. Although learners tend to avoid the violated constraints, naturally, they cannot avoid some mistakes. Further analysis shows that learners actually have difficulty in fulfilling particular constraints while posing the problems. Based on this analysis, it is possible to detect the difficulty of learners' actions from the model perspective. Hence, it is possible to give accurate feedback and appropriately support the learners.

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The relation between the problem posing and problem solving skills of prospective elementary mathematics teachers

Cited by 44 publications

References 8 publications

Portrait of a Second-Grade Problem Poser

Portrait of a Second-Grade Problem Poser

Problem Solving and Problem Posing Skills of Prospective Mathematics Teachers About the ‘Sets’ Subject

Model-based analysis of thinking in problem posing as sentence integration focused on violation of the constraints

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