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

Abstract

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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