The Importance Of Problem Posing

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In everyday life, people naturally pose problems. Even a three year-old child may pose problems such as “Why is the earth round?”, “Why 1 and 1 equals 2?” The process of posing questions encourages us to think, to explore, to make connections between what we learned and new knowledge and to understand the world better (Xie, 2016). In our dynamic contemporary society, we often have to adapt to many unpredictable situations such as changing jobs and changing homes. Knowing how to identify and formulate mathematical problems can help us develop thought processes and skills applicable to the decision-making processes in such situations. In the school setting, students learn to focus on the outcomes of their problem solving efforts and have little …show more content…

Even though some problem posing studies were published between 1960 and 1970, problem posing only started receiving attention after the National Council of Teachers of Mathematics’ curriculum and Evaluation Standard for School Mathematics for the time in 1989 documented the importance of integrating problem posing into mathematics instruction. It explicitly states that students should have some experience recognizing and formulating their own problems (NCTM, 1989). Later on, the professional standards for teaching mathematics (NCTM, 1991) emphasized the importance of providing opportunities for students to pose their own problem. The NCTM (1999, 2001) highlighted problem posing as part of the reform effort of math education and emphasized the importance of problem posing as a means of classroom intervention to promote mathematics as a worthy intellectual activity. The CCSSM stated that “mathematically proficient students at various grade levels are able to identify relevant external mathematical resources, such as digital content located on a website, and use them to pose or solve problems” (NGACBP & CCSSO, 2010, p.7). Polya (1945) pointed out that if a student never solves a problem invented by himself, this student’s mathematical experience is …show more content…

In free situations, the problem is not given. Students are asked to pose problems on a natural situation without any restriction. Directions may be “John received 20 gifts last Christmas. Use the information and make up as many problems as you can.” Semi-structured problem posing situations refer to ones in which students are provided with open situation and are asked to explore the problem structure, and then complete the problems by applying knowledge, skills, concepts and relationships from their previous mathematical experiences. For example, students are required to pose word problem based on the given equation (e.g. 2 +6 = 8). Examples of semi-structured problem posing can also include posing problems based on diagrams and pictures. Structured problem posing situations refer to situations where students pose problems by reformulating already solved problems or by varying the conditions or questions of given problems. For example, a word problem “David received 6 boxes of candies from his friend. Each box has 10 candies. How many candies did David receive from his friends? Explain how did you find your answer? Findings from previous research on mathematical problem posing appear to suggest that individuals are more successful posing mathematical problems under structured posing situations than under free posing situations

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