Date

2019-04-28

Author

Alkan, Cafer Sinan
Akyüz, Didem

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Purpose For many people mathematics is one of the subjects that they have difficulty with. Yet, mathematics underlines many subjects in the real world. Thus, there have been many studies that investigate the ways of supporting students' understanding of mathematical learning such as using different models, real-life contexts, and problem-solving process. Today, many school programs focus on students’ problem-solving skills. Many countries renewed instructional programs in the way of encouraging problem-solving method. Similarly, problem solving becomes a more efficient element in school programs in Turkey. In other words, studying on problem solving processes and strategies also get essential in mathematics educations. The purpose of this study is to investigate the fifth and sixth grade middle school students’ use of strategies in the problem-solving process related to sets, whole numbers, fractions and decimal numbers and to evaluate their approaches and level of understanding during these non-routine problems. Method 29 fifth grade and 29 sixth grade students from a public school participated in the study. Students solved six non-routine mathematics problems related to problem-solving strategies such as guess and check, making a drawing, working backward, arithmetic strategy, algebraic strategy and organizing data. The students were given sufficient time for the problems and they worked on them individually. All problems included five sub-questions in order to understand their thinking process such as "what is given and asked in the problem?". The answers of these questions were analyzed in detail in order to understand their reasoning. Content analysis was used to categorize students' answers. During the analysis each student's answers were coded and then similar answers are regrouped. Results and Discussions During the instruction, students were able to develop and use different strategies for nonroutine problems. Fifth grade students were able to put at least two different strategies for each problem. They even used four different strategies in one of the problems. Sixth grade students were also able to put at least two different strategies for each problem. These results revealed that students have flexible thinking. Both fifth and sixth graders could comprehend the strategies and use them in similar problems. Furthermore, at least 76 % (22 students) of both fifth and sixth grade students were able to re-write the problem with their own words and explain the given as well as asked information in the problem. However, most of them had difficulties in organizing and relating the given information to reach the correct solution. They 711 also had problems in implementing their plans appropriately. The results indicated, even though students can rewrite the problems or find solution strategies; they often failed to find the correct answer. One of the reasons was students’ difficulties in planning to find the solution. Additionally, they had difficulties to apply the plan in correct order. Thus, it might be important to give students opportunities where they can practice non-routine problems and planning. During the solution of these problems, teachers need to not only focus on the answers but also the process of the students' solution strategies. Moreover, teachers need to ask students their plan to reach the correct answer and also check whether they can apply the plan they wrote. As students have more opportunities to solve these problems, they will develop more flexible mathematical thinking and reasoning

Subject Keywords

Problem-solving, Numbers, Fifth and sixth grade students

URI

https://hdl.handle.net/11511/77237
http://www.egitim.hacettepe.edu.tr/bildiri.html

Collections

Department of Mathematics and Science Education, Conference / Seminar