Matematiksel muhakeme; matematiksel tahminleri oluşturma, matematiksel tartışmaları geliştirme ve değerlendirme, matematiksel bilgileri çeşitli şekillerde sunma becerilerini içermektedir (NCTM, 1989). Bunların yanı sıra NCTM (2000), ilköğretim seviyesinde öğrencilerin sahip olması gereken matematiksel muhakeme becerilerini (analiz etme, genelleme yapma, bağlantılar oluşturma, karar verme, rutin olmayan problem çözme) belirlemiştir. Bu çalışmanın amacı ortaokul beşinci sınıf öğrencilerinin yaşamsal bir beceri olan ve matematiğin temel becerilerinden biri olan muhakeme etme becerilerini araştırmaktır. Çalışma 2015-2016 eğitim öğretim yılının birinci döneminde Giresun ilindeki bir ortaokulda okuyan beşinci sınıf öğrencilerinden oluşan toplam 28 öğrenciyle yapılmıştır. Bu çalışma nitel araştırma desenlerinden durum çalışması olarak değerlendirilebilir. Çalışmada Özsoy (2007) tarafından geliştirilen "Problem Çözme Testi"nden seçilen dört test sorusu açık uçlu problem durumu olarak kullanılmıştır. Bu açık uçlu dört soru için oluşturulan altı gruba 1 ders saati uygulama süresi gerçekleştirilmiştir. Uygulama esnasında her bir problem için öğrencilerin çözümlerini, düşüncelerini ve sürece yönelik yanıtlarını açıklamaları istenmiştir. Elde edilen veriler Marzano (2000) tarafından geliştirilen, geçerlilik ve güvenirliği Pilten (2008) tarafından sağlanan "Aşamalı Puanlama Ölçeği" kullanılarak analize tabi tutulmuştur. Her bir problem basamaklarına göre değerlendirilmiş, bu değerlendirme iki araştırmacı tarafından yapılmış ve her basamağın uyuşum yüzdesi hesaplanmıştır. Elde edilen bulgular Marzano (2000)'nun " Çözüm yolu sonucun doğruluğuna karar verme, Rutin olmayan problemler çözme, Çözüme ilişkin mantıklı tartışmalar geliştirme, Genelleme yapma, Uygun muhakemeyi belirleme ve kullanma" gibi muhakeme alt basamaklarında öğrencilerin zorlandıklarını ortaya koymaktadır

Mathematical reasoning consists of creating mathematical estimations, developing and evaluating mathematical arguments. It also includes abilities of presenting mathematical information in various ways (NCTM, 1989). Besides, the mathematical reasoning abilities of the children who belong to the primary education level are stated by NCTM. The aim of this study is to search the reasoning abilities of 5th graders which can be considered as one of the vital skills and the numeracy skills. The research of this study was conducted in a Middle School located in Giresun, within the first semester of 2015-2016 school year. 28 5thgraders were included in this research. This study is a case study from the qualitative research patterns. In this study four multiple-choice questions were elected from Problem Solving Test developed by Özsoy (2007) and they were used as open ended problems. For these four open ended questions each group was given one-hour lesson in order to solve these questions and it is applied by researchers. The students were expected to explane their solutions, thought and their answers related to the process for each of the questions. The acquired information was analyzed with the “4-Point Rating Scale'” developed by Marzano (2000) and provided validity and reliability. Every problem was evaluated by its own step. This evaluation was conducted by two researchers and the percentage of agreement of each step was calculated. The acquired finds show that students have difficulty in reasoning substeps like “ Deciding the accuracy of solution way, Solving nonroutine problems, Developing logical discussion related to the solution, Generalazing, Determining and Adopting the suitable reasoning” Marzano (2000)Reasoning contains many different ways of thinking and is closely related to high level thinking skills. Individuals, who are able to reason, should express their opinions by providing justifications within a rational framework. Reasoning is justifying the opinions, which we consider as correct, also in new situations. Conducting this process in an accurate manner is of great importance for producing mathematical knowledge. According to NCTM (1989), mathematical reasoning consists of skills such as making mathematical assumptions, developing and evaluating mathematical arguments, and presenting mathematical knowledge in various manners. In addition, NCTM (2000) states the mathematical reasoning skills, which elementary school students should possess. According to NCTM (2000) standards, it is emphasized that the reasoning skill levels of the second grade elementary school students should be high enough to make assumptions about generalizations and evaluate the assumptions they encounter. The aim of this study is to examine the fifth grade elementary school students’ reasoning skills, which are a vital skill and one of the fundamental skills of mathematics. The study was conducted with 26 fifth grade students, who were studying at a Secondary School in Dereli district of Giresun province in the first semester of 2015-2016 academic year. These 26 students were divided into 6 groups. 4 groups consisted of 4 students whereas; 2 groups consisted of 5 students. In heterogeneous groups, more enriched ideas can be produced. Therefore the teachers, who had been instructing their mathematics lessons for a year, created the groups by considering the last grades students obtained from their mathematics course in a heterogeneous way. This study can be considered a case study, which is one of the qualitative research patterns and aims at explaining an existing situation. Method In the research, four multiple choice questions from ‘’Problem Solving Test’’ developed by Özsoy (2007), were used as open ended problem case data collection tool. Six groups were granted one course hour for these four open ended questions; the implementation was conducted by the researchers. The students were asked to explain their solutions, opinions, and answers regarding the process throughout the implementation. The retrieved data were analyzed through using ‘’Gradual Scoring Scale’’ of Marzano (2000), validity and reliability of which was assured by Pilten (2008). The data were analyzed according to five sub-dimensions of the scale, which are related to the question, including ‘’determining the accuracy of solution, solving non-routine problems, developing logical arguments about the solution, generalizing, determining and using the convenient reasoning’’. Total scores and percentages of each group were determined according to this scale. Each problem was evaluated according to the dimensions by two researchers, furthermore agreement percentages of each step were calculated. Findings, Discussion and Conclusion According to the evaluation of the data by the first researcher, the number of groups, which were more successful based on total scores of the four stages in the first and fourth questions, is higher. In the third question, there are groups, total scores of which equaled to zero according to the results of reasoning stages. The first group was able to reason in the first and fourth question, whereas; the second group was able to reason in the first, second, and fourth question. Moreover, the third group was able to conduct reasoning in the first, second, and fourth questions; the fourth group was able to reason in the fourth question; the sixth group was able to conduct reasoning in the first and second questions. The fifth group had difficulty with reasoning in all questions. The groups, which failed to correctly determine the solution, had difficulty with proceeding with next stages. This situation was the most apparent in the third question. According to the evaluation of the data by the second researcher, majority of the groups were more successful in terms of the total scores of reasoning stages in the first and fourth questions. For the third question, there are groups, which did not make any judgements thus did not obtain any scores. The first group was able to reason in the first and fourth question, whereas; the second group was able to reason in the first, second, and fourth question. Moreover, the third group was able to conduct reasoning in the first, second, and fourth questions; the fourth group was able to reason in the fourth question; the sixth group was able to conduct reasoning in the first, second, and fourth questions. The fifth group had difficulty with reasoning in all questions. In the third question, none of the groups were able to display their reasoning skills. According to Marzano (2000) the results obtained by two researchers suggest that in the dimension of reasoning in determining the accuracy of the solution, fourth and fifth groups had more difficulty with determining the accuracy of the solution than other groups; in the dimension of reasoning in solving non-routine problems, fourth and fifth groups had difficulty in this process; in the dimension of reasoning in developing logical arguments for the solution, most of the groups had difficulty in this process. According to Marzano (2000) the results obtained by two researchers suggest that the groups had more difficulty at the stage of generalizing in reasoning; and in the dimension of determining and using the convenient reasoning, the second and third groups had more skills in determining and using the convenient reasoning. Based on the findings obtained, majority of the groups had a successful process in determining the accuracy of the solution, solving non-routine problems, developing logical arguments, generalizing, determining and using the convenient reasoning according to the subdimensions of the scale of Marzano (2000). This may result from the fact that this problem situation is one of those, which students constantly come across with. The results obtained from the second problem suggest that the groups were able to conduct reasoning in half at the stages of determining the accuracy of solution, solving non-routine problems, developing logical arguments about the solution, generalizing, determining and using the convenient reasoning. However, in the third problem none of the groups were able to understand the problem or make any judgements thus failed to conduct reasoning. The fact that students were unable to reason may be because they did not come across such a problem or the problem is a non-routine one. In the evaluation of the fourth problem, majority of the groups developed arguments about the solution and determined the accuracy of the solution thus conducted reasoning. However, since the problem had visual content, the groups did not conduct reasoning, instead they approached the problem in a solution-oriented manner. In conclusion, reasoning requires high level thinking skills and has a cognitive dimension. An individual, who has learned how to learn, can improve his/her reasoning skills. Furthermore, an individual living through reasoning questions and discovers, is curious and can make generalizations. In order to enable students and individuals to acquire this skill, the question ‘’how did you think?’’ must be one of the fundamental questions, and consequently they must be promoted to question the answer