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Tamsayılar, matematik öğretiminde birçok konuya temel teşkil eden, birçok sayı kümesinin temelini oluşturan ve günlük hayatta uygulama alanı bulabilen kavramlardan birisidir. Öğrencilerin tamsayılara yönelik kavram imajlarının araştırılmasının tamsayı kavramının öğrenilme süreçlerine katkı getireceği öngörülmektedir. Özellikle öğrencilerin tamsayı kavramından ne anladıklarının kendi bakış açılarıyla belirlenmesi daha geçerli tespitlerin yapılarak öğrencilerin eksiklerinin giderilmesine olanak sağlayabilir. Bu nedenle çalışmanın amacı, öğrenci gözüyle tamsayılara yönelik kavram imajlarının değerlendirilmesidir. Bu doğrultuda çalışma, nitel araştırma yöntemlerinden durum çalışması kullanılarak düzenlenmiştir. Çalışmanın katılımcılarını 2015-2016 eğitim-öğretim yılında Sakarya ilinde bir devlet okulunda öğrenim gören 7. sınıf 27 öğrenci oluşturmaktadır. Öğrencilerin tamsayılara yönelik kavram imajlarını belirlemek üzere, veriler araştırmacılar tarafından hazırlanan 7 açık uçlu sorudan oluşan “Tamsayı Kavram Testi”nden (TKT) elde edilmiştir. Öğrenci cevapları detaylı bir şekilde incelenerek betimsel analiz ile çözümlenmiştir. Araştırmanın bulgularına göre; öğrencilerin çoğunluğunun tamsayı kavramını anlamlandırmada istenilen düzeyde olmadıkları; kendi açılarından bölme ve çarpma işlemlerinde yaşadıkları zorluklar nedeniyle tamsayı imajlarının yeterli düzeyde oluşmadığı tespit edilmiştir. Bu nedenle öğrencilerin tamsayılarla işlem yapmada birçok hata yaptıkları gözlenmiştir. Bu durum öğrencilerde kavram yanılgılarının oluşmasına ve bu kavramları öğrenirken zorluk yaşamalarına sebep olabilir. Öğrencilere tamsayı tanımının ezberletilmesi ve işlemlerin ağırlıklı olarak yapılmasının yerine kavramla ilgili yeterince etkinlik düzenlenerek öğrencilerin kavram tanımları ile kavram imajlarını birbirine yakınlaştıracak öğrenme ortamları düzenlenebilir.
Summary is one of the concepts that form the foundation of many subjects in mathematics teaching, which form the foundation of many set of numbers and which can find an area of application in everyday life. The study of the student's conceptual imagery to the summary is expected to contribute to the learning processes of the summary concept. Specifically, determining what students understand from the concept of totality from their own perspective can enable the disadvantages of students to be removed by making more valid findings. Therefore, the purpose of the study is to evaluate the conceptual images aimed at the student's view. In this way, the study was organized using the quality research methods of state study. The participants in the study consist of 7th grade 27 students who study in a state school in Sakarya in the 2015-2016 educational year. To determine the conceptual images of the students to the summary, the data was obtained from the "Total Concept Test" (TKT) consisting of 7 open end questions prepared by the researchers. The student’s answers are analyzed in detail by illustrative analysis. According to the findings of the study, it has been found that the majority of students are not at the desired level in understanding the concept of totality; because of the difficulties they experience in the processes of division and collapse from their respective points of view, their totality images are not sufficiently formed. Therefore, there are many errors that students have made when dealing with the total numbers. This situation can cause students to develop conceptual errors and to experience difficulties in learning these concepts. Instead of remembering the definition of the whole and making the processes mainly, sufficient activities related to the concept can be organized and learning environments can be organized that will bring the conceptual definitions of the students closer to the conceptual images.
Integers are one of the concepts that form the basis of many subjects in the teaching of mathematics, which form the basis of many sets of numbers and which can find application areas in everday life. It’s envisaged that the research of the concept images of the students will contribute to the learning process of the integers. The fact that students understand from the concept of integer can be determined by their own perspectives, which can make it possible to correct the deficiencies of the learners by making more valid determinations. For this reason the aim of the study is to evaluate the concept images of the student’s eye for the integers. So the study was organised using case studies from qualitative research methods. The participants of the study are 27 students in the 7th grade who are studying at a public school in Sakarya in the academic year of 2015-2016. The data have obtained “The Concept of Integers Test” (CIT) that is prepared by researchers and has seven open-ended questions for determining students’ the concept images toward the integers. Students’ responses are examined with details and are analysed with descriptive analysis. According to the research’s findings; it is found that the majority of students have not enviable level in making sense of the concept of integers. Also, it is found that students have not enough level toward the integers images, because of the difficulties in the divison and the multiplication operations in terms of themselves. Therefore, it is observed that students have a lot of mistakes in doing operations with integers. This situation may cause occuring misconceptions of students and may cause the diffuculties in learning this concepts. Instead of memorized the definition of integers to students and doing operations mainly, it may be arranged learning environments that is caused the concept definitions to become closer to the concept images.
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