## Matematik ve Fen Bilgisi Öğretmen Adaylarının İntegral Konusundaki Kazanımlarının İncelenmesi

#### Abstract

Bu çalışmada, matematikte önemli bir yere sahip olan ve öğrenilmesi güç matematik konularından biri olan integral konusu ele alınmıştır. Bu konu kapsamında Milli Eğitim Bakanlığı 2013 ve 2017 Ortaöğretim Matematik Dersi Öğretim Programları incelenmiş ve ulaşılması beklenen kazanımlar belirlenmiştir. Bu kazanımlar doğrultusunda uzman görüşleri alınarak 9 alt kazanım belirlenmiş ve bu alt kazanımlara uygun 25 çoktan seçmeli sorudan oluşan "İntegral Kazanım İnceleme Testi" hazırlanmıştır. Hazırlanan test, 2016-2017 eğitim öğretim yılında bir devlet üniversitesinin eğitim fakültesi Matematik ve Fen Bilimleri Eğitimi Bölümünde bulunan 257 öğretmen adayına uygulanmış ve yapılan analizler sonucunda testin güvenirliği .864 olarak bulunmuştur. Adayların integral konusunda zayıf olduğu kazanımlar incelenmiş ve Matematik ve Fen Bilgisi öğretmen adaylarının "Trigonometrik fonksiyonların integralini alır" ve "İntegral sorusunu değişken değiştirme yöntemini kullanarak çözer" kazanımlarında eksikliklerinin olduğu bulunmuştur. Ayrıca, Matematik Eğitimi öğretmeni adaylarının Fen Bilgisi öğretmeni adaylarına göre integral konusunda daha fazla kazanıma sahip olduğu görülmüştür. 1. ve 4. sınıf düzeyleri ile 2. ve 3. sınıf düzeyleri arasında ise anlamlı bir fark bulunmazken diğer sınıflar arasında anlamlı bir farklılık ortaya çıkmıştır Mathematics, which is the basis of many researches from past to present, is a discipline that unfortunately many people have difficulties and have a learning difficulty. Identification and elimination of these difficulties are very important. When the relevant literature are reviewed, it is seen that integral that is often used in many areas such as mathematics, physics, statistics, engineering and architecture, is one of the most difficult math topics (Durmuş, 2004; Tatar vd., 2008; Gürbuz vd., 2011). When the Turkish education system is examined, “Integral” is firstly at the 12th grade level. Ministry of National Education 2013 High School Mathematics Curriculum consists of two sections as “Definite and Indefinite Integral” and “Definite Integral Applications”. Moreover, there are 7 acquisitions in the “Definite and Indefinite Integral” section and 1 acquisition in the “Definite Integral Applications” section (MEB, 2013). When the Ministry of National Education 2017 High School Mathematics Curriculum is examined, it is seen that this curriculum consists of two sections as “Indefinite Integral” and “Definite Integral and its Applications”. There are 2 acquisitions in the “Indefinite Integral” section and 4 acquisition in the “Definite Integral and its Applications” section (MEB, 2017). The fact that students have a learning difficulty most against integral within the math topics, suggests that one or more of these acquisitions may be lacking. In 2017 High School Mathematics Curriculum which aim to reach a total of 6 acquisitions about integral, specifically identifying which sub-acquisitions are deficient provide important information for resolving learning difficulties. This study was designed to be a quantitative research and descriptive data are used to identify students’ integral acquisitions. A test was developed to determine the acquisitions that lead to learning difficulty related to integral in the description process. First, 9 sub-acquisitions were determined considering the Ministry of National Education High School Mathematics Curriculum and the items were prepared according to these acquisitions. It was obtained that a test which consisted 30 multiple choice items. Next, the test was administered to 257 students, who enrolled at Department of Mathematics and Science Education of a university which is located in the central Turkey in the academic year of 2016-2017. As the result of the analysis obtained using Test Analysis Program [TAP], the reliability coefficient of Kuder-Richardson 20 (KR-20) was found to be .864; the mean discrimination index .53 and the mean item difficulty .58. Thus, “Integral Acquisition Investigation Test (IAIT)” which consisted 25 multiple choice items, was obtained. We examined acquisitions in the integral of Mathematics and Science Education Students according to the programs and class levels. Furthermore, we investigated the weak acquisitions of the students about integral. In this study, the integral has been explained again by the same lecturer, because the students’ readiness in Mathematics Education and Science Education are different levels. The data were analyzed using SPSS 23 program and significance level was taken as .01 As the result of the parametric analysis, we found a significant difference between IAIT scores and programs. Students of Mathematics Education program have achieved higher scores than the students of Science Education and so it was seen that they have more acquisitions about integral. Moreover, as the results of the analysis it was obtained a significant difference between the scores of the students and class levels: 1st-2nd, 1st-3rd, 2nd-4th and 3rd-4th. On the other hand, when the mean test scores according to the programs were examined, it was found to be 77.31 for Mathematics Education; 42.05 for Science Education and also 60.44 for Mathematics and Science Education. In addition, it was examined which sub-acquisitions were weak of the students about integral. It was obtained AK7 numbered acquisition “Integrates trigonometric functions” for Mathematics Education; AK4 numbered acquisition “Integrates using u-substitution” for Sciences Education were lower than the others. In the study of Tatar et al., 2008, it was emphasized that the students of Mathematics Education had more learning difficulties than the students of Science Education. However, in this study, it was obtained the students of Mathematics Education have less learning difficulty than Science Education. It was obtained a significant difference between the scores of the students and class levels. There was no significant difference between 1st and 4th also 2nd and 3rd grades. However, there was a significant difference between the other classes. Furthermore, it was seen that the students the test scores of the students in the 1st and 4th grades are lower. Reasons for being low can be investigated in another study by interviewing the students. Moreover, as a results of the analysis for acquisitions, it was observed that AK7 numbered acquisition “Integrates trigonometric functions” and AK4 numbered acquisition “Integrates using u-substitution” acquisitions were weak for Mathematics and Science Education Students. In this study, we deal with integral being one of the most difficult math topics to learn and having an important place in mathematics We have determined the acquisitions desired to be reached for integral. We prepared the “Integral Acquisition Investigation Test” with high validity, reliability, item difficulty and discrimination by taking these acquisitions into account. By administering this test, we examined acquisitions and acquisitions of Mathematics and Science Education Students about integral. Furthermore, we investigated according to the programs and class levels whether there were significant differences, or not. We determined which sub-acquisitions were weak of the students about integral. In other study, diagnostic assessments can be provided for the different faculties and departments about integral. The reasons for the significant difference in the class levels can be investigated detail. New studies can be done to resolve weak acquisitions determined in this study. Moreover, the weak acquisitions can be examined by considering 4 sub-acquisitions instead of the 9 sub-acquisitions which was determined in this study.