Publication: Matematik öğretmen adaylarının belirli integral konusundaki temsil tercihlerinin uzamsal yetenek ve akademik başarı bağlamında incelenmesi
Abstract
MATEMATİK ÖĞRETMEN ADAYLARININ BELİRLİ İNTEGRAL KONUSUNDAKİ TEMSİL TERCİHLERİNİN UZAMSAL YETENEK VE AKADEMİK BAŞARI BAĞLAMINDA İNCELENMESİ Yüksek öğrenim matematiğinin öğretim ve öğreniminde sıklıkla problem yaşandığı ifade edilen konulardan biri belirli integral kavramıdır. Öğrencilerin belirli integral konusunda zengin kavram tanım ve imajlarına sahip olmaları ve süreci anlamlandırabilmelerinde çoklu temsil bilgileri önemli bir yere sahiptir. Bu çalışmada belirli integral konusunda kullanılan temsiller ile görsel-uzamsal yetenek ve akademik başarı arasındaki ilişkiye bakılmıştır. Araştırma nitel yorumlayıcı paradigma’ya sahip özel durum çalışmasıdır. Bir devlet üniversitesinin Matematik Öğretmenliği ikinci sınıf programına kayıtlı 45 öğrencisi üzerinde durum çalışması yapılmıştır. Veri bağlamında ağırlıklı olarak nitel olan çalışmada, aynı zamanda nicel tekniklerden de yararlanılmıştır. Farklı uzamsal yetenek ve akademik başarı seviyelerine göre seçilen altı öğrenciyle yapılan görüşmeler, veri kaybını asgariye indirgemek için kaydedilmiştir. Araştırmada elde edilen nicel veriler bir istatistik paket kullanılarak, nitel veriler ise sınıflandırma yöntemi ve betimsel istatistik teknikleri kullanılarak analiz edilmiş ve yorumlanmıştır. Bulgular, adayların, belirli integral problemlerini çözme sürecinde çoklu temsil kullanma becerilerinin yeteri kadar iyi olmadığını göstermiştir. Görüşmelerle desteklenen sonuçlarda, uzamsal görselleme yeteneğinin farklı temsil kullanma becerisini etkilediği, temsil dönüşüm becerisinin de akademik başarıyı etkilediği belirlenmiştir. Özellikle kavram bilgisinin geliştirilmesi gerekliliği üzerinde duran araştırma sonuçları, ders içeriğinin farklı temsillerle zenginleştirilmesinin önemine değinmiştir. Belirli integral, Çoklu Temsiller, Akademik Başarı, Uzamsal Görselleme Yeteneği
CONSIDERATION OF PRE-SERVİCES MATHEMATICS TEACHERS’ PREFERENCES OF REPRESENTATION IN TERMS OF DEFINITE INTEGRAL WITHIN THE CONTEXT OF CERTAIN SPATIAL ABILITIES AND ACADEMIC ACHIEVEMENT One of the issues which has been said to be bound to problems in higher education mathematics is the concept of the definite integral. The locus of students’ multiple representation knowledge within the scope of the definite integral is significant in terms of having rich concept definition-image and signification of the process. The study aims at considering the effects of visual-spatial abilities on the representations used in the definitive integral and the effects of the representations used on academic achievement. The research is a case study having qualitative paradigm. Within the context, a case study with 45 pre-services teachers from Mathematics Teaching Department of a state university has been conducted. Within the study which has been qualitative in terms of data, both qualitative and quantitative data gathering techniques have been employed. The interviews with 6 students selected in accordance with different spatial abilities and academic achievement were recorded in order to minimise data loss. The qualitative data obtained from the study were analysed and interpreted through a statistic programme and quantitative data was analysed and interpreted through classification method and descriptive statistical techniques. The findings obtained from the study indicated that the skills of pre-services teachers in using multiple representations within the process of solving certain definite integral problems were not sufficient as required. In the results supported through the findings obtained from the interviews, it was specified that spatial visualisation ability affected the skill of different representation use and representation transformation ability affected academic achievement. Within the context, while the results of the research emphasises the significance of developing conceptual knowledge, the importance of enriching the lesson contents with different representations was signified. KEY WORDS: Definite Integral, Multiple Representations, Academic Achievement, Spatial Visualization Ability
CONSIDERATION OF PRE-SERVİCES MATHEMATICS TEACHERS’ PREFERENCES OF REPRESENTATION IN TERMS OF DEFINITE INTEGRAL WITHIN THE CONTEXT OF CERTAIN SPATIAL ABILITIES AND ACADEMIC ACHIEVEMENT One of the issues which has been said to be bound to problems in higher education mathematics is the concept of the definite integral. The locus of students’ multiple representation knowledge within the scope of the definite integral is significant in terms of having rich concept definition-image and signification of the process. The study aims at considering the effects of visual-spatial abilities on the representations used in the definitive integral and the effects of the representations used on academic achievement. The research is a case study having qualitative paradigm. Within the context, a case study with 45 pre-services teachers from Mathematics Teaching Department of a state university has been conducted. Within the study which has been qualitative in terms of data, both qualitative and quantitative data gathering techniques have been employed. The interviews with 6 students selected in accordance with different spatial abilities and academic achievement were recorded in order to minimise data loss. The qualitative data obtained from the study were analysed and interpreted through a statistic programme and quantitative data was analysed and interpreted through classification method and descriptive statistical techniques. The findings obtained from the study indicated that the skills of pre-services teachers in using multiple representations within the process of solving certain definite integral problems were not sufficient as required. In the results supported through the findings obtained from the interviews, it was specified that spatial visualisation ability affected the skill of different representation use and representation transformation ability affected academic achievement. Within the context, while the results of the research emphasises the significance of developing conceptual knowledge, the importance of enriching the lesson contents with different representations was signified. KEY WORDS: Definite Integral, Multiple Representations, Academic Achievement, Spatial Visualization Ability