The thinking-about-derivative test for undergraduate students: development and validation

Utkun Aydın (MEF Author)Two studies were conducted for the development and validation of a multidimensional test to assess undergraduate students' mathematical thinking about derivative. The first study involved two phases: question generation and refinement of the Thinking-about-Derivative Test (TDT). The second study included four phases as follows: test administration, generalizability analysis, confirmatory factor analysis, and subgroup validity analysis. Findings suggested that the 30-item multiple-choice TDT, which comprises 6 mathematical thinking aspects, enactive, iconic, algorithmic, algebraic, formal, and axiomatic thinking, demonstrates acceptable levels of reliability and validity. Followed by additional cross-validation studies, the TDT may be a useful tool for mathematics education researchers and mathematicians. Directions for future research and implications for educational practice are discussed.WOS:000365728500005Scopus - Affiliation ID: 60105072Social Sciences Citation IndexQ3ArticleUluslararası işbirliği ile yapılmayan - HAYIRAralık2015YÖK - 2015-1

Evaluating the impact of computers on the learning and teaching of calculus

Calculus has held its importance in the core undergraduate mathematics curriculum. The introduction of low cost microcomputers about 1979 has led some people to reconsider the content of the calculus curriculum. This investigation was about how microcomputer technology has been integrated into the teaching and learning of calculus to improve students' understanding. The study mainly focused on whether and how computers could influence students' learning of calculus concepts. The rationale for using microcomputer technology to enhance calculus learning was explored through interviews with teachers. But the main issue of concern here was whether and how, for first year engineering students, computers could influence their learning of calculus concepts. Following a survey conducted with teachers in sixth form colleges and universities, an experiment in realistic classroom environments was conducted because of the desire to obtain an in-depth insight into the impact of computers on students' learning of calculus concepts. Four groups in four different universities were involved in this main study; two served as computer groups (the computer was used in teaching); two served as non-computer groups (the computer was not used in teaching). Calculus (Differential and Integral) was taught over two semesters in all universities. The flow of ideas in this study shows several stages in the design where both quantitative and qualitative approaches were used in the collection and the analysis of data. The reason for combining quantitative and qualitative approaches was to demonstrate convergence in results, and to add scope and breadth to the study. Furthermore, this mixed approach was expected to bring meaningful information about the process of learning because classrooms as a whole, and also individual students and their idiosyncrasies could be analysed using these two approaches. Data was gathered from three sources in the main study. The pre-test was administered prior to the instruction in differentiation and integration and the post-test was given upon the completion of these topics. At the end of the post-test, computer groups were asked to complete a computer attitude questionnaire in order to gain background information. The pre-test and the post-test data were collected using a specially developed diagnostic test. The diagnostic test included 10 questions, some of them having several items dealing with similar content. Each item on the diagnostic test was scored on its own six-point scale, developed by the researcher and checked by a specialist in this field. The data from the pre-test, post-test and computer attitude questionnaire was coded, and analysis of variance and other techniques were used to analyze the results. In a follow-up post-testing, a few students were interviewed from each group in order to substantiate inferences deduced from the quantitative data. A pilot study of the test was performed with two separate samples of 14 and 18 A-level students, which served to check its administration and to improve the final version. Some questions were deleted and others were revised using item analysis information. Among a complex pattern of results reflecting the different teaching approaches, the computer groups did better than the non-computer groups, particularly on questions requiring drawing the graph of a derivative by looking at its function and recognising the graph of a function by looking at the derivative graph. Thus, the use of computers over an extended period of time and their availability when carrying out graphical tasks seem to make an impact on the performance of the students on graphical interpretations. Treatments in each group improved understanding much more so for A-level students than non-A-level students because the weaker students lag behind the rest of the class. In all groups the students showed a remarkable consistency in their errors. These results are interpreted in the light of previous research on understanding of calculus and recommendations are made to teachers and researchers

Kesirlerde Kavramsal ve İşlemsel Performans

This study investigates the performances of the students in using knowledge and skills on conceptual and computational tasks using fractions. An essay type test including 14 conceptual and computational questions was developed and administered to 145 5th grade students who were studying in a private elementary school in Ankara. Students performed differently in questions, which were related to the same conceptual objective, according to the types of fractions they include. In the computational questions, performance in subtraction and multiplication of different kinds of fractions was lower than the performance in addition of different kinds of fractions.Bu çalışmada öğrencilerin kesirler konusunda sahip oldukları bilgi ve becerileri kavramsal ve işlemsel durumlarda kullanma performansları incelenmiştir. Bu çalışma kapsamında, 14 tane kavramsal ve işlemsel som içeren sınav hazırlanmış ve Ankara’da bir özel ilköğretim okulunda 5. sınıfta okuyan 145 öğrenciye uygulanmıştır. Öğrenciler, aynı hedefi farklı durumlarda ölçen kavramsal performansa yönelik sorularda, sorunun içerdiği kesir çeşitlerine göre farklı performans göstermişlerdir, işlemsel performansa yönelik somlarda ise farklı tipte kesirler arasındaki çarpma ve çıkarma işlemlerinde, toplama işlemine kıyasla daha düşük performans göstermişlerdir

Sınıf Öğretmeni Adaylarının Prizma Bilgileri: Tanım ve Örnekler Oluşturma

This study aimed to investigate prospective primary teacher’s knowledge on prism by exploring the definitions and examples generated by them. Four prospective teachers participated in the study. The five open ended questions used in the study as the data collection tool require drawing an example, explaining the properties, drawing different examples, constructing different definitions, and constructing examples from daily life related to prism. Definitions and examples generated by the participants about prism were analyzed based on accessibility, correctness, richness, and generality criteria (Zazkis & Leikin, 2008). As a result of the analysis, participants' knowledge related to the prism was found to be inadequate. The findings also inform that the mathematics lessons content in the primary teacher teaching program must be looked over in the perspective of generating definitions and examples. Key Words: Definition, Exemplify, Misconceptions, Teacher training, Prism   SUMMARYBu araştırma, sınıf öğretmeni adaylarının prizma kavramına ilişkin bilgilerini oluşturdukları tanım ve örneklendirmeleri inceleyerek ortaya çıkarmayı amaçlamaktadır. Araştırmaya aşırı veya aykırı durum örneklemesi ile belirlenen 2’si kız ve 2’si erkek olmak üzere toplam dört öğretmen adayı katılmıştır. Veri toplama aracı olarak çalışmada kullanılan beş açık uçlu soru prizma ile ilgili örnek çizim, özelliklerin açıklanması, farklı örnekler çizilmesi, farklı tanımların oluşturulması ve günlük hayattan örnekler verilmesini gerektirmektedir. Verilerin analizi betimsel analiz yöntemiyle erişebilirlik, doğruluk, zenginlik ve genelleştirme kriteri (Zazkis & Leikin, 2008) kullanılarak incelenmiştir. Yapılan analizler sonucunda; katılımcıların konu alan bilgilerinin yetersiz olduğu görülmüştür. Elde edilen bulgulara göre, sınıf öğretmenliği programındaki, matematikteki konu alan bilgisini ihtiva eden derslerin içerikleri, kavramların tanımlanması ve örneklendirilmesi göz önünde bulundurularak gözden geçirilmesi gerektiği düşünülmüştü

Problem solving method with handout material: max min word problems

The problem‐solving method with handout material is an instructional method, which includes handout material prepared by taking Polya's problem‐solving stages. The handout material consists of a short review of the theorems related to max‐min word problems, general procedure for solving max‐min word problems, comprehension guides, and problems with unfinished solution steps. The purpose is to assist students in seeing uses and applications of max‐min principles in real life, and to improve reading comprehension and problem‐solving skills