Adnan Baki

Design and development of an innovative individualized adaptive and intelligent e-learning system for teaching-learning of probability unit: Details of UZWEBMAT

In this study, an innovative adaptive and intelligent web based e-learning system, UZWEBMAT (Turkish abbreviation of Adaptive and INtelligent WEB based MAThematics teaching-learning system) was designed, developed and implemented. This e-learning system was intended for learning and teaching secondary school level permutation-combination-binomial expansion and probability subjects. Content which was prepared according to Turkish curriculum for secondary school mathematics course was transformed into learning objects in three different ways in accordance with VAK (Visual-Auditory-Kinesthetic) learning styles. Primary/secondary/tertiary learning styles of learners registering the system are determined and each learner receives the content appropriate for his/her dominant learning style. Also, they can be directed to contents of other styles according to their performances thanks to an expert system. Learning objects constituting the content were prepared according to constructivist approach. An active role for the learner was the purpose. Tips and intelligent solution supports within the learning objects were presented with expert system support to the learners. With this structure, UZWEBMAT bears the characteristics of intelligent tutoring system as well as an adaptive e-learning environment. All the movements of learners studying with UZWEBMAT are recorded and the necessary information is reported to both learners and teachers in a visualized way.

Learning objects in high school mathematics classrooms: Implementation and evaluation

Learning Objects (LOs) within their new features, give new opportunities to learners and educators. LO based learning environments are mostly used within web environments, especially through distance education. This study presents an application about the use of LOs in a real classroom environment. In this application, a Learning Object Repository (LOR) relevant to secondary school mathematics curricula has been prepared and published on the web. The research sample consists of thirty students from a high school at 9th grade. In order to answer the research questions about the implementation of LOs for mathematics teaching in a high school classroom, qualitative and quantitative data were obtained both from the teacher and students participated in the study. The analysis of the data illustrated that students were easily able to follow the instructions of LOs and practise activities within LOs. The attitudes and approaches of students were generally positive. In despite of inconveniency with the teachers familiar instructional practices, she also expressed her positive opinions about the learning and motivational effects of LOs. These findings support the idea that the use of LOs can be an effective learning tool in high school mathematics classrooms.

The effects of UZWEBMAT on the probability unit achievement of Turkish eleventh grade students and the reasons for such effects

Abstract This study aimed at determining the effects of UZWEBMAT (Turkish abbreviation of Adaptive and INtelligent WEB based MAThematics teaching–learning system) on the probability unit academic achievement of students and the underlying reasons for these effects. The study was conducted in an Anatolian High School located in a district of Trabzon province, Turkey in the fall semester of the academic year 2011–2012. The research sample consisted of 106 eleventh grade students and 2 mathematics teachers. Semi-experimental method was used in the study. Pre-Probability Unit Achievement Test (pre-PUAT), Post-Probability Unit Achievement Test (post-PUAT), Scale for Evaluation of the UZWEBMAT by Students (SEUS), Student Interview Form (SIF), and Teacher Interview Form (TIF) were used for collecting data. Research results indicated that there was a statistically significant difference in favor of the experimental group (EG) students between the academic achievement of the EG students and that of the control group (CG) students. In addition, male EG students were found to be more successful than female EG students. However, no statistically significant relationship was found between the learning styles and the academic achievements of the EG students with different learning styles (visual–auditory–kinesthetic). In addition, no statistically significant relationship was detected between the genders and the academic achievements of the EG students having different learning styles. It was concluded that the higher achievement of the EG students resulted from the fact that they received education in accordance with their learning styles via UZWEBMAT, the learning objects included in UZWEBMAT had appropriate structural characteristics, students enjoyed learning in that environment, and students had continuous interest in the lesson.

Integrating computerized adaptive testing into UZWEBMAT

Highlights? Assessment is an important part of learning process. ? Adaptive assessment provides an individualized assessment environment for learners. ? UZWEBMAT was developed for teaching probability unit from 11th grade students. ? Adaptive assessment module was added to UZWEBMAT system. ? Individual assessment may be more efficient for learners. This study deals with the design and development process of computerized adaptive testing module integrated into UZWEBMAT. UZWEBMAT is an expert system supported adaptive and intelligent individualized e-learning environment. It was devoted to teach probability subject. A question bank was created in the study in the first place. This question bank was administered to learners in the form of work sheets. These tests were analyzed according to Item Response Theory. Model-data adaptivity was tested at the end of the analyses. It was deduced that data can be adapted to 3PL. Items non-compliant with 3PL were extracted from the question bank. At the end of these operations, final question bank containing 752 questions in total was obtained. Learners taught with UZWEBMAT took end-of-subject tests for permutation, combination, binomial expansion and probability containing 20, 20, 15 and 20 questions respectively. Besides, learners completing all subjects took end-of unit test containing 30 questions. Items in these tests were dynamically selected from the question bank pursuant to adaptive assessment. While test was dynamically being formed, the question providing the furthest information regarding current estimated ability level of examinee was determined and it was presented to next examinee. Ability level of the examinee was re-estimated and updated according to the answer of each question. Thanks to this module, learners individually taught with UZWEBMAT are provided with adaptive assessment in accordance with their own qualifications and capacities. In contrast to classical tests, individual assessment becomes a reality through adaptive assessment which provides the opportunity to know learners according to their ability levels.

Archimedes with Cabri: Visualization and Experimental Verification of Mathematical Ideas

This column will publish short (from just a few paragraphs to ten or so pages), lively and intriguing computer-related mathematics vignettes. These vignettes or snapshots should illustrate ways in which computer environments have transformed the practice of mathematics or mathematics pedagogy. They could also include puzzles or brain-teasers involving the use of computers or computational theory. Snapshots are subject to peer review. This snapshot explores a classic geometry theorem of Archimedes. The author shows how the use of a dynamic geometry environment can deepen and guide the process of proof. The Cabri environment enabled exploration in a new way that connected steps in the proof to geometric properties and intuitions that served as a foundation for deductive reasoning.

Characterizing student mathematics teachers’ levels of understanding in spherical geometry

This article presents an exploratory study aimed at the identification of students’ levels of understanding in spherical geometry as van Hiele did for Euclidean geometry. To do this, we developed and implemented a spherical geometry course for student mathematics teachers. Six structured, task-based interviews were held with eight student mathematics teachers at particular times through the course to determine the spherical geometry learning levels. After identifying the properties of spherical geometry levels, we developed Understandings in Spherical Geometry Test to test whether or not the levels form hierarchy, and 58 student mathematics teachers took the test. The outcomes seemed to support our theoretical perspective that there are some understanding levels in spherical geometry that progress through a hierarchical order as van Hiele levels in Euclidean geometry.

Farklı Programlarda İstatistik Dersi Veren Öğretim Elemanlarının Uygulamalarının İstatistik Okuryazarlığı Bağlamında Değerlendirilmesi

In this study it was aimed to evaluate the practices of instructors teaching statistics courses in different undergraduate programs in terms of statistical literacy. Through this aim, statistics courses of nine instructors from nine different undergraduate programs were observed during a semester in a state university. Qualitative data of this study consisted of classroom observations, field notes and interviews conducting with instructors. Data was analyzed with the rubric, including the aspects of the statistical literacy components to evaluate statistical literacy practices. Chi-Square independent test was performed to determine whether the differences between programs are statistically significant. Differences were seen between programs and components the practices of instructors in statistics courses. In their practices, instructors mostly referred to basic concepts component and they referred to statistical process component at least. As a result of Chi-Square analysis it was seen that all of differences based on statistics practices between components and aspects according to programs were statistically significant. And key aspects were identified for statistical literacy based on the practices of statistics courses. Important steps would be taken to raise undergraduate students’ statistical literacy levels if these aspects are taken into consideration at determining the course context and designing the practices.

Matematiksel Modelleme Yeterliklerini Geliştirme ve Değerlendirme Yaklaşımlarının Sınıflandırılması

Muhakeme ve iliskilendirme becerisine sahip, cevresiyle uyumlu, ureten ve yasami boyunca karsilastigi problemleri cozebilen bireylerin yetistirilmesi okul matematiginin en temel amacidir. Bu amacin tam merkezinde matematiksel modelleme yeterlikleri yer almaktadir. Ilgili alan yazin incelendiginde matematiksel modelleme yeterliklerinin gelistirilmesine ve degerlendirilmesine yonelik bircok calismaya rastlanmaktadir ve benimsenen yaklasimlarin birbirinden farkli oldugu anlasilmaktadir. Ancak ilgili alan yazinda soz konusu bu farkli yaklasimlarin sistematik siniflandirilmasi, nasil gelistirilebilecegi ve matematiksel modellemenin ogrenme ortamlarina nasil entegre edilebilecegi ayrintili olarak ele alinmamistir. Bu calismada, kapsamli bir alan yazin taramasi yapilarak matematiksel modelleme yeterliklerini gelistirme, matematiksel modellemeyi ogrenme ortamina entegre etme ve degerlendirme yaklasimlari karsilastirmali olarak cozumlenerek siniflandirilmistir. Bu calisma sonunda, yaklasimlara ve ornek uygulamalara bagli olarak ortaya koyulan siniflandirmalarin matematiksel modelleme yeterliklerini gelistirme ve degerlendirme calismalarina ve tartismalarina isik tutacagi dusunulmektedir.

Examining Students’ Generalizations of the Tangent Concept: A Theoretical Perspective

Abstract The concept of a tangent is important in understanding many topics in mathematics and science. Earlier studies on students’ understanding of the concept of a tangent have reported that they have various misunderstandings and experience difficulties in transferring their knowledge about the tangent line from Euclidean geometry into calculus. In this study, we examine students’ understanding of the tangent concept from the viewpoint of generalization. The findings of the study reveal differences in students’ generalizations regarding the tangent concept. We discuss the causes of these differences and provide a theory to account for them. In light of the results, some suggestions are made for improving the teaching of the concept of a tangent.

ÖĞRETMENLERİN ESKİ MATEMATİKÇİLERİN YAŞAM ÖYKÜLERİNE YÖNELİK GÖRÜŞLERİ VE DERSLERDE YER VERME DURUMLARI

Bu calismada, matematik tarihinin ogretimde kullanilmasi ile ilgili bir kursa katilan ortaokul matematik ogretmenlerinin kurs programi suresince derslerde eski matematikcilerin yasam oykulerinden faydalanilmasina iliskin goruslerinin ve yasam oykulerine yer verme durumlarinin incelenmesi amaclanmistir. Ozel durum calismasi yonteminin kullanildigi bu arastirmada veriler, yari yapilandirilmis mulakatlar ve yapilandirilmamis gozlemler yardimiyla toplanmistir. Veriler, betimsel ve icerik analizine tabi tutulduktan sonra, tablolar halinde sunulmustur. Calismanin sonunda, kurstan sonra ogretmenlerin derslerde eski matematikcilerin yasam oykulerinin kullanimi konusundaki olumlu goruslerinde ve yasam oykulerine yer verme durumlarinda kurs ocesine gore artis oldugi gorulmustur. Arastirmanin sonuclarina bagli olarak, diger ogretmenlere de derslerinde eski matematikcilerin yasam oykulerini kullanmalari onerilmistir.