Bülent Güven

Using Dynamic Geometry Software to Gain Insight into a Proof

The ability of a student to obtain, analyze, measure and compare the many instances of a mathematical proposition in a dynamic geometry environment gives him/her opportunities to make conjectures and test a proposition. These roles for dynamic geometry software are widely acknowledged as having the potential to enrich the teaching of geometry. Furthermore, Hoyles and Jones (1998) claim that dynamic geometry, supported by ‘‘what if’’ and ‘‘what if not’’ questions, has the potential to promote links between empirical and deductive reasoning. A classic set of problems in Euclidean plane geometry consists of finding the path of a point that is subject to given constraints. Its systematic study goes back to a lost work (in two books) of Apollonius of Perga, Plane loci (Botana and Valcarce 2003). Except for the simplest loci, such as lines, circles and perhaps the conics, this subject is usually avoided in most geometry texts. This is due to the common difficulties faced when mentally visualizing various objects with different movements. With the emergence of dynamic geometry software, the locus problems have attracted new interest from researchers. Using the locus generation features of these software one can easily obtain the locus of a point under some constraints. Although there are some minor differences, different dynamic geometry software, behave in a similar way when obtaining loci. In general, two objects must be selected: the first one, usually a point called the driving point or mover, is bound to a path, whereas the other, the locus point, must depend somehow on the first one. Since the element

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.

Students discovering spherical geometry using dynamic geometry software

Dynamic geometry software (DGS) such as Cabri and Geometers’ Sketchpad has been regularly used worldwide for teaching and learning Euclidean geometry for a long time. The DGS with its inductive nature allows students to learn Euclidean geometry via explorations. However, with respect to non-Euclidean geometries, do we need to introduce them to students in a deductive manner? Do students have quite different experiences in non-Euclidean environment? This study addresses these questions by illustrating the student mathematics teachers’ actions in dynamic spherical geometry environment. We describe how student mathematics teachers explore new conjectures in spherical geometry and how their conjectures lead them to find proofs in DGS.

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.

The effect of project-based learning on students’ statistical literacy levels for data representation

The point of this study is to define the effect of project-based learning approach on 8th Grade secondary-school students’ statistical literacy levels for data representation. To achieve this goal, a test which consists of 12 open-ended questions in accordance with the views of experts was developed. Seventy 8th grade secondary-school students, 35 in the experimental group and 35 in the control group, took this test twice, one before the application and one after the application. All the raw scores were turned into linear points by using the Winsteps 3.72 modelling program that makes the Rasch analysis and t-tests, and an ANCOVA analysis was carried out with the linear points. Depending on the findings, it was concluded that the project-based learning approach increases students’ level of statistical literacy for data representation. Students’ levels of statistical literacy before and after the application were shown through the obtained person-item maps.

Tasarlanan Hizmet-İçi Eğitim Kursunun Ortaokul Matematik Öğretmenlerinin Teknoloji Kullanım Düzeylerine Etkisi

By this research, it is aimed to determine the effect of in-service training was designed due to Rieber and Welliver’s (1989) technology integration model to the secondary school mathematics teachers’ technology usage level. The in-service course was conducted over a 15-week period and 13 secondary school mathematics teachers from Bayburt participated in the course. When the course program was being structured, some software and learning objects developed for mathematics teaching were utilized. The applications were supported by worksheets and activity examples appropriate for the curriculum. In this study where data were gathered using interviews and observations, the case study method was used. The collected data was analysed by means of qualitative and quantitative analysis methods. When the findings were checked, it can be seen a result that teachers took advantage of technology for composing deep conceptual comprehension and structuring concepts by students centred explores and used technology in their lessons frequently. By this manner, it was resulted that the designed course positively affected to teacher’s technology usage levels.

Problem types used in math lessons: the relationship between student achievement and teacher preferences

The purpose of this study was to determine the relationship between the problems teachers preferred in mathematics lessons and student achievement in different types of problems. In accordance with this purpose, nine mathematics teachers were interviewed, and corresponding problems were prepared and administered to 225 eighth-grade students. The findings indicate that problem types are dependent on teacher preferences. It was found that curriculum-dependent and routine problems were dominant for teacher preferences. Students are more successful at with missing data, problems that are visual and do not require the use of different strategies. They have lower success at long problems, those that contain irrelevant data, problems that require the use of different strategies and difficult problem types. It was found that problem types at which students were successful and which teachers preferred were related. These results relay information about problems used in the learning environment and effect of proble...

Critical views of 8th grade students toward statistical data in newspaper articles: Analysis in light of statistical literacy

AbstractUnderstanding and interpreting biased data, decision-making in accordance with the data, and critically evaluating situations involving data are among the fundamental skills necessary in the modern world. To develop these required skills, emphasis on statistical literacy in school mathematics has been gradually increased in recent years. The critical views of 8th graders with respect to statistical data presented in several newspaper articles were investigated from various aspects through this descriptive study. The study was conducted in a middle school with 9 students at the 8th grade level. The statistical data included in news articles selected from different national newspapers published in Turkey were used to collect the data. Through clinical interviews, the evaluations of the students were determined from the aspects of consistency, sample, data collection, data analysis, data presentation, and data support; the reasoning behind the students’ evaluations was also discussed. As a result, it...

Ortaokul Sekizinci Sınıf Öğrencilerinin İstatistiksel Süreçteki Deneyimlerinin İncelenmesi

This study aims at making 8th grade students go through a statistical process and gain experience in this matter and revealing their behaviors, experiences, and difficulties at each stage of this process. Activities were designed in a way allowing the students to experience a statistical process. Then the students were made to get involved in these activities through group work. Data were collected via statistical process activities, the reflection papers of the students concerning the process, and the video-recordings of classroom discussions. The activities were prepared based on Ben-Zvi and Arcavi (2001) as well as expert opinions. The students posed questions that could be directly answered by the help of relevant texts rather than problems that could be solved through data analysis. The groups formed their tables and charts by focusing on just one feature or variable though the data in the activities involved features of more than one variable. As making an inference by interpreting data requires experience, it is recommended in this study that activities be prepared in a way allowing the use of skills of this sort.