Melike Yigit Koyunkaya

In recent years, researchers have advanced the Technological, Pedagogical, and Content Knowledge (TPACK) framework to describe both in-service and pre-service teachers ’ knowledge related to effectively integrating technology. This study is a systematic literature review about pre-service mathematics teachers ’ (PSMTs) development of TPACK, and the review is limited to the peer reviewed articles published between 2005 and 2013 (February). The main purpose of this study is to investigate and analyze the articles in mathematics education research that have explored how PSMTs develop their TPACK and how their development impacts their future teaching of mathematics. Specifically, the literature review attempts to identify PSMTs’ development of the components of the TPACK framework, their perspectives for their future teaching, how their development of TPACK can be measured, and strategies to develop their TPACK. Findings show that PSMTs’ active involvement in technology-enhanced lesson...

This study is an ongoing research aiming to develop four prospective secondary mathematics teachers’ skills in designing and teaching technology-based lesson plans within the scope of 14week Teaching Practice course. The Dynamic Geometry Task Analysis and Instrumental Orchestration frameworks have been chosen as the conceptual basis of the study. In this study, qualitative research paradigm has been adopted and action research methodology aiming to plan a cyclical process of designing technology-based lesson plans through modifying, implementing and reflecting has been used. Data mainly consisted of individual/group interviews, lesson observations/field notes and multiple versions of lesson plans. Data analysis process is in progress, however, preliminary results focusing on one task of one participant indicated that the participant developed, evaluated and implemented her technology-based task in the light of adopted frameworks.

This study explored the theory and applications of complementary colors using a technology-based activity designed from the perspective of STEAM education. Complementary colors and their areas of use were examined from the perspective of physics, mathematics and art, respectively. The study, which benefits from technology, makes the theory of complementary colors accessible to all through practical applications and provides a multidisciplinary, integrated and innovative technique of teaching the subject of colors, which could be used to teach complementary colors.

This department showcases students' in-depth thinking and work on problems previously published in Teaching Children Mathematics. The problem scenario in the December 2013/January 2014 issue involves concepts of formal and informal measurement and encourages students to use different units to measure and compare.

"The introduction of dynamic geometry software (DGS) has afforded teachers and learners with new opportunities for mathematical modeling and explorations. Even though some powerful DGS packages have been available for more than 20 years, they are not widely used in the teaching and learning of geometry (Laborde, 2001). The goal of this study is to produce a comprehensive review of research evidence on the roles of DGS in pre-service teachers’ (PSTs) learning of geometry to improve their education programs. Searches of three databases (ERIC, JSTOR, and PsychINFO) for peer reviewed articles published in scholarly journals between 2000 and 2012 were conducted. To get a more comprehensive understanding of the theoretical underpinnings of the roles of DGS, broad search terms were used, including ‘Dynamic Geometry Software’, ‘DGS’, and ‘PSTs’ using of DGS’. Only empirical studies including impacts of DGS, how DGS can be used, and the challenges faced by PSTs in using DGS were used in the analysis"

Matematik öğretimi ve öğrenimini açıklayan birçok akademik çalışmada,
öğrenme modelinde, standartlarda ve öğretim programlarında bağlantı kurma ve ilişkilendirme yapmanın önemi vurgulanmıştır. İlişkilendirmenin yanı sıra, matematik öğretimi ve öğrenimine yönelik çağdaş yaklaşımların pek çoğunda etkinlik adı verilen bir öğrenme birimine vurgu yapılmaktadır. Bu durum etkinlikleri ve etkinlik temelli öğrenmeyi matematik eğitiminin merkezine taşımaktadır. Matematik öğretimi yapılırken ilişkilendirmenin kurulabileceği en uygun öğrenme
birimlerinden bir tanesi de matematik öğrenme etkinlikleridir. Bu bağlamda, günlük yaşamla ilişkilendirmenin ne olduğunu, nasıl yapılacağını geliştirilen veya var olan etkinlikler üzerinden incelemenin faydalı olacağı düşünülmektedir. Bu çalışmanın
temel amacı ortaöğretim matematik öğretmen adaylarının günlük yaşam ile matematiği ilişkilendirmenin ne olduğu ve nasıl yapılması gerektiği hakkındaki düşüncelerini belirlemek ve düşüncelerini geliştirdikleri bir grup günlük yaşam ile ilişkilendirilmiş matematik öğrenme etkinliğine nasıl yansıttıklarını incelemektir. Çalışmada nitel araştırma paradigmalarından durum çalışması kullanılmıştır. Bu çalışma bir devlet üniversitesinin dördüncü sınıfından eğitim gören 33 (11 grup)
matematik öğretmen adayı ile yapılmıştır. Öğretmen adaylarına serbest yazma yaptırılmış ve günlük yaşam ile ilişkilendirilmiş matematik öğrenme etkinliği geliştirmeleri istenmiştir. Toplanan veriler içerik analizi yöntemi ile analiz edilmiştir. Matematik öğretmen adaylarının günlük yaşam ile ilişkilendirmenin gerekliliği ve önemini savunurken, bu durumu geliştirmiş oldukları matematik öğrenme etkinliklerine yansıtmada zorluk çektikleri belirlenmiştir.

Öz: Bu çalışmanın temel amacı, ortaöğretim matematik öğretmen i adaylarının teknolojik pedagojik alan bilgi (TPAB) düzeylerinin ve gelişimlerinin incelenmesidir. Bu amaç doğrultusunda, bu çalışma bir ders kapsamında öğretim deneyi yöntemi kullanılarak tasarlanmıştır. Çalışmanın katılımcıları, bir devlet üniversitesinin Ortaöğretim Matematik Öğretmenliği bölümünde öğrenim gören 28 tane 4. sınıf öğrencisinden oluşmaktadır. Çalışmada, nitel araştırma paradigması benimsenerek öğretim deneyi yöntemi kullanılmıştır. Bu yöntem kullanılarak 16 hafta boyunca haftada 4 saat olmak üzere öğretmen adaylarına teknolojinin matematik eğitimine entegre edilmesi, çeşitli matematik/geometri yazılımlarının kullanılması, eğitimde kullanılan interaktif uygulamalar, web siteleri ve çeşitli teknolojik uygulamalar tanıtılmış ve çalışmanın verileri toplanarak, içerik ve doküman analiz yöntemi ile analiz edilmiştir. Çalışmanın bulguları, uygulanan öğretim ile öğretmen adaylarının teknoloji bilgilerinin, teknolojik pedagoji bilgilerinin, teknolojik alan bilgilerinin ve TPAB düzeylerinin geliştiğini göstermektedir. Tasarladıkları etkinlikler ve ders planları ve yazdıkları haftalık yansımalar ve serbest yazılar incelendiğinde, öğretmen adaylarının matematik öğrenmeyi ve öğretmeyi kolaylaştırmak ve daha faydalı hale getirmek için teknolojiyi nerede ve nasıl kullanacaklarına dair becerilerinin geliştiği görülmüştür. Bu bağlamda, eğitim fakültelerindeki öğretmen yetiştirme programlarına teknoloji entegre edilmiş veya teknoloji tabanlı derslerin eklenmesinin veya bu derslerin içeriklerinin geliştirilerek arttırılmasının gerekli olduğu düşünülmektedir. Anahtar Kelimeler: Teknolojik pedagojik alan bilgisi, öğretim deneyi yöntemi, matematik eğitiminde teknoloji Abstract: The main purpose of this study was to examine pre-service secondary mathematics teachers' (PSMTs) levels and development of technological, pedagogical and content knowledge (TPACK). In line with this purpose, this study was designed to use teaching experiment methodology within a course. The participants of the study were 28 fourth grade PSMTs. The qualitative research paradigm was adopted and the the teaching experiment methodology was used in the study. By using this method, PSMTs were taught about how to integrate technology into mathematics education, how to use various mathematics and geometry dynamic software, interactive applications that are used in mathematics education , various websites and technological tools related to education during 16 weeks and four hours in each week. The data was collected during the experiment, and analyzed by using content analysis and document analysis methods. The results show that PSMTs' technological knowledge, technological pedagogical knowledge, technological content knowledge and TPACK levels were developed by applying the teaching experiment methodology. Particularly, when the activities they designed, lesson plans, reflections and free writings were examined in detail, it was observed that PSMTS' skills about how to integrate technology in order to ease the learning and teaching of mathematics and utilizing it were developed. Within this context, it is thought that technology integrated courses or technology based courses should be embedded or the context of these courses were developed in the teacher education programs.

Students need to construct strong knowledge of angles as well as relationships between angles and side lengths in a triangle to succeed in geometry. Although many researchers pointed out the importance of angles and angle-related concepts, students and teachers have had limited knowledge of these concepts. This study is a part of a larger study, and examines pre-service secondary mathematics teachers’ (PSMTs) mental constructions of relationships between angles and side lengths in a right triangle (RASR). The Action-Process-Object-Schema (APOS) learning theory was used as the theoretical lens and clinical interview methodology was used as the methodology in the study. The study was conducted with four PSMTs, but it focuses on one of PSMTs, Linda, who revealed evidence of schema for RASR. As a result of fine-grained analysis of Linda’s responses to the tasks, this article reports the mental constructions enough to develop a schema for RASR. The model describes that schema for 2-line angles, right triangles and relationships between opposite angles and side lengths and process level for some relationships including ‘Pythagorean Theorem’, ‘The hypotenuse is always the longest side in a right triangle’, ‘Special right triangles’, ‘Complementary Angles’, and ‘Triangle inequalities’ are enough to construct a schema for RASR

In our country, one of the important concepts proposed by the recent curricula has been 'activities' since 2005. From this point of view, both mathematics educators and teachers should focus on and discuss about the importance of activities. This study is designed to examine pre-service secondary mathematics teachers' (PSMTs) perceptions about mathematics learning activities (MLA). Participants are twenty-seven PSMTs. The data include 3 different groups. The first group consists of PSMTs' free writings that describe their definitions of MLA. The second group consists of observation notes of the class discussions which are related to the structure of MLA and MLA's required properties. The last one consists of MLA samples that were designed by PSMTs. In consequence of data analysis, results show that PSMTs did not reach consensus on a unique definition or particular properties of MLA; the definitions spreaded out a broad perspective. PSMTs defined the activity as the classroom application that is connected with real life and other disciplines, compatible with the objectives in teaching programs, is designed to improve students' cognitive skills, student-centered, interesting, easy to learn, and appropriate for groupwork. But, it is found out that PSMTs did not reflect the properties of MLA while they were designing the activities. The results of the study indicated that PSMTs' perceptions of activities and their skills of designing an activity must be improved. Extended Abstract Purpose and Significance: In our country, activites play an important role in the Teaching Programs published by Ministry of National Education (MoNE). Regarding the importance of the activities, teachers and students' roles as well as the teaching-learning processes were redefined in our country. Teachers were taken from the position of teaching and took placed to the position of " helper " in order to show the ways of learning of mathematics to students (Saylan & Yurdakul, 2005). At the same time, students moved from passive position to active position, and they started to take the responsibility of their own learning of mathematics (Umay, Duatepe, & Akkuş-Cıkla,

We have used GeoGebra, a dynamic geometry software environment, to explore how Year 4 students understand definitions of angles. Seven students defined angle and then completed several activities adapted for the dynamic environment. Afterward, students again shared their definitions of angles. We found that even a short investigation using dynamic geometry software could support students' development of angle definitions. We share tasks and investigation ideas using GeoGebra to support students' learning about angles.

ABSTRACT This month's problem examines the standing long jump, an Olympic event until 1912. Students will jump as far as they can from a standing position and measure the distance by using different units, such as cubes, feet, and inches. A good problem can capture students' curiosity and can serve many functions in the elementary school classroom: to introduce specific concepts the teacher can build on after students recognize the need for additional mathematics or to help students see where to apply already-learned concepts. We encourage teachers to use the monthly problem and suggested instructional notes in their classrooms and report solutions, strategies, reflections, and misconceptions to the journal audience.

Pre-service secondary mathematics teachers' (PSMTs) understanding and ability of constructing a proof is not only important for their own learning process, but also important for these PSMTs to help their future students learn how to do proofs. Therefore, this study is focused on and explains PSMTs' behaviors that they revealed throughout the proving process of a proposition. In this qualitative case study, the participants were fifteen volunteer PSMTs from a public university in Turkey. The participants were given a proposition which they were asked to think aloud and prove it on the blackboard. The findings of this study show that PSMTs' behaviors and thoughts regarding the given proposition were limited. In detail, PSMTs had difficulties in application of mathematical language and notations, understanding the meaning of the given proposition, knowing where to get started on a proof, using examples efficiently, using appropriate and efficient methods to construct the proof, and defining logical structures of the proposition to construct the proof.

This study describes mathematics education graduate students’
understanding of relationships between sine and cosine of two base
angles in a right triangle. To explore students’ understanding of
these relationships, an elaboration of Skemp’s views of instrumental
and relational understanding using Tall and Vinner’s concept image
and concept definition was developed. Nine students volunteered to
complete three paper and pencil tasks designed to elicit evidence of
understanding and three students among these nine students volunteered
for semi-structured interviews. As a result of fine-grained
analysis of the students’ responses to the tasks, the evidence of
concept image and concept definition as well as instrumental and
relational understanding of trigonometric ratios was found. The unit
circle and a right trianglewere identified as students’concept images,
and the mnemonic was determined as their concept definition for
trigonometry, specifically for trigonometric ratios. It is also suggested
that students had instrumental understanding of trigonometric
ratios while they were less flexible to act on trigonometric ratio tasks
and had limited relational understanding. Additionally, the results
indicate that graduate students’ understanding of the concept of
angle mediated their understanding of trigonometry, specifically
trigonometric ratios.

The concept of angles is one of the foundational concepts to develop of geometric knowledge, but it remains a difficult concept for students and teachers to grasp. Exiting studies claimed that students’ difficulties in learning of the concept of angles are based on learning of the multiple definitions of an angle, describing angles measuring the size of angles, and conceiving different types of angles such as 0-line angles, 1- line angles, and 2-line angles. This study was designed to gain better insight into pre-service secondary mathematics teachers’ (PSMTs) mental constructions of the concept of angles from the perspective of Action-Process-Object-Schema (APOS) learning theory. The study also explains what kind of mental constructions of angles is needed in the right triangle context. The four PSMTs were chosen from two courses at a large public university in the Midwest United States. Using Clements’ (2000) clinical interview methodology, this study utilized three explanatory interviews to gather evidence of PSMTs’ mental constructions of angles and angle measurement. All of the interview data was analyzed using the APOS framework. Consistent with the existing studies, it was found that all PSMTs had a schema for 2-line angles and angle measurement. PSMTs were also less flexible on constructions of 1-line and 0-line angles and angle measurement as it applied to these angles. Additionally, it was also found that although PSMTs do not have a full schema regarding 0-line and 1-line angles and angle measurement, their mental constructions of 1-line and 0-line angles and angle measurement were not required in right triangles, and the schema level for 2-line angles was sufficient for constructions of right triangle context.

The introduction of dynamic geometry software (DGS) has afforded teachers and learners with
new opportunities for mathematical modeling and explorations. Even though some powerful DGS
packages have been available for more than 20 years, they are not widely used in the teaching and
learning of geometry (Laborde, 2001). The goal of this study is to produce a comprehensive review of
research evidence on the roles of DGS in pre-service teachers’ (PSTs) learning of geometry to improve
their education programs. Searches of three databases (ERIC, JSTOR, and PsychINFO) for peer reviewed
articles published in scholarly journals between 2000 and 2012 were conducted. To get a more
comprehensive understanding of the theoretical underpinnings of the roles of DGS, broad search terms
were used, including ‘Dynamic Geometry Software’, ‘DGS’, and ‘PSTs’ using of DGS’. Only empirical
studies including impacts of DGS, how DGS can be used, and the challenges faced by PSTs in using DGS
were used in the analysis

With the advent of the Common Core State Standards (CCSS), more researchers are
eager to learn the features of the new standards and concerned about how the CCSS can
impact their work. This research study will compare the characteristics of the CCSS for
Mathematics (CCSSM) with an array of international written learning expectations for
mathematics. We designed a cross-national study to examine how the topic of quadratic
equations and functions is introduced in four different countries: the Caribbean, China,
Turkey, and the U.S. These standards were analyzed under three dimensions of
characteristics: content, mathematical reasoning, and cognitive level. The results show
that all the standards introduce the foundational concepts of quadratic functions,
however, with various procedural and conceptual expectations.