Ayhan Kursat Erbas

The Contribution of Personality Traits, Motivation, Academic Risk-Taking and Metacognition to the Creative Ability in Mathematics

The purpose of this study was to investigate the extent to which personality traits, motivation, academic risk-taking, and metacognition explain the mathematical creative ability of high school students. The participants were 217 9th-grade students that were exceptionally high achievers. The participants responded to a set of measures about personality traits, motivation, academic risk-taking, metacognition, and creative ability in mathematics. The results revealed that although openness to experience and consciousness were significantly correlated with creative ability in mathematics, extraversion, agreeableness, and neuroticism were not correlated with the creativity scores. Moreover, intrinsic goal orientation followed by openness to experience was the most significant predictor of mathematical creative ability. Academic risk-taking was not significantly correlated with creative ability. Although knowledge of cognition and regulation of cognition showed moderate correlations with creative ability in mathematics, they failed to predict creative ability.

Developing teachers' models for assessing students' competence in mathematical modelling through lesson study

ABSTRACT Applications and modelling have gained a prominent role in mathematics education reform documents and curricula. Thus, there is a growing need for studies focusing on the effective use of mathematical modelling in classrooms. Assessment is an integral part of using modelling activities in classrooms, since it allows teachers to identify and manage problems that arise in various stages of the modelling process. However, teachers’ difficulties in assessing student modelling work are a challenge to be considered when implementing modelling in the classroom. Thus, the purpose of this study was to investigate how teachers’ knowledge on generating assessment criteria for assessing student competence in mathematical modelling evolved through a professional development programme, which is based on a lesson study approach and modelling perspective. The data was collected with four teachers from two public high schools over a five-month period. The professional development programme included a cyclical process, with each cycle consisting of an introductory meeting, the implementation of a model-eliciting activity with students, and a follow-up meeting. The results showed that the professional development programme contributed to teachers’ knowledge for generating assessment criteria on the products, and the observable actions that affect the modelling cycle.

Pre-service Teachers’ Developing Conceptions about the Nature and Pedagogy of Mathematical Modeling in the Context of a Mathematical Modeling Course

ABSTRACT Adopting a multitiered design-based research perspective, this study examines pre-service secondary mathematics teachers’ developing conceptions about (a) the nature of mathematical modeling in simulations of “real life” problem solving, and (b) pedagogical principles and strategies needed to teach mathematics through modeling. Unlike other studies that have focused on single-topic and lesson-sized research sites, a course-sized research site was used in this study. Having been through several iterations over three teaching semesters, the 15-week long course was implemented with 25 pre-service secondary mathematics teachers. Findings revealed that pre-service teachers developed ideas about the nature of mathematical modeling involving what mathematical modeling is, the relationship between mathematical modeling and meaningful understanding, and the nature of mathematical modeling tasks. They also realized the changing roles of teachers during modeling implementations and diversity in students’ ways of thinking. The researchers’ conceptual development, on the other hand, involved realizing the critical aspect of the “teacher role” played by the instructor during modeling implementations, and the need for more experience of modeling implementations for pre-service teachers.

Mathematics teachers’ knowledge and skills about questioning in the context of modeling activities

Abstract Asking effective questions has been considered to be one of the most important indicators of good teaching since questioning is an important instructional tool and the ability to ask effective questions requires sophisticated pedagogical reasoning. Teachers can facilitate students’ higher-level thinking through effective questions. However, teachers’ utilization of effective and higher-level questions is usually limited in traditional settings. The goal of this study is to investigate how secondary mathematics teachers’ knowledge and skills of questioning change when they are engaged in professional development activities based on the modeling perspective. The program included five cycles each of which lasted a month. Each cycle consisted of meetings before and after the implementation of a model-eliciting activity and its implementation. The results showed that the professional development program had a positive effect on teachers’ ability to ask qualitatively different questions in order to move students’ thinking forward.

İlköğretim Matematik Öğretmen Adaylarının Değişim Oranı ile İlgili Düşünme Biçimlerinin Bir Modelleme Etkinliği Bağlamında İncelenmesi

Ogretmen adaylarinin matematiksel modelleme konusunda mesleki bilgi ve becerilerini gelistirmeyi hedefleyen genis kapsamli bir calismanin parcasi olarak, bu calismada nufus artisini konu alan bir modelleme etkinligi baglaminda ilkogretim matematik ogretmen adaylarinin “degisim orani” kavrami uzerine dusunme bicimleri incelenmektedir. Calismanin katilimcilarini bir devlet universitesinin ilkogretim matematik ogretmenligi bolumunde son sinifa devam eden 9 ogretmen adayi olusturmaktadir. Bir matematiksel modelleme dersi kapsaminda yapilan calismanin veri kaynaklarini; grup calismalarindan derlenen yazili raporlar ve calisma kâgitlari, etkinlik sonrasi dusunce raporlari ve arastirmaci alan notlari olusturmaktadir. Bulgulara gore, calismanin katilimcilari “zamana bagli nufus artis orani (hizi)” ifadesini yuzdelik ve egim olmak uzere iki farkli sekilde yorumlamistir. Ogretmen adaylarinin yuzdelik yorumlari daha yogun olmakla birlikte modelleme etkinligi baglaminda nufus verilerindeki yil araliklarinin esit verilmemesi bazi katilimcilari egim yorumuna yonlendirmistir. Ortaya cikan bu iki farkli dusunme sekli, ogretmen adaylarinin yuzdelik ve egim yorumu arasindaki farki ve bu ikisi arasindaki matematiksel iliskiyi yorumlamada zorlandiklarini gostermektedir. Ayrica “rate of change” kavraminin Turkce ifadesi ile ilgili problemli bir durum da gozlemlenmistir. Calismanin sonuclari, ogretmen adaylarinin konu ile ilgili zorluklarinin muhtemel kaynagi olan birimli oran ve birimsiz oran kavramlari arasindaki fark dikkate alinarak tartisilmistir.