Muhammed Fatih Dogan

• PhD
• Adıyaman University

Örnekler matematik yaparken bir öğrenme ve öğretim aracı olarak kullanılmaktadır. Bundan dolayı örnekler matematik öğretim sürecinde merkezi bir rol oynamaktadır. Ancak örneklerin sınıf ortamında matematik öğretimi için nasıl kullanıldığı genellikle öğretmenin ellinde olup, bu süreç her zaman öğrencilerin matematik öğretimini desteklemeyebilir. Bu...

In this study, the mathematical modeling process of in-service middle school mathematics teachers who participated in a mathematical modeling workshop within the scope of a professional development program were examined. This study is a multi-case study with the participation of six teachers (two women; four men) and investigates how teachers handl...

Kaliteli eğitimin bir bileşeni olarak etkili öğretim geleneksel eğitim anlayışında öğrencilerin sınav başarısı ile birebir eşlenirken günümüzde etkili öğretim uygulamaları çok daha kapsamlı olarak ele alınmaktadır. Eğitim-öğretim süreçlerindeki bu yenilikçi bakış açısı doğrultusunda öğretmenlerin öğretim pratiklerinde de yenilikler ve gelişimler sö...

Understanding functional relationships is a critical aspect of students’ algebraic reasoning, and the manner in which students develop early concepts of function provides an important foundation for later ideas in secondary and upper-level mathematics. Typical school treatment of function relies on a correspondence approach, in which function is in...

The teachers' pedagogical understanding of modeling applications is one of the most critical issues in teaching mathematical modeling. The interventions used by the teacher during the implementation of the tasks are the mirror of their pedagogical knowledge. For this reason, teacher interventions, which have a decisive effect on defining the teache...

Artan göç dalgalarıyla birlikte Türkiye’deki okulların kültürel ve etnik yapısı gün geçtikçe daha çeşitli hale gelmiş ve adil matematik öğrenme fırsatlarına odaklanma gerekliliği ortaya çıkmıştır. Bu çalışmanın amacı sınıf öğretmenlerinin ve ortaokul matematik öğretmenlerinin kültürel çeşitlilik gösteren öğrencilerin matematik öğrenme fırsatlarına...

Bu bölümde bir matematiksel modelleme probleminin bir ortaokul sınıfındaki uygulama süreci detaylı olarak ele alınmıştır.

Bu araştırmanın amacı, hata temelli aktivitelerin 7. Sınıf veri analizi alt öğrenme alanına ait çizgi grafiği, ortalama, medyan ve mod kavramlarını öğrenmeye etkisini belirlemektir. Araştırma hatalı örneklerle istatistik kavramlarının öğretilmesine dayalı yarı deneysel bir çalışma modelidir. Çalışmanın katılımcıları 2018-2019 öğretim yılında 7. sın...

This paper explores how in-service teachers enrolled in a graduate proof course interpret, understand, and use generic examples as part of their proving and justification activities. Generic examples, which are capable of proving and justifying with strong explanatory power, are particularly important for teachers considering teaching proof in thei...

This paper introduces a quadratic growth learning trajectory, a series of transitions in students’ ways of thinking (WoT) and ways of understanding (WoU) quadratic growth in response to instructional supports emphasizing change in linked quantities. We studied middle grade (ages 12–13) students’ conceptions during a small-scale teaching experiment...

This study aims to examine pre-service teachers' competencies in designing authentic mathematical modelling tasks. The participants of this study were 22 pre-service teachers enrolled in a mathematical modelling course during their second year in a mathematics teacher education program. The participants designed 20 problems, which were evaluated ba...

This study investigated how pre-service teachers evaluate mathematical arguments including generic examples. By using written responses of 71 PSTs, the results revealed six criteria used by PSTs, which were being explanatory, being general, correctness, mode of representation, mode of argumentation, and structure of the argument. The criteria sugge...

Bu bölümde, “İspat nedir?”, “İspat etkinliği nedir?”, “İspat yapma sürecin- de öğrencinin ve öğretmenin rolü nelerdir?” ve “Matematik derslerinde ispat yapma etkinlikleri uygulanırken nelere dikkat edilmelidir?” sorularına cevap aranmaktadır. Bu bağlamda, farklı sınıf seviyelerine uygun bir ispat tanımı paylaşılmakta ve ispat öğretiminin üç temel b...

Bu çalışmanın amacı, matematiksel modellemeyle ilgili bir çalıştaya katılan matematik ve fen bilimleri öğretmenlerinin matematiksel modelleme anlayışlarının değişimini incelemektir. Çalışma 2018-2019 eğitim öğretim yılında, Adıyaman’daki çeşitli ortaokullarda görev yapan 9 matematik ve 9 fen bilimleri öğretmeninin katılımıyla gerçekleşmiştir. Öğret...

Bir durum çalışması olan bu çalışmanın amacı matematiksel modelleme ve disiplinler arası matematiksel modelleme konulu kapsamlı bir eğitime katılmadan önce matematik ve fen bilimleri öğretmenlerinin disiplinler arası matematiksel modelleme problemlerinin özellikleri ve bu tür problemlerin sınıfta uygulanabilirliğine yönelik mevcut bilgilerini ortay...

Although reasoning and proof in learning and teaching mathematics is crucial and have gained more presence in school mathematics, both students and their teachers face great difficulties when engaging in proving activities. One potential cause for such difficulties might be due to teachers' conception of proof. However, to date, there are few, if a...

This study examined the criteria used by prospective mathematics teachers in determining whether a problem was a mathematical modeling problem. Two data collection tools were used in this case study. The first was a written evaluation form which consists of four problems developed by 27 prospective teachers individually that enrolled in a Mathemati...

This paper argues for creating learning trajectories of children's mathematics by integrating evidence of shifts in the mathematics of students, theory of goal-directed instructional design, and evidence of instructional supports. We networked two theories in support of this stance: a radical constructivist theory of learning, and Duality, Necessit...

Farklı disiplinlerin birlikte ele alındığı yaklaşımlar son yıllarda eğitim sisteminde etkisini daha çok hissettirmeye başlamıştır. Bu araştırmada bir Disiplinler Arası Matematiksel Modelleme (DMM) etkinliğinin çözüm sürecinde ortaya çıkan durumların incelenmesi amaçlanmıştır. Bir durum çalışması olan araştırmanın çalışma grubunu, 9 matematik ve 9 f...

Mathematical play has a fairly short history, with strong roots further back in time (e.g., Papert, Montessori), and understanding the role of mathematical play from early childhood to adulthood is, as yet, unmapped. This working group will provide a community space to explore and discuss mathematical play broadly, ranging from early childhood to u...

ABSTRACT: This study aimed to analyze the role of computer-assisted instruction (CAI) on students’ achievement concerning the subject of ‘probability’. The experimental pre-and post-test with control group research design was carried out with 48 seventh grade students by conducting The Probability Achievement Test (PAT) to all groups. Data were ana...

Understanding function is a critical aspect of algebraic reasoning, and building up functional relationships is an activity increasingly encouraged at the elementary and middle school levels. This study identifies how one group of middle-school students leveraged their rate of change thinking to inform the development and understanding of correspon...

A persistent challenge in supporting students' proof activity is fostering the transition from less formal, empirical arguments to formal deductive arguments. A number of researchers have begun to investigate students' thinking with examples, addressing how example use can support conjecture understanding, exploration, and proof. We extend this lin...

Examples can be a powerful tool for students to learn to prove, particularly if used purposefully and strategically, but there is a pressing need to better understand the nature of productive example use. Therefore, we examined the characteristics of the successful and unsuccessful cases of proving in the context of a number theory task across the...

This study characterizes s of quadratic function from a variation perspective in the context of a quantitatively rich instructional setting. We studied middle grade (ages 12-13) ceptions during a small-scale teaching experiment aimed at fostering an understanding of quadratic function as a growth situation with a constant difference in rate of chan...

This paper explores the nature of students' quantitative reasoning and conceptions of functions supporting their ability to symbolize quadratic function rules, and the meanings students make of these rules. We analyzed middle school students' problem solving activity during a small group teaching experiment (n=6) emphasizing quadratic growth throug...

This article presents an Exponential Growth Learning Trajectory (EGLT), a trajectory identifying and characterizing middle grade students’ initial and developing understanding of exponential growth as a result of an instructional emphasis on covariation. The EGLT explicates students’ thinking and learning over time in relation to a set of tasks and...

Examples play a critical role in the exploration and proving of conjectures. Although proof has been studied extensively, the precise ways in which examples might facilitate successful proofs are not well documented or understood. Working within a larger set of studies that argue for the value of examples in proof-related activity, in this paper we...

The role of the body, particularly gesture, in supporting mathematical reasoning is an emerging area of research in mathematics education. In the present study, we examine students providing a justification for a task about a system of alternating gears, which captures key concepts of number in terms of even/odd patterns. Some participants were dir...

Gesture and language are deeply intertwined, and attending to both simultaneously when examining mathematical processes is a complex yet rewarding task. We share our budding research methodology for analyzing gesture and language and discuss the methodology from a generic perspective that can be easily adapted to different contexts, participants, a...

This paper presents the results of two studies aimed at identifying the ways in which successful provers (students and mathematicians) engage with examples when exploring and proving conjectures. We offer a framework detailing the participants' actions guiding a) their example choice and b) their example use as they attempt to prove conjectures. Th...

Although students' difficulties in developing and understanding proofs in mathematics is well documented, less is known about how students' example use may support their proof practices, particularly at the middle school level. Research on example use suggests that strategic thinking with examples could play an important role in exploring conjectur...

Examples play a critical role in mathematical practice, particularly in the exploration of conjectures and in the subsequent development of proofs. Although proof has been an object of extensive study, the role that examples play in the process of exploring and proving conjectures has not received the same attention. In this paper, we present a fra...