Matemati̇k Eği̇ti̇mi̇nde Sözsüz İspatlar: Kuramsal Bi̇r Çalişma

Polat, Kübra; Demircioğlu, Handan

doi:10.14582/duzgef.686

DUZGEF

2016

DOI: 10.14582/duzgef.686

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Matemati̇k Eği̇ti̇mi̇nde Sözsüz İspatlar: Kuramsal Bi̇r Çalişma

Kübra Polat¹,

Handan Demircioğlu²

Abstract: Bu çalışmada matematik eğitiminde ispat ve sözsüz ispat kavramlarının rolü ve önemi üzerine odaklanılmıştır. Sözsüz ispatlar; gerçek ispatlar olarak kabul edilemeyecek fakat özel bir ifadenin niçin doğru olduğunu hatta bir matematiksel ifadenin doğruluğunu ispatlarken nasıl ele alınacağının görülmesine yardımcı olacak diyagram veya resimler olarak tanımlanmaktadır. Sözsüz ispatların gerçek ispatlar olup olmadığına dair tartışmaların olmasıyla beraber sözsüz ispatlara yönelik kullanılan ifadelerde de ortak bir … Show more

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Cited by 3 publications

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Investigation of the Effects of Nonverbal Proof Based Education for Preservice Mathematics Teachers

Demircioğlu

2021

International Journal of Educational Studies in Mathematics

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Nonverbal proofs are diagrams or illustrations that will help us see what a mathematical expression means, why it is true, and how it is proved. The aim of this study is to examine the effects of nonverbal proof-based education on preservice mathematics teachers. The study was conducted using case study research methods, one of the qualitative research designs. The participants of the study consisted of 31 preservice mathematics teachers. The data were collected in writing at the beginning and end of the process with questions directed to preservice teachers. These questions in the data collection tool were used to compare the responses of the preservice teachers who had an experience with nonverbal proof in the pre and post assesment and compare the changes. In the analysis of the data, descriptive analysis, which is a qualitative data analysis, was used. Firstly, each preservice teacher's responses in the post assesment are classified according to their similarities and differences and then are categorized. Then, the answers in the pre assesment were examined and the responses were compared whether there was a change or not. The findings of the study showed that the preservice mathematics teachers' experience of nonverbal proof effect on the recognition of the given image and establishing a relationship with different mathematics subjects.

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Investigation of the Effects of Nonverbal Proof Based Education for Preservice Mathematics Teachers

Demircioğlu

2021

International Journal of Educational Studies in Mathematics

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High School Students’ and Their Teacher’s Experiences with Visual Proofs

Polat

Akgün

2023

Erzincan Üniversitesi Eğitim Fakültesi Dergisi

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Proof is one of the main components of both mathematics and mathematics education. However, students and teachers at every level have difficulties in proof and proof teaching. Presenting alternative proof methods to students will not only provide rich learning environment but also allow the student to have different perspectives by providing alternative ways they can apply for constructing a proof. Visual proofs are one of the alternative proof methods. Although visual proofs are considered as useful tools in mathematics education, there are very few studies about the application of these proofs, especially in the high school curriculum. The visual proofs are seen as valuable tools for mathematics education; it is planned to investigate the views of high school students and their teacher about visual proof. Case study method is used in the study. Participants of the study consisted of four high school students who are ninth-graders. For the second semester sixteen activities of visual proofs were applied. Afterwards, interviews were carried out with the students and their teacher about their views on the visual proofs during the instruction period. The teacher said that after the visual proof activities the students started to wonder where the formulas come from, in other words, they started questioning, their interest levels increased, and the formulas were kept in their minds more. The high school students stated that they found the visual proof activities enjoyable, and they were happy when they understood the visual proofs and unhappy when they could not understand them.

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Görsel İspat Becerisinin, van Hiele Geometrik Düşünme Düzeyleri ve Uzamsal Yetenek ile İlişkisi

Polat

Oflaz²,

Akgün³

2019

Erciyes Journal of Education

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In mathematics the process of visualization requires the process of forming and manipulating images to explore and understand. Indeed, according to mathematicians, it is difficult to understand without visualization. There is consensus that visual proofs are important tools in mathematics education. However, there is no consensus on the effects of the visualization on proof. Therefore, this study aims to reveal the relationship between van Hiele levels of geometric thinking, spatial ability and visual proofs. In this study, relational survey method is used. The study is conducted on 85 pre-service elementary mathematics teachers studying in the Faculty of Education at a public university located in Turkey. The data is analyzed via Spearman correlation. In the study, it was seen that most of the elementary mathematics teachers were at the 3rd level of van Hiele's geometric thinking. Another result is that there is a significant relationship between van Hiele's level of geometric thinking and visual proof skills. However, there is no significant relationship between visual proof skills and spatial ability. The relationship between visual proofs skills and spatial ability can be investigated deeply with qualitative research. Moreover, experimental studies can be done to investigate the effect of training on visual proofs on the level of van Hiele geometric thinking.

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Matemati̇k Eği̇ti̇mi̇nde Sözsüz İspatlar: Kuramsal Bi̇r Çalişma

Cited by 3 publications

References 5 publications

Investigation of the Effects of Nonverbal Proof Based Education for Preservice Mathematics Teachers

Investigation of the Effects of Nonverbal Proof Based Education for Preservice Mathematics Teachers

High School Students’ and Their Teacher’s Experiences with Visual Proofs

Görsel İspat Becerisinin, van Hiele Geometrik Düşünme Düzeyleri ve Uzamsal Yetenek ile İlişkisi

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