Mathematically Gifted High School Students’ Approaches to Developing Visual Proofs (VP) and Preliminary Ideas about VP

Uğurel, Işıkhan; Moralı, Hasibe Sevgi; Karahan, Özge; Boz, Burçak

doi:10.18404/ijemst.61686

Cited by 9 publications

(5 citation statements)

References 18 publications

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“…After reviewing the results of numerous studies in this field, it can be summarized that visualization in proof teaching has a positive impact on academic performance in many cases, as evidenced by [20,27,28,30]. However, there are also studies that have shown no effect, as indicated by [35].…”

Section: Discussionmentioning

confidence: 99%

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Graph Theory: Enhancing Understanding of Mathematical Proofs Using Visual Tools

et al. 2023

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Mathematical culture is an essential part of general culture, and mathematical proof is the essence of mathematical culture, which plays an essential role in education for sustainable development. The presented research focuses on the following issue: Can the use of visual tools contribute to a better understanding of mathematical proofs presented within the framework of courses in graph theory? The research focuses on Czech university students of computer science. The presented results were achieved in a pedagogical experiment based on a pre-test, treatment and post-test design carried out during three academic years before the COVID pandemic period. In the pre-test and post-test phases, students were tested to determine their level of mathematical logic knowledge. Visual applications were used in teaching in the treatment phase. The research results clearly showed that the use of visual tools supporting formal explanation of mathematical proofs results in better understanding of the abstraction of the presented process and thus contributes significantly to sustainability in mathematical education. Thanks to the use of the mentioned visual tools during the COVID pandemic period, when schools had to switch to on-line education, the students’ results were comparable to those from face-to-face classes.

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Section: Discussionmentioning

confidence: 99%

“…Demonstration and visualization make the subject much clearer and more comprehensible [17][18][19][20][21]. Teaching/learning model using suitable visual tools represents one of the sustainable trends to develop, pay attention and interest to [22].…”

Section: Graph Theory Educationmentioning

confidence: 99%

Graph Theory: Enhancing Understanding of Mathematical Proofs Using Visual Tools

et al. 2023

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“…Another studies can be found in (Kilic, 2013), (Štrausová, 2012), (Robová, 2013), (Autexier et al 2012), (Knill and Slavkovsky, 2013), (Ugurel et al 2016). …”

Section: Graph Theory At the University Of Hradec Královémentioning

confidence: 99%

Visualization As A Convenient Tool To Support The Teaching Of Mathematical Proofs

Ševčíková¹,

Milková²,

Pekarkova³

2017

European Proceedings of Social and Behavioural Sciences

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Subjects dealing with graph theory and combinatorial optimization belong among the basic subjects of informatics study. Their aim is above all to develop and deepen students' capacity for logical and algorithmic thinking. Mathematical proofs that are inseparable part of these subjects do not belong to popular topics among students due to the difficulty to understand this field of mathematics. Within educational process we are searching for various tools to help students deal with this area of mathematics. Suitable visualization could become a very convenient instrument used to enhance understanding of theorems and their proofs. Using visualization and deep analysis of the topic together with discussion on mutual relationships between solutions to problems allows the teacher to enhance student's logical thinking and support their understanding to more complex proofs. In the paper we provide a justification for the importance of the mathematical proofs for students of informatics at first. Secondly, we introduce a research study examining an impact of visual applications on understanding of mathematical proofs; we implemented presentations instructed within the Discreet mathematics course, which are used to visualize proofs of mathematical theorems in the area of the graph theory, and we analysed students' approaches to proofs visualization and proofing in general.

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“…Heinze and Reiss (2004) state that formal proof can be done by experts, and this will not happen in school mathematics. On the other hand, according to Ugurel, Morali, Karahan and Boz (2016), everyone has the capacity to understand the proofs of theorems. For many students, however, the proof is a ritual without understanding (Ball, Hoyles, Jahnke, & Movshovitz-Hadar, 2002).…”

Section: Introductionmentioning

confidence: 99%

Ortaöğretim Matematik Öğretmen Adaylarının Sözsüz İspat Becerilerinin Bağlamsal İncelenmesi: 1’den n’ye Kadar Olan Tamsayıların Toplamı Durumu

Polat

Demircioğlu

2021

Adıyaman Üniversitesi Eğitim Bilimleri Dergisi

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Recently, studies have been carried out on alternative proof methods due to the change in the perspective of teaching proof and the difficulties of learners in proof. In this context, proof without words, which are presented as an alternative to proof teaching, defined by diagrams or visual representations and require the student to explain how proof is, are discussed in this study. The aim of this study is to examine pre-service mathematics teachers' explanations of proof without words about the sum of consecutive numbers from 1 to n. The data were collected by the proof of the sum of consecutive integers. 27 pre-service teachers from a university in the Middle Anatolia region participated in this study, which was conducted using a basic qualitative research design. At the end of the study, it was seen that most of the preservice teachers were unable to explain the proof without words of the sum of integers from 1 to n. One of the reason for this may be related to the spatial thinking skills of pre-service teachers. However, there are pre-service teachers who can interpret the visual given in the proof correctly, use the necessary mathematical knowledge, but cannot generalize using the given visual. The reasons why the pre-service teachers could not express the general situation are considered as the lack of algebraic thinking.

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Mathematically Gifted High School Students’ Approaches to Developing Visual Proofs (VP) and Preliminary Ideas about VP

Cited by 9 publications

References 18 publications

Graph Theory: Enhancing Understanding of Mathematical Proofs Using Visual Tools

Graph Theory: Enhancing Understanding of Mathematical Proofs Using Visual Tools

Visualization As A Convenient Tool To Support The Teaching Of Mathematical Proofs

Ortaöğretim Matematik Öğretmen Adaylarının Sözsüz İspat Becerilerinin Bağlamsal İncelenmesi: 1’den n’ye Kadar Olan Tamsayıların Toplamı Durumu

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