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Kurt Gödel wrote (1964, p. 272), after he had read Husserl, that the notion of objectivity raises a question: "the question of the objective existence of the objects of mathematical intuition (which, incidentally, is an exact replica of the question of the objective existence of the outer world)". This "exact replica" brings to mind the close analogy Husserl saw between our intuition of essences in Wesensschau and of physical objects in perception. What is it like to experience a mathematical proving process? What is the ontological status of a mathematical proof? Can computer assisted provers output a proof? Taking a naturalized world account, I will assess the relationship between mathematics, the physical world and consciousness by introducing a significant conceptual distinction between proving and proof. I will propose that proving is a phenomenological conscious experience. This experience involves a combination of what Kurt Gödel called intuition, and what Husserl called intentionality. In contrast, proof is a function of that process - the mathematical phenomenon - that objectively self-presents a property in the world, and that results from a spatiotemporal unity being subject to the exact laws of nature. In this essay, I apply phenomenology to mathematical proving as a performance of consciousness, that is, a lived experience expressed and formalized in language, in which there is the possibility of formulating intersubjectively shareable meanings., (Copyright © 2015. Published by Elsevier Ltd.)

Copyright of International Journal of Educational Psychological Studies (EPS) is the property of Refaad for Studies, Research & Development and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

This research aims to determine the influence of learning independence, gender, and mathematical beliefs on mathematical proof. This research uses a survey method with correlational analysis. The population in this study were students from one of the Ngawen 1 High Schools and sampling using the Purposive Sampling technique for this research was students in classes X.6, X.8, and XI.9. The instruments used are mathematics proof tests and non-test instruments in the form of independence learning questionnaires and mathematics beliefs questionnaires using the Linkert Scale. Data analysis was carried out using the SPSS 23.0 program, consisting of descriptive analysis, data analysis prerequisite tests, and hypothesis testing. This research concludes that together learning independence, gender, and mathematical beliefs have an effect on mathematical proofs, learning independence has a positive effect on mathematical proofs, gender has no effect on mathematical proofs, mathematical beliefs have no effect on mathematical proofs, students in class X.6, X.8 and XI.9 SMA N 1 Ngawen.

This research article is about "Introducing a Supportive Framework to Address Students' Misconceptions and Difficulties in Learning Mathematical proof techniques (MPT): A Case of Debark University". This study aims to develop, introduce, and implement a supportive framework to overcome students' misconceptions and difficulties in MPT. The framework, named IR2CP2CE, was developed, introduced, and implemented at Debark University in Ethiopia using various data-gathering instruments such as questionnaires, interviews, classroom observations, and document analysis from students and instructors. The study collected data over four months, including the implementation of a supportive framework using mixed, quasi-experimental, and pragmatism research approaches, designs, and paradigms respectively. The internal reliability of the data-gathering instruments was interpreted using Cronbach's coefficient, Spearman-Brown, Spearman correlations, Kuder-Richardson 20 and 21, and difficulty and discrimination indices. The results showed that the implementation of the supportive framework led to significant improvements in students' academic performance in MPT, regardless of factors such as gender, academic year category, and preliminary knowledge and proving skills. This study recommends additional imperatives for practice and future research. [ABSTRACT FROM AUTHOR]

Argumentation as an aspect of problem-solving has been studied in mathematics education. However, mathematical proof still needs to be resolved further. This study investigates students' mathematical argumentation skills when proving mathematical statements based on their self-efficacy. The research subjects were 43 mathematics education students at a university in Aceh Province who had taken a number theory course. The study used a qualitative approach with a case study design: students’ mathematical proving self-efficacy. Data was obtained using self-efficacy questionnaires and mathematical proof test instruments that experts have validated, while the data triangulation used was an in-depth interview. The results of this study reveal that students' mathematical argumentation skills in proving mathematical statements have differences based on their self-efficacy. The mathematical argumentation ability of students with high self-efficacy involves all aspects of argumentation well so that the construction of the proof is scientifically correct. Meanwhile, the argumentation ability of students with moderate or low self-efficacy still does not involve essential aspects of argumentation. So, the proof results are not scientifically correct because they have not arrived at the proper conclusion.

Experiences at the educational personnel education institution, Department of Mathematics Education Institute of Teacher Training and Education Pontianak (IKIP) shows that students often had difficulty in proving propositions (theorems in mathe-matics). The alternative offered through this study was to develop students' abilities in proof through mathematical communication. The study method used in this study was qualitive research, case study. The subjects used in this study consisted of two un-dergraduate students who had been taught real analysis introductions and. The data collection tool used was tests and interview. Data analysis techniques used was de-scriptions: data reduction, data display and conclusion. Based on the results of re-search, study of theory and discussion, it could be concluded in this study that the student obstacles in answering mathematical proof questions are the students have difficulty in writing mathematical symbolic and inability in mathematical proof. But after being given didactic anticipation by mathematical communication, the ability of students to answer mathematical proof questions has increased. Thus, mathematical communication can be used as an alternative to overcome obstacles or difficulties for students in solving mathematical proof problems.

Copyright of Necatibey Faculty of Education Electronic Journal of Science & Mathematics Education is the property of Balikesir University, Necatibey Faculty of Education and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

This study aims to comprehensively analyze the improvement of students ' mathematical development ability through the concept of three zone learning, with the type of research is quantitative and quasi experiment design. Examples of research as many as two classes amounted to 82 pre service teacher. Data analysis by calculating gain normalization. Results: based on the Post Hoc test, the level of the category that has a positive score of 0.012 with the upper category and the middle category means that the average score of students from the upper category is better than the middle category, then also for the level that has a positive score of 0.028 with the upper category and the lower category which means that the average score of students from the upper category is better than the lower category. As for the positive value of 0.016 with the middle category and the lower category means the average of the middle category is better. From the results showed that for levels with upper, middle and lower categories, the effect is greater in improving students.

The emerging of formal mathematical proof is an essential component in advanced undergraduate mathematics courses. Several colleges have transformed mathematics courses by facilitating undergraduate students to understand formal mathematical language and axiomatic structure. Nevertheless, college students face difficulties when they transition to proof construction in mathematics courses. Therefore, this descriptive-explorative study explores prospective teachers' mathematical proof in the second semester of their studies. There were 240 pre-service mathematics teachers at a state university in Surabaya, Indonesia, determined using the conventional method. Their responses were analyzed using a combination of Miyazaki and Moore methods. This method classified reasoning types (i.e., deductive and inductive) and types of difficulties experienced during the proving. The results conveyed that 62.5% of prospective teachers tended to prefer deductive reasoning, while the rest used inductive reasoning. Only 15.83% of the responses were identified as correct answers, while the other answers included errors on a proof construction. Another result portrayed that most prospective teachers (27.5%) experienced difficulties in using definitions for constructing proofs. This study suggested that the analytical framework of the Miyazaki-Moore method can be employed as a tool to help teachers identify students' proof reasoning types and difficulties in constructing the mathematical proof.

Tujuan penelitian ini adalah untuk mendiskripsikan penerapan strategi REACT (Relating, Experiencing, Applying, Cooperating, Transferring) untuk mengembangkan kemampuan mahasiswa dalam mengkonstruksi bukti. Jenis penelitian yang digunakan adalah deskriptif dengan pendekatan kualitatif. Subjek penelitian adalah mahasiswa program studi pendidikan matematika yang sedang menempuh mata kuliah Analisis Real. Hasil peneltian adalah strategi yang diberikan berupa memberi kesempatan kepada mahasiswa untuk menghubungkan teorema satu dengan teorema lain (Relating), menuliskan kembali bukti sesuai dengan bahasa sendiri dan penggunaan bukti non formal sebagai bantuan (Experiencing), memanipulasi bentuk pernyataan berdasarkan prinsip logika dasar (Applying), saling memeriksa kebenaran proses pembuktian (Cooperating), dan membuktikan pernyataan yang dikembangkan (Transferring). REACT berdampak pada berkembangnya kemampuan mahasiswa dalam mengonstruksi bukti yaitu mahasiswa mampu menggunakan teroema sebelumnya untuk digunakan dalam proses pembuktian, melakukan manipulasi bentuk logika matematika sebagai strategi awal memulai proses pembuktian, menggunakan bantuan bukti non formal untuk menentukan langkah pembuktian selanjutnya, memeriksa kevalidan proses pembuktian dan mampu melakukan pembuktian kontradiksi. The concern of this study is to describe the application of REACT (Relating, Experiencing, Applying, Cooperating, Transferring) strategies to develop students' abilities in constructing evidence. This type of research used is descriptive with a qualitative approach. The research subjects were students of mathematics education study programs who were taking Real Analysis courses. The result of the research is a strategy given in the form of allowing students to connect one theorem with another (Relating), rewriting evidence according to their language and using non-formal evidence as an aid (Experiencing), manipulating statement forms based on basic logic principles (Applying), checking the correctness of the verification process (cooperating), and proving the statements developed (Transferring). REACT has an impact on the development of students' abilities in constructing evidence, namely students can use the previous theorem to be used in the proving process, manipulate mathematical logic forms as an initial strategy to start the proof process, use non-formal evidence to determine the next step of evidence, check the validity of the proof process and be able to do a proof of contradiction.

Abstract: Various mathematical abilities require a high level of struggle to be achieved, one of which is the ability to solve mathematical proof problems. Several factors are also associated with this ability, including adversity quotient and resilience. This research aimed to look at the effect of adversity quotient and resilience on the mathematical proof problem-solving ability. This research used a quantitative approach with a correlational method. The sample in this study were 31 students randomly selected from all students of the Mathematics Education Study Program at Universitas Sulawesi Barat who programmed Abstract Algebra course in the academic year of 2019/2020, amounting to 71 students. The analysis technique used is multiple linear regressions. The results of hypothesis testing indicate that adversity quotient and resilience affect the mathematical proof problem-solving ability positively both individually and simultaneously. Abstrak: Berbagai kemampuan matematis memerlukan daya juang tinggi untuk berhasil dicapai, salah satunya kemampuan pemecahan masalah pembuktian matematis. Beberapa faktor pun dikaitkan dengan kemampuan tersebut, antara lain adversity quotient dan resiliensi. Penelitian ini bertujuan untuk melihat pengaruh adversity quotient dan resiliensi terhadap kemampuan pemecahan masalah pembuktian matematis. Penelitian ini menggunakan pendekatan kuantitatif dengan metode korelasional. Sampel pada penelitian ini sebanyak 31 mahasiswa yang dipilih secara acak dari seluruh mahasiswa Program Studi Pendidikan Matematika Universitas Sulawesi Barat yang memprogramkan mata kuliah Struktur Aljabar tahun akademik 2019/2020 yang berjumlah 71 mahasiswa. Teknik analisis yang digunakan adalah regresi linear berganda. Hasil pengujian hipotesis menunjukkan bahwa adversity quotient dan resiliensi berpengaruh positif terhadap kemampuan pemecahan masalah pembuktian matematis baik secara sendiri-sendiri maupun secara simultan.

Group Isomorphism is one of the sub topic in the Algebra Structure. This sub topic required prerequisite material about the bijective function. If this prerequisite material is not mastered, it will be difficult to study Isomorphism Group material. There are still many students who found difficulties to solve probative questions about Group Isomorphism. The major problem are they were forgetting and not understanding the prerequisite material. Therefore, it should be a further research on the ability of students to prove the questions of proof and errors in preparing evidence about Group Isomorphism.

Intending to improve the teaching and learning of the notion of mathematical proof this study seeks to uncover the kinds of flaws in postgraduate mathematics education student teachers. Twenty-three student teachers responded to a proof task involving the concepts of transposition and multiplication of matrices. Analytic induction strategy that drew ideas from the literature on evaluating students’ proof understanding and Yang and Lin’s model of proof comprehension applied to informants’ written responses to detect the kinds of flaws in postgraduates’ proof attempts. The study revealed that the use of empirical verifications was dominant and in situations. Whereby participants attempted to argue using arbitrary mathematical objects, the cases considered did not represent the most general case. Flawed conceptualizations uncovered by this study can contribute to efforts directed towards fostering strong subject content command among school mathematics teachers.

Several studies related to mathematical proof have been done by many researchers on high-level materials, but not yet examined on the material of transformation geometry. The aim of this research is identification learning obstacles pre-service teachers on transformation geometry. This study is qualitative research; data were collected from interview sheets and test. There were four problems given to 9 pre-service mathematics teachers. The results of this research were as follows: learning obstacles related to the difficulty in applying the concept; related to visualize the geometry object; related to obstacles in determining principle; related to understanding the problem and related obstacles in mathematical proofs such as not understanding and unable to express a definition, not knowing to use the definition to construct the proof, not understanding the use of language and mathematical notation, not knowing how to start the proof.

An increasing number of learning goals refer to the acquisition of cognitive skills that can be described as ‘resource-based,’ as they require the availability, coordination, and integration of multiple underlying resources such as skills and knowledge facets. However, research on the support of cognitive skills rarely takes this resource-based nature explicitly into account. This is mirrored in prior research on mathematical argumentation and proof skills: Although repeatedly highlighted as resource-based, for example relying on mathematical topic knowledge, methodological knowledge, mathematical strategic knowledge, and problem-solving skills, little evidence exists on how to support mathematical argumentation and proof skills based on its resources. To address this gap, a quasi-experimental intervention study with undergraduate mathematics students examined the effectiveness of different approaches to support both mathematical argumentation and proof skills and four of its resources. Based on the part-/whole-task debate from instructional design, two approaches were implemented during students’ work on proof construction tasks: (i) a sequential approach focusing and supporting each resource of mathematical argumentation and proof skills sequentially after each other and (ii) a concurrent approach focusing and supporting multiple resources concurrently. Empirical analyses show pronounced effects of both approaches regarding the resources underlying mathematical argumentation and proof skills. However, the effects of both approaches are mostly comparable, and only mathematical strategic knowledge benefits significantly more from the concurrent approach. Regarding mathematical argumentation and proof skills, short-term effects of both approaches are at best mixed and show differing effects based on prior attainment, possibly indicating an expertise reversal effect of the relatively short intervention. Data suggests that students with low prior attainment benefited most from the intervention, specifically from the concurrent approach. A supplementary qualitative analysis showcases how supporting multiple resources concurrently alongside mathematical argumentation and proof skills can lead to a synergistic integration of these during proof construction and can be beneficial yet demanding for students. Although results require further empirical underpinning, both approaches appear promising to support the resources underlying mathematical argumentation and proof skills and likely also show positive long-term effects on mathematical argumentation and proof skills, especially for initially weaker students.

An increasing number of learning goals refer to the acquisition of cognitive skills that can be described as 'resource-based,' as they require the availability, coordination, and integration of multiple underlying resources such as skills and knowledge facets. However, research on the support of cognitive skills rarely takes this resource-based nature explicitly into account. This is mirrored in prior research on mathematical argumentation and proof skills: Although repeatedly highlighted as resource-based, for example relying on mathematical topic knowledge, methodological knowledge, mathematical strategic knowledge, and problem-solving skills, little evidence exists on how to support mathematical argumentation and proof skills based on its resources. To address this gap, a quasi-experimental intervention study with undergraduate mathematics students examined the effectiveness of different approaches to support both mathematical argumentation and proof skills and four of its resources. Based on the part-/whole-task debate from instructional design, two approaches were implemented during students' work on proof construction tasks: (i) a sequential approach focusing and supporting each resource of mathematical argumentation and proof skills sequentially after each other and (ii) a concurrent approach focusing and supporting multiple resources concurrently. Empirical analyses show pronounced effects of both approaches regarding the resources underlying mathematical argumentation and proof skills. However, the effects of both approaches are mostly comparable, and only mathematical strategic knowledge benefits significantly more from the concurrent approach. Regarding mathematical argumentation and proof skills, short-term effects of both approaches are at best mixed and show differing effects based on prior attainment, possibly indicating an expertise reversal effect of the relatively short intervention. Data suggests that students with low prior attainment benefited most from the intervention, specifically from the concurrent approach. A supplementary qualitative analysis showcases how supporting multiple resources concurrently alongside mathematical argumentation and proof skills can lead to a synergistic integration of these during proof construction and can be beneficial yet demanding for students. Although results require further empirical underpinning, both approaches appear promising to support the resources underlying mathematical argumentation and proof skills and likely also show positive long-term effects on mathematical argumentation and proof skills, especially for initially weaker students. [ABSTRACT FROM AUTHOR]

The Euclidean ideal of mathematics as well as all the foundational schools in the philosophy of mathematics have been contested by the new approach, called the "maverick" trend in the philosophy of mathematics. Several points made by its main representatives are mentioned - from the revisability of actual proofs to the stress on real mathematical practice as opposed to its idealized reconstruction. Main features of real proofs are then mentioned; for example, whether they are convincing, understandable, and/or explanatory. Therefore, the new approach questions Hilbert's Thesis, according to which a correct mathematical proof is in principle reducible to a formal proof, based on explicit axioms and logic. [ABSTRACT FROM AUTHOR]

Algebraic thinking, combinatorial thinking and reasoning skills are considered as playing central roles within teaching and learning in the field of mathematics, particularly in solving complex open-ended mathematical problems Specific relations between these three abilities, manifested in the solving of an open-ended ill-structured problem aimed at mathematical modeling, were investigated. We analyzed solutions received from 33 groups totaling 131 students, who solved a complex assignment within the mathematical contest Mathematics B-day 2018. Such relations were more obvious when solving a complex problem, compared to more structured closed subtasks. Algebraic generalization is an important prerequisite to prove mathematically and to solve combinatorial problem at higher levels, i.e., using expressions and formulas, therefore a special focus should be put on this ability in upper-secondary mathematics education.

An interview with Charles McCarty by Piotr Urbańczyk concerning mathematical explanation.