Philosophy of mathematical practice: a primer for mathematics educators

Hamami, Yacin; Morris, Rebecca Lea

doi:10.1007/s11858-020-01159-5

Cited by 35 publications

(17 citation statements)

References 93 publications

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“…Matematika yang digunakan di tempat kerja juga bersifat praktis. Hasil analisis menunjukkan bahwa filosofi praktik matematika bersifat multidisiplin (Hamami et al, 2020). Oleh karena itu, guru matematika hendaknya memahami struktur matematika terlebih dahulu untuk menerapkannya dalam pengajaran matematika.…”

Section: Pendahuluanunclassified

Koneksi Matematis Siswa pada Tugas Matematis Berbasis Hasil Pertanian: Konteks, Konsep, dan Prosedur Matematis

Fatimah

2021

jel

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The mathematical connection is a crucial ability possessed by vocational high school students in solving problems by their field of expertise. Agriculture is a field of expertise that requires a lot of mathematical connection skills to solve various problems. Increasing the ability of students' mathematical connections can be facilitated by the teacher by constructing mathematical tasks in the agricultural sector. This qualitative research using the case study method describes the construction of mathematical tasks based on agricultural products and the mathematical connection ability of students in solving the task. Mathematical task construction is carried out by integrating agricultural product contexts and mathematical concepts. The mathematical task was used in Grade X Agribusiness Expertise students of Agricultural Product Processing. Data retrieval of students' mathematical connection abilities was carried out through tests, observation results, answer sheets, and interviews that focused on connecting contexts with mathematical concepts, connections between mathematical concepts, and connections to mathematical procedures. The results of the student data analysis showed that the ability of mathematical connections was hampered by the ability of the connection between mathematical concepts. It is necessary to increase student's mathematical connections by constructing mathematical tasks with various mathematical concepts.

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Section: Pendahuluanunclassified

Koneksi Matematis Siswa pada Tugas Matematis Berbasis Hasil Pertanian: Konteks, Konsep, dan Prosedur Matematis

Fatimah

2021

jel

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“…The validity of the theorem in mathematics can be demonstrated by the existence of proof (CadwalladerOlsker, 2011;Ozan et al, 2021). Furthermore, proof and reasoning play important roles to show the truth of the solution of mathematical problems in learning mathematics (Hamami & Morris, 2020;Varghese, 2009;Wittmann, 2021). The ability to construct a proof for mathematicians, mathematics teachers, and mathematics students becomes one of the important things and as an assessment of student performance in learning advanced mathematics such as abstract algebra and real analysis (Moore, 2016;Thomas et al, 2015;Wasserman et al, 2018).…”

Section: Introductionmentioning

confidence: 99%

“…The process of constructing the proof can be seen as a process of mathematical problemsolving (Hamami & Morris, 2020;Nunokawa, 2010;Weber, 2001;Zimmermann, 2016). Problem-solving strategy is often influenced by the knowledge and skill of an individual in obtaining proof solutions (Hughes et al, 2019;Weber, 2001).…”

Section: Introductionmentioning

confidence: 99%

Metacognitive failure in constructing proof and how to scaffold it

Wulan

Subanji

Muksar

2021

ajpm

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This research aims to describe the students’ metacognitive failure in constructing proof and the scaffolding support. The participants of this qualitative case study were eight preservice mathematics teachers of six-semester, State University of Malang. We carried out a test about proof construction problems in Abstract Algebra. Then we verified the data using triangulation of constant comparative method from a test and a task-based interview with the stimulated recall. The results indicated two groups of students in proving strategy. Group I performed “appropriate” syntactic strategy and Group II vice versa. Blindness was experienced by the subject that does not recognize errors detection or the ambiguity of the proof. Mirage occurred when the subject recognizes an error detection on the proper strategy or application of a theorem, then is unable to verify the truth of his work. Misdirection appeared when the subject recognizes a lack of progress, then uses an incomplete or irrelevant concept. Vandalism emerged with no progress or detection of errors of the strategy then the subject performs some irrelevant steps to the issue or uses a misconception. Practically, the teachers can use these results for learning innovations in scaffolding-based proof courses. The scaffolding might need some development and application in supporting students to overcome difficulty in proving mathematical sentences.

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“…Proofs of the latter kind are often called explanatory." (Hamami & Morris, 2020, p. 1119. While intuitive, this distinction has been the subject of much debate.…”

Section: Introductionmentioning

confidence: 99%

“…On the one hand, proving that a theorem holds is independent of human interpretation: it is a matter of providing a rigorous proof. A commonly-used definition is that "a mathematical proof is rigorous whenever it can be routinely translated into a formal proof (Mac Lane 1986, p. 377)" (Hamami & Morris, 2020, p. 1117. Formalization has a long and important history going back through Russell to Leibnitz, who sought for a universal scientific language by which mathematicians could "judge immediately whether propositions presented to us are proved ... with the guidance of symbols alone, by a sure truly analytical method."…”

Section: Introductionmentioning

confidence: 99%

Investigating insight and rigour as separate constructs in mathematical proof

Sangwin¹,

Kinnear²

2021

Preprint

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In this paper we investigate undergraduate mathematics students' conceptions of rigour and insight. We conducted comparative judgement experiments in which students were asked to judge different proofs of the same theorem with five separate criteria: rigour, insight, understanding, simplicity and assessment marks. We predicted, and our experiment found, that rigour is a reliable construct. We predicted that insight is also a reliable construct but asking students to judge on the basis of ``which proof gives you more insight into why a theorem is true'' did not result in a reliable judging scale. Our analysis suggests two distinct dimensions: rigour and marks contribute to one factor whereas simplicity and personal understanding relate to a second factor. We suggest three reasons why insight was related almost equally to both factors. First, while comparative judgement was suitable for assessing some aesthetic criteria it may not be suited to investigating students conceptions of insight. Second, students may not have developed an aesthetic sense in which they appreciate insight in ways which are regularly discussed by mathematics educators. Lastly, insight may not be a coherent and well-defined construct after all.

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Philosophy of mathematical practice: a primer for mathematics educators

Cited by 35 publications

References 93 publications

Koneksi Matematis Siswa pada Tugas Matematis Berbasis Hasil Pertanian: Konteks, Konsep, dan Prosedur Matematis

Koneksi Matematis Siswa pada Tugas Matematis Berbasis Hasil Pertanian: Konteks, Konsep, dan Prosedur Matematis

Metacognitive failure in constructing proof and how to scaffold it

Investigating insight and rigour as separate constructs in mathematical proof

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