scholarly journals UNDERSTANDING ON STRATEGIES OF TEACHING MATHEMATICAL PROOF FOR UNDERGRADUATE STUDENTS

2018 ◽  
Vol 37 (2) ◽  
Author(s):  
Syamsuri Syamsuri ◽  
Indiana Marethi ◽  
Anwar Mutaqin
Keyword(s):  
Undergraduate Students ◽  
Mathematical Thinking ◽  
Mathematical Proof ◽  
Public University ◽  
Structural Method ◽  
Worked Example ◽  
Proof Construction ◽  
Main Instrument

Abstract:Many researches revealed that many students have difficulties in constructing proofs. Based on our empirical data, we develop a quadrant model to describe students’ classification of proof result. The quadrant model classifies a students’ proof construction based on the result of mathematical thinking. The aim of this article is to describe a students’ comprehension of proof based on the quadrant model in order to give appropriate suggested learning. The research is an explorative research and was conducted on 26 students majored in mathematics education in public university in Banten province, Indonesia. The main instrument in explorative research was researcher itself. The support instruments are proving-task and interview guides. These instruments were validated from two lecturers in order to guarantee the quality of instruments.Based on the results, some appropriate learning activities should be designed to support the students’ characteristics from each quadrant, i.e: a hermeneutics approach, using the two-column form method, learning using worked-example, or using structural method. Keywords:proof, proving learning, undergraduate, quadrant model   MEMAHAMI STRATEGI PENGAJARAN PEMBUKTIAN MATEMATIS DI PERGURUAN TINGGI Abstrak: Banyakpeneliti pendidikan matematika menyatakan bahwa siswa mengalami kesulitan dalam mengonstruksi bukti. Berdasarkan kajian empiris, penulis membangun suatu model kuadran untuk mendeskripsikan kategori konstruksi bukti yang dibangun siswa. Model kuadran tersebut mengklasifikasikan konstruksi bukti berdasarkan cara berpikir matematis saiwa. Adapun tujuan dari artikel ini ialah mendeskripsikan pemahaman siswa dalam mengonstruksi bukti berdasarkan model kuadran serta memberikan saran strategi pembelajarannya. Penelitian ini merupakan penelitian eksploratif yang melibatkan 26 mahasiswa Jurusan Pendidikan Matematika pada universitas negeri di Provinsi Banten. Instrumen utama dalam penelitian eksploratif adalah peneliti sendiri. Instrumen pendukungnya ialah tugas pembuktian matematis dan panduan wawancara. Kedua instrumen pendukung tersebut telah divalidasi untuk menjamin kualitas instrumen yang digunakan. Hasil penelitian ini memberikan saran terkait aktivitas pembelajaran yang seharusnya dilakukan oleh pengajar agar sesuai dengan karakteristik berpikir siswa dalam mengonstruksi bukti pada masing-masing kuadran, misalnya : pendekatan heurmenistik, menggunakan metode dua-kolom, pembelajaran worked-example ataupun menggunakan metode terstruktur. Kata Kunci: bukti, pengajaran bukti, mahasiswa, model kuadran

Using Moment-by-Moment Reading Protocols to Understand Students’ Processes of Reading Mathematical Proof

2021 ◽  
Vol 52 (5) ◽  
pp. 510-538
Author(s):  
Paul Christian Dawkins ◽  
Dov Zazkis
Keyword(s):  
Undergraduate Students ◽  
Mathematical Proof ◽  
Think Aloud ◽  
Reading Behaviors ◽  
Mathematical Proofs ◽  
Think Aloud Protocols ◽  
Set Up ◽  
Novice Readers ◽  
The Way

This article documents differences between novice and experienced undergraduate students’ processes of reading mathematical proofs as revealed by moment-by-moment, think-aloud protocols. We found three key reading behaviors that describe how novices’ reading differed from that of their experienced peers: alternative task models, accrual of premises, and warranting. Alternative task models refer to the types of goals that students set up for their reading of the text, which may differ from identifying and justifying inferences. Accrual of premises refers to the way novice readers did not distinguish propositions in the theorem statement as assumptions or conclusions and thus did not use them differently for interpreting the proof. Finally, we observed variation in the type and quality of warrants, which we categorized as illustrate with examples, construct a miniproof, or state the warrant in general form.

scholarly journals DEDUCTIVE OR INDUCTIVE? PROSPECTIVE TEACHERS’ PREFERENCE OF PROOF METHOD ON AN INTERMEDIATE PROOF TASK

2020 ◽  
Vol 11 (3) ◽  
pp. 417-438
Author(s):  
Tatag Yuli Eko Siswono ◽  
Sugi Hartono ◽  
Ahmad Wachidul Kohar
Keyword(s):  
Undergraduate Students ◽  
Prospective Teachers ◽  
Deductive Reasoning ◽  
Mathematical Proof ◽  
Inductive Reasoning ◽  
Analytical Framework ◽  
State University ◽  
Mathematics Courses ◽  
Proof Construction ◽  
Transition To Proof

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.

scholarly journals Indonesian Undergraduate Students’ Perspectives of Sustainable Economic Education: A Survey Study

Pedagogika ◽  
2020 ◽  
Vol 139 (3) ◽  
pp. 219-238
Author(s):  
Wahjoedi ◽  
Magistyo Purboyo Priambodo ◽  
Febry Wijayanti ◽  
Agung Haryono
Keyword(s):  
Higher Education ◽  
Undergraduate Students ◽  
Teaching Practices ◽  
Industry 4.0 ◽  
Public University ◽  
Economic Education ◽  
Survey Study

This study was designed to uncover perceptions of 230 undergraduate students at a public university in Indonesia, concerning sustainable economic education issues in higher education settings. The results of this study suggested that the respondents held positive beliefs on the issue of sustainable economic education issues. Despite this, they voiced multifaceted perspectives on the refinement of economic teaching practices. This paper ends with suggestions for the stakeholders to improve the quality of classroom teachings which corresponds to the age of industry 4.0.

VISUAL REPETITION OF EDUCATIONAL INFORMATION AT SCHOOL AND UNIVERSITY

2019 ◽  
pp. 41-50
Author(s):  
О. V. Ivanova
Keyword(s):  
Undergraduate Students ◽  
Educational Material ◽  
Educational Process ◽  
Mathematical Statistics ◽  
Crossword Puzzle ◽  
Conceptual Apparatus ◽  
Knowledge Types ◽  
Educational Information

The article discusses one of the stages of the educational process with the use of modular visualization that is systematization and synthesis of educational material. Various forms of visual repetition when studying the discipline “Theory of Probability and Mathematical Statistics” for undergraduate students who study non-mathematical profiles are presented. The concept of modular visualization is revealed, all types of each of the presented forms of visual repetition are described: through the conceptual apparatus (types: crossword puzzle, mathematical dictation, work with definitions, classification of concepts), transformation of knowledge (types: reference summary, proof of theorems, work with formulas, dictionary knowledge), by means of large-modular supports (types: table, flowchart, graph-diagram). Examples of each type of visual repetition of educational information on the discipline “Theory of Probability and Mathematical Statistics” developed by SMART Notebook and HTML are given. The technology of constructing various forms of visual repetition is presented schematically.

Dynamics of the processes in metal machining

1998 ◽  
Vol 2 ◽  
pp. 115-122
Author(s):  
Donatas Švitra ◽  
Jolanta Janutėnienė
Keyword(s):  
High Frequency ◽  
Machine Tools ◽  
Metal Cutting ◽  
Cutting Tool ◽  
Low Frequency ◽  
Metal Cutting Machine ◽  
Cutting Machine ◽  
Metal Machining

In the practice of processing of metals by cutting it is necessary to overcome the vibration of the cutting tool, the processed detail and units of the machine tool. These vibrations in many cases are an obstacle to increase the productivity and quality of treatment of details on metal-cutting machine tools. Vibration at cutting of metals is a very diverse phenomenon due to both it’s nature and the form of oscillatory motion. The most general classification of vibrations at cutting is a division them into forced vibration and autovibrations. The most difficult to remove and poorly investigated are the autovibrations, i.e. vibrations arising at the absence of external periodic forces. The autovibrations, stipulated by the process of cutting on metalcutting machine are of two types: the low-frequency autovibrations and high-frequency autovibrations. When the low-frequency autovibration there appear, the cutting process ought to be terminated and the cause of the vibrations eliminated. Otherwise, there is a danger of a break of both machine and tool. In the case of high-frequency vibration the machine operates apparently quiently, but the processed surface feature small-sized roughness. The frequency of autovibrations can reach 5000 Hz and more.

Paepalanthus fabianeae (Eriocaulaceae): A New Microendemic Species from a Morphologically Coherent Clade

2020 ◽  
Vol 45 (4) ◽  
pp. 794-801
Author(s):  
Caroline Oliveira Andrino ◽  
Marcelo Fragomeni Simon ◽  
Jair Eustáquio Quintino Faria ◽  
André Luiz da Costa Moreira ◽  
Paulo Takeo Sano
Keyword(s):  
New Species ◽  
Iucn Red List ◽  
Phylogenetic Position ◽  
Similar Species ◽  
Infrageneric Classification ◽  
Espinhaço Range ◽  
Nuclear Its ◽  
Two Populations

Abstract—We describe and illustrate Paepalanthus fabianeae, a new species of Eriocaulaceae from the central portion of the Espinhaço Range in Minas Gerais, Brazil. Previous phylogenetic evidence based on analyses of nuclear (ITS and ETS) and plastid (trnL-trnF and psba-trnH) sequences revealed P. fabianeae as belonging to a strongly supported and morphologically coherent clade containing five other species, all of them microendemic, restricted to the Espinhaço range. Due to the infrageneric classification of Paepalanthus being highly artificial, we preferred not assigning P. fabianeae to any infrageneric group. Paepalanthus fabianeae is known from two populations growing in campos rupestres (highland rocky fields) in the meridional Espinhaço Range. The species is characterized by pseudodichotomously branched stems, small, linear, recurved, and reflexed leaves, urceolate capitula, and bifid stigmas. Illustrations, photos, the phylogenetic position, and a detailed description, as well as comments on habitat, morphology, and affinities with similar species are provided. The restricted area of occurrence allied with threats to the quality of the habitat, mainly due to quartzite mining, justifies the preliminary classification of the new species in the Critically Endangered (CR) category using the guidelines and criteria of the IUCN Red List.

MEDIATEXT IS A TOOL THAT DETERMINES THE QUALITY OF INFORMATION

2020 ◽  
Vol 6 (3) ◽  
pp. 158-164
Author(s):  
Navruza Yakhyayeva ◽  
Keyword(s):  
Functional Properties ◽  
Linguistic Features ◽  
Text Linguistics ◽  
Quality Of Information ◽  
The Creation ◽  
Linguistic Units ◽  
Scientific Classification

The quality and content of information in the article media text is based on scientific classification of linguistic features. The study of functional styles of speech, the identification of their linguistic signs, the discovery of the functional properties of linguistic units and their separation on the basis of linguistic facts is one of thetasks that modern linguistics is waiting for a solution. Text Linguistics, which deals with the creation, modeling of its structure and the study of the process of such activity, is of interest to journalists today as a science.

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