scholarly journals Characteristics of Undergraduate Students’ Mathematical Proof Construction on Proving Limit Theorem

2019 ◽  
Vol 3 (15) ◽  
pp. 153
Author(s):  
S Netti ◽  
S Herawati
Keyword(s):  
Limit Theorem ◽  
Undergraduate Students ◽  
Mathematical Proof ◽  
Proof Construction

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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

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.

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 Profile of Students' Errors in Mathematical Proof Process Viewed from Adversity Quotient (AQ)

2018 ◽  
Vol 3 (2) ◽  
pp. 155
Author(s):  
Arta Ekayanti ◽  
Hikma Khilda Nasyiithoh
Keyword(s):  
Error Analysis ◽  
Mathematical Proof ◽  
Qualitative Approach ◽  
Real Analysis ◽  
Construction Process ◽  
Process Skill ◽  
Analysis Process ◽  
Proof Construction ◽  
Error Process ◽  
Test Result

Mathematical proof is an important aspect in mathematics, especially in analysis. An error in the mathematical proof construction process often occurs. This study aims to analyze the students’ errors in producing proof. Each of the categories of students’ Adversity Quotient (AQ) is identified related to the type of students’ error. The type of students’ errors used according to Newmann’s Error Analysis. This study used a qualitative approach. This study was conducted to 25 students who were taking real analysis course. Documentation, test, and interview were used to gather the data. Analyzing the students’ test result and then interviewing them for each AQ category were done for the analysis process. The results show that there are 48% climber students, 52% camper students, and no one is identified as a quitter student. Climber students tend to make some proving error such as transformation error, process skill error, and encoding error while camper students make the comprehension error, transformation error, process skill error, and encoding error when they are producing proof.

Linguistic Conventions of Mathematical Proof Writing at the Undergraduate Level: Mathematicians' and Students' Perspectives

2019 ◽  
Vol 50 (2) ◽  
pp. 121-155 ◽  
Author(s):  
Kristen Lew ◽  
Juan Pablo Mejía-Ramos
Keyword(s):  
Undergraduate Students ◽  
Academic Language ◽  
Mathematical Proof ◽  
Mathematical Language ◽  
Undergraduate Level ◽  
Proof Writing ◽  
Linguistic Conventions

This study examined the genre of undergraduate mathematical proof writing by asking mathematicians and undergraduate students to read 7 partial proofs and identify and discuss uses of mathematical language that were out of the ordinary with respect to what they considered conventional mathematical proof writing. Three main themes emerged: First, mathematicians believed that mathematical language should obey the conventions of academic language, whereas students were either unaware of these conventions or unaware that these conventions applied to proof writing. Second, students did not fully understand the nuances involved in how mathematicians introduce objects in proofs. Third, mathematicians focused on the context of the proof to decide how formal a proof should be, whereas students did not seem to be aware of the importance of this factor.

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