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.

The interplay of glossing with text difficulty and comprehension levels

2021 ◽  
pp. 136216882110204
Author(s):  
Seyede Faezeh Hosseini Alast ◽  
Sasan Baleghizadeh
Keyword(s):  
Undergraduate Students ◽  
First Language ◽  
Think Aloud ◽  
Text Difficulty ◽  
L2 Reading ◽  
Think Aloud Protocols ◽  
Significant Difference ◽  
The Impact ◽  
L2 Reading Comprehension ◽  
Underlying Processes

The aim of this experiment was to investigate how glossing influences second language (L2)reading comprehension in relation to text difficulty and the two local and global meaning representations. Fifty-eight undergraduate students were asked to read three easy, moderate, and difficult texts and, following each passage, answer twenty comprehension questions targeting local and global concepts in one of the two first-language-glossed and unglossed conditions. Half of the participants in each group were supposed to think aloud while reading. The results revealed a significant difference between the performance of glossed and unglossed groups on comprehension of local concepts in all three difficulty levels. However, the impact of glossing on comprehension of global concepts was significantly influenced by text difficulty. The qualitative analysis of think-aloud protocols suggested a substantial difference in glossing functionality on fluency between the easy and the difficult texts. Furthermore, it is suggested that revisiting the glossing effect in combination with text difficulty on the reading product and underlying processes might reconcile some divergent hypotheses on glossing impact on fluency.

Who said it? Voices in news translation, from a semiotic perspective

Semiotica ◽  
2015 ◽  
Vol 2015 (207) ◽  
pp. 411-441 ◽  
Author(s):  
Rovena Troqe ◽  
Jacques Fontanille
Keyword(s):  
Translation Studies ◽  
Think Aloud ◽  
News Production ◽  
Think Aloud Protocols ◽  
Semiotic Approach ◽  
Semiotic Perspective ◽  
General Method ◽  
The Way

AbstractIn Translation studies, it has long been understood that when translation is integrated into journalism, concepts such as equivalence and authorship become highly problematic. However, there is still no reference to a general method that might explain why news production impacts the very process of translation and affects the translated texts themselves. In this paper, we introduce a new semiotic approach that measures shifts in translated texts by using semiotic modalities and relates these shifts to axiologies by actants of the practice of translation. Translated texts by an Italian weekly magazine are adopted as a case study and an analysis of the textual corpora is coupled with think-aloud protocols by editors. The semiotic approach reveals that the actantial dynamics are conflictual: while the translators’ performance is compatible with the equivalence value, journalists endorse values that result in the content of the original being altered. The divergence between the axiology of the actant initiating the practice and the axiology pursued by the translators affects the way the concept of translation is generated.

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

Analysis of Expert Readers in Three Disciplines

2011 ◽  
Vol 43 (4) ◽  
pp. 393-429 ◽  
Author(s):  
Cynthia Shanahan ◽  
Timothy Shanahan ◽  
Cynthia Misischia
Keyword(s):  
High School ◽  
Focus Group ◽  
High School Teachers ◽  
Teacher Educators ◽  
Think Aloud ◽  
School Teachers ◽  
Focus Group Discussions ◽  
Group Discussions ◽  
Reading Behaviors ◽  
Think Aloud Protocols

The purpose of this study is to describe educationally relevant differences in literacy use among three subject-matter disciplines—history, chemistry, and mathematics. These analyses were drawn from an investigation of the teaching of disciplinary literacy in high schools. The purpose of the overall project was to improve the literacy-teaching preparation in a secondary preservice teacher education program, but this study sought to identify specific features of literacy and literacy use only in the three disciplines. It is the first expert-reader study to consider the reading of mathematicians and chemists (though other kinds of scientists have been studied in this way). To conduct this investigation, three teams were assembled, one for each discipline, including two disciplinary experts (historians, chemists, and mathematicians), two teacher educators who prepare high school teachers to teach those disciplines, and two high school teachers from each discipline. Using think-aloud protocols, transcripts from focus group discussions, a recursive process of member checking, and a cross-disciplinary consideration of reading approaches identified in each discipline, the study identified important differences in the reading behaviors of the six disciplinary experts. Although much of the work was based on think-aloud protocols and interviews with the disciplinary experts, the teachers and teacher educators participated with the disciplinary experts in focus-group discussions of the protocols, and their reactions and insights helped the disciplinary experts to articulate their approaches and to determine implications of the reading behaviors that were observed. Differences were evident in sourcing, contextualization, corroboration, close reading and rereading, critical response to text, and use of text structure or arrangement and graphics.

Construction of a Deductive Model by Simulation of a Traditional Archaeological Study

1974 ◽  
Vol 39 (2Part1) ◽  
pp. 243-252
Author(s):  
M. Borillo
Keyword(s):  
Historical Continuity ◽  
Analytical Scheme ◽  
Set Up ◽  
The Way

AbstractThis article is based on 2 observations. First, I note the quality of certain traditional archaeological studies, focusing on evaluation of results obtained and of information used. Second, I observe the incoherence of many of the constructions of "analytical" archaeologists, who sometimes naively imagine that it is possible to substitute sophisticated algorithms for analysis of the logic and archaeological meaning of problems in prehistory.The goal of this work is twofold: (1) to set up a model for analysis of traditional archaeological works that resolves the linguistic and logical difficulties encountered during extraction of the information they contain; and (2) to give an example of the way in which "description" and "calculation" may be integrated into a logical analytical scheme, so that the problem of "interpretation" (that is, of proceeding from formalisms to meaning) is resolved without reproducing the shortcomings of traditional discourse. These shortcomings include a preponderance of personal intuition, an absence of explicit justifications, and numerous incoherences.This paper is meant to be a contribution to efforts to reestablish the bases of archaeological reasoning in their historical continuity, beyond the mechanistic oppositions tending to mask the dialectic between "new" and "traditional" archaeology.The paper is translated from its original French by Claudine Farrand.

scholarly journals Facebook as e-learning tool for higher education institutes

2014 ◽  
pp. 440-448 ◽  
Keyword(s):  
Undergraduate Students ◽  
System Development ◽  
Smart Cities ◽  
Educational Institutions ◽  
E Learning ◽  
Intelligent Technology ◽  
Technological Opportunities ◽  
The Relationship ◽  
The Way

World is changing day by day in every aspect of life. A Smart City is an answer to different challenges such as socio-economic development and quality of life. In the way intelligent technology has brought enormous changes in urban development by altering the relation of production, consumption and distribution, it is now bringing enormous changes to the education sector. By providing technological opportunities for various ways of communication, the relationship between instructors and students has improved. Taking consideration of Facebook popularity in students, we argue that it can be used for educational purposes as well. A research study was conducted to analyze the student’s responses towards the use of Facebook for educational purposes based on a use case of educational institutions in Pakistan. We distributed 180 questionnaires among graduate and undergraduate students, out of which we received 140 completed questionnaires. The questionnaire was designed based on the four variables: Student’s perception, Academic Contribution, Student Faculty Relationship, and Concerns for Privacy and Distraction. The results demonstrate the willingness of students to use Facebook and social media for educational purposes alongside with their use for social purposes. The way, the enhanced link between students and faculty can contribute to the enrichment of cooperation and interaction in terms of connectivity between people, urban eco-system development and Smart Cities.

scholarly journals Visual Considerations in the Presentation of Mathematical Proofs

Seminar.net ◽  
2010 ◽  
Vol 6 (1) ◽  
Author(s):  
Lara Alcock ◽  
Matthew Inglis
Keyword(s):  
Undergraduate Students ◽  
Learning Resources ◽  
Electronic Learning ◽  
Mathematical Proofs ◽  
Teaching Situations ◽  
The Way

This article is about visual issues in the presentation of mathematics within teaching situations. It focuses particularly on the presentation of proofs to undergraduate students. We describe some of the decisions that a lecturer must make when presenting a written proof, from the layout of individual equations to the layout of a whole argument on the page. We consider the way in which these decisions are made explicit for lecturers who construct electronic learning resources termed e-Proofs, and conclude by discussing the constraints and affordances of this technology.

Phonological variation *

2020 ◽  
pp. 18-28
Author(s):  
Gerjan van Schaaik
Keyword(s):  
Vowel Quality ◽  
Phonological Variation ◽  
Vowel Reduction ◽  
Vowel Length ◽  
Sound System ◽  
Set Up ◽  
Predictable Variation ◽  
The Way

The principle of “one letter—–one sound” introduced in the introduction of this chapter explains why Turkish writing is based on a phonological alphabet, and that such a system takes no account of a pronunciation that deviates from the spelling. For free or predictable variation rules can be set up describing the circumstances under which such variation occurs. Besides vowel reduction (stress induced) and differences in vowel quality (vowel length), phenomena such as contraction in rapid speech are discussed, as well as expansion—the way in which foreign words are adapted to the Turkish sound system and included in the vocabulary. The fully predictable effects of front and back vowels on the quality of certain consonants and other types of assimilation are treated in the final sections.

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