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.

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.

A Comparative Study on New Generation Learning and Awareness

2020 ◽  
pp. 59-76
Author(s):  
Sabri Erdem ◽  
Gizem Turcan ◽  
Rukiye Büşra Tekin
Keyword(s):  
Learning Environments ◽  
Undergraduate Students ◽  
Evolutionary Process ◽  
The Other ◽  
Learning Resources ◽  
Electronic Learning ◽  
Convenience Sampling ◽  
New Generation ◽  
Academic Year ◽  
And Training

Considering the evolutionary process of education and training from past to present, access to information is possible in many different ways such as written, visual, auditory, virtual, online, offline, one-to-one, or in classrooms regardless of age, place, and time. Within the scope of this study, a questionnaire was applied to undergraduate students who were studying at two different universities in Ankara and Izmir during 2018-2019 academic year by convenience sampling method. The survey data gathered from these universities were analyzed and compared to assess student awareness of new generation learning environments. According to the results of this survey, it is found that the undergraduate students had awareness about the new generation learning environments and that the awareness increases towards the upper grades. On the other hand, it is also found out that YouTube is the most preferred platform among the electronic learning resources.

Investigating the Availability, Accessibility and use of E-Learning Resources by Undergraduate Students in University of Ilorin, Kwara State

2015 ◽  
Vol 3 (1) ◽  
Author(s):  
Oluyinka Titilope Afolayan
Keyword(s):  
Undergraduate Students ◽  
Survey Design ◽  
Virtual Classroom ◽  
Learning Resources ◽  
Learning Tools ◽  
Transfer Of Knowledge ◽  
Educational Benefits ◽  
E Learning ◽  
Main Instrument ◽  
Effective Use

The availability and use of e-learning resources in the acquisition and transfer of knowledge have been observed as a steering agent that facilitates the realization of major educational benefits in a developing economy. This study investigated the availability, accessibility, and use of e-learning tools by undergraduate students in the University of Ilorin, Nigeria, including the challenges limiting the full exploitation of e-learning resources for optimal usage and efficient e-service delivery. The methodology adopted for this research was purely survey design using the questionnaire approach as the main instrument for data collection. From the findings, limited availability, accessibility and usage of e-learning resources by the undergraduate students were revealed. The findings further showed that the major challenges hindering the effective use of e-learning resources amongst University of Ilorin students include lack of sophisticated e-learning resources such as teleconferencing, video conferencing, virtual classroom among others and high cost in the procurement of facilities that support e-learning. Based on these findings, recommendations are made towards addressing the challenges encountered by students in the utilization of e-learning resources in higher institutions of learning.

Expert and Novice Approaches to Reading Mathematical Proofs

2012 ◽  
Vol 43 (4) ◽  
pp. 358-390 ◽  
Author(s):  
Matthew Inglis ◽  
Lara Alcock
Keyword(s):  
Eye Movements ◽  
Mathematics Education ◽  
Undergraduate Students ◽  
Logical Structure ◽  
Surface Features ◽  
Mathematical Proofs ◽  
Proof Validation ◽  
Expert And Novice ◽  
University Level

This article presents a comparison of the proof validation behavior of beginning undergraduate students and research-active mathematicians. Participants' eye movements were recorded as they validated purported proofs. The main findings are that (a) contrary to previous suggestions, mathematicians sometimes appear to disagree about the validity of even short purported proofs; (b) compared with mathematicians, undergraduate students spend proportionately more time focusing on “surface features” of arguments, suggesting that they attend less to logical structure; and (c) compared with undergraduates, mathematicians are more inclined to shift their attention back and forth between consecutive lines of purported proofs, suggesting that they devote more effort to inferring implicit warrants. Pedagogical implications of these results are discussed, taking into account students' apparent difficulties with proof validation and the importance of this activity in both schooland university-level mathematics education.

scholarly journals Self-Regulation and “Time Off”: Evaluations and Reflections on the Development of a Blended Course

2018 ◽  
Vol 9 (1) ◽  
Author(s):  
Natalie Spadafora ◽  
Zopito Marini
Keyword(s):  
Undergraduate Students ◽  
Self Regulation ◽  
Academic Experiences ◽  
Ongoing Research ◽  
Capstone Course ◽  
Course Content ◽  
Digital World ◽  
Premier Cycle ◽  
University Course ◽  
The Way

Changes in both the landscape of education and digital technology are giving rise to interesting, innovative, and potentially effective pedagogical possibilities. As educators of the 21st century, we are witnessing continuous changes in the way we teach as well as the way students learn. This study is a part of an ongoing research program aimed at evaluating the pedagogical effectiveness of blended teaching. More specifically, this paper aims to describe some of our reflections as we developed, delivered, and carried out an evaluation of a university course taught using a blended format. Undergraduate students (n=109) in a fourth-year capstone course participated in this study. We report on the students’ perceptions of the effectiveness of the delivery method of the course, while focusing on the struggles they encountered, including difficulties keeping up with the course content, particularly on the weeks where the lecture was online, as well as a struggle to stay organized and connected with their peers and their assignments. Self-regulation turned out to be a major determinant of success in this type of course. We conclude with suggestions to improve students’ social and academic experiences as they navigate learning in a digital world. Les changements survenus à la fois dans le paysage de l’éducation et dans la technologie numérique donnent naissance à des possibilités pédagogiques intéressantes, innovatrices et potentiellement efficaces. En tant qu’éducateurs du XXIe siècle, nous assistons à des changements continus dans la manière dont nous enseignons ainsi que dans la manière dont les étudiants apprennent. Cette étude s’inscrit dans le cadre d’un programme de recherche en cours qui a pour objectif d’évaluer l’efficacité pédagogique de l’enseignement hybride. Plus spécifiquement, cet article vise à décrire certaines de nos réflexions au fur et à mesure que nous élaborons, livrons et exécutons l’évaluation d’un cours universitaire enseigné selon un format hybride. Des étudiants de premier cycle (n=109) inscrits dans un tout dernier cours de quatrième année ont participé à cette étude. Nous présentons un rapport sur la manière dont les étudiants ont perçu l’efficacité de la méthode employée pour enseigner ce cours, tout en mettant l’accent sur les problèmes qu’ils ont rencontrés, y compris les difficultés à faire face au contenu du cours, en particulier durant les semaines où les cours magistraux étaient présentés en ligne, ainsi que sur leurs difficultés à rester organisés et connectés avec leurs camarades de classe et avec leurs devoirs. Il s’avère que l’autorégulation est un élément important pour la réussite de ce type de cours. Pour conclure, nous présentons des suggestions pour améliorer l’expérience sociale et académique des étudiants dans leur parcours de l’apprentissage au sein d’un monde numérique.

scholarly journals Taking over someone else's e-learning design: challenges trigger change in e-learning beliefs and practices

2014 ◽  
Vol 22 ◽  
Author(s):  
Karen M. Scott
Keyword(s):  
Longitudinal Research ◽  
New Teacher ◽  
Learning Technology ◽  
Learning Resources ◽  
Learning Beliefs ◽  
Learning Resource ◽  
Beliefs And Practices ◽  
E Learning ◽  
The Subject ◽  
The Way

As universities invest in the development of e-learning resources, e-learning sustainability has come under consideration. This has largely focused on the challenges and facilitators of organisational and technological sustainability and scalability, and professional development. Little research has examined the experience of a teacher dealing with e-learning sustainability when taking over a course with an e-learning resource and associated assessment. This research focuses on a teacher who was inexperienced with e-learning technology, yet took over a blended unit of study with an e-learning resource that accounted for one-fifth of the subject assessment and was directed towards academic skills development relevant to the degree program. Taking a longitudinal approach, this research examines the challenges faced by the new teacher and the way she changed the e-learning resource and its implementation over two years. A focus of the research is the way the teacher's reflections on the challenges and changes provided an opportunity and stimulus for change in her e-learning beliefs and practices. This research has implications for the way universities support teachers taking over another teacher's e-learning resource, the need for explicit documentation of underpinning beliefs and structured handover, the benefit of teamwork in developing e-learning resources, and provision of on-going support.Keywords: e-learning sustainability; e-learning beliefs and practices; reflection; longitudinal research(Published: 30 July 2014)Citation: Research in Learning Technology 2014, 22: 23362 - http://dx.doi.org/10.3402/rlt.v22.23362

scholarly journals The influence of interactive and static infographics on the academic achievement of reflective and impulsive students

2021 ◽  
pp. 147-162
Author(s):  
Dina Ismaeel ◽  
Ensaf Al Mulhim
Keyword(s):  
Academic Achievement ◽  
Cognitive Style ◽  
Learning Environments ◽  
Undergraduate Students ◽  
Significant Interaction ◽  
Cognitive Styles ◽  
Learning Resources ◽  
Information Presentation ◽  
E Learning ◽  
Presentation Methods

This article examines the influence of static/interactive infographics on reflective/impulsive students’ academic achievement. The study sample consisted of 80 undergraduate students who were divided into two groups according to their cognitive style (reflective/impulsive). Each group was further divided into two sub-groups based on the type of infographics (static/interactive) to be evaluated. The findings showed that interactive infographics are more effective than static infographics in improving academic achievement. Reflective students outperformed impulsive students in terms of academic achievement, and there was a significant interaction between interactive infographics and reflective students. This study may serve as a guide for educators and designers of learning resources in selecting the most appropriate forms of technology conforming to students’ varying cognitive styles. Implications for practice or policy: The designers of e-learning environments must focus on the cognitive style of each learner. The design of those environments must take into account the diversity of information presentation methods to meet the various cognitive styles. Students' academic achievement can be improved by the use of interactive infographics due to their richness in material, multimedia approach, and interactivity that stimulate and communicate with learners’ senses and positively affect their acquisition of information.

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