Mathematical Writings Research Articles

The Effects of Cooperative Learning on Creative Writing and Self-Efficacy in Portuguese and Mathematics

Cooperative learning is a pedagogical practice widely endorsed in the literature to enhance students’ creative writing skills. This methodology promotes the development of originality, fosters openness to new ideas, provides opportunities for interaction and tossing ideas around, and subsequently contributes to boosting creative textual production. This study aims to assess the impact of incorporating cooperative learning strategies on developing creative writing skills and enhancing self-efficacy among 6th-grade students. Additionally, this study reflects on using cooperative learning methods in the classroom setting, namely the roundtable and the cooperative graffiti. The participants were 34 students from two classes of the 6th grade of the 2nd cycle of basic school: an experimental group, where cooperative learning applies, and a control group, conducted using a traditional lecture. The study used a quasi-experimental design, incorporating pre-test and post-test. The non-parametric Wilcoxon signed-rank test was used to assess within-group changes in pre-test and post-test scores for both the experimental and control groups. The findings from both classes suggest that cooperative learning is more effective than a traditional lecture in building creative writing skills and self-efficacy in Portuguese (first language) and maths.

Preservice Teachers’ Experiences With, Beliefs About, Self-Efficacy In, and Instructional Practices for Mathematical Writing

ABSTRACT Students across grades K-12 may communicate their mathematical understanding via writing. Mathematical writing (MW) can include journaling about prior mathematical experiences, reflecting on a problem-solving strategy, providing feedback on a peer’s strategy, and generating a mathematical proof. Although there are a wide range of MW activities, many teachers report that they do not provide MW instruction or utilize writing activities with their students. Such instructional decisions are tied to teachers’ prior experiences with MW, beliefs about MW, and self-efficacy in teaching MW. Thus, in an effort to increase MW instruction for K-12 students, this study examined pre-service teachers’ (PSTs’) prior MW experiences and the impact of an online learning module on self-efficacy in teaching, beliefs about, and instructional decisions for MW. Participants were 111 elementary, special, or dual-education PSTs at one of the two universities. Findings indicated that PSTs had minimal prior MW experiences in their K-16 schooling but believed that MW was important before the module. After the module, PSTs’ self-efficacy in teaching MW significantly increased. Further, PSTs’ saw greater benefits of MW and demonstrated more sophisticated ways to utilize MW in mathematics teaching and learning.

Cultural Transitions in Mathematical Discourse: Unveiling Mathematical Writing Hurdles during the Rite of Passage

This qualitative case study delves into the intricate landscape of mathematical writing challenges faced by first-year university students undergoing the critical transition from school-level to university-level mathematical discourse. Conducted at a prominent South African university, the research, employing a purposive sampling technique, engaged thirty first-year mathematics students. Guided by the community of practice theory by Lave and Wenger, alongside van Gennep’s rite of passage analytical lens, the study sought answers to the question: What are the mathematical writing challenges encountered by first-year university students during their rite of passage period? Thematic analysis, informed by Adu's (2019) coding framework, was utilized to systematically examine common themes and patterns within the qualitative data. The findings illuminated key hurdles during this transitional phase, prominently including the inconsistency in working with mathematical notations, erroneous use of universal and existential quantifiers, and a notable confusion between the acts of illustrating and proving in mathematical contexts. In response to these challenges, the study advocates for the explicit incorporation of mathematical writing instruction to scaffold students during this rite of passage. Furthermore, it recommends a shift in the emphasis of first-year mathematics courses—suggesting a redirection from a content-centric approach to one that prioritizes the cultivation of students' new identities. This entails focused attention on teaching the customs, traditions, and adept ways of constructing and articulating mathematical proofs in the university context. The implications of this study extend beyond the immediate challenges identified, offering actionable recommendations to enhance the pedagogical strategies employed in the crucial transition period for first-year mathematics students.

Utilizing Emergent AI Chatbot Technology to Generate Mathematical Writing Models for Elementary Students With Learning Disabilities

Mathematical writing (MW) can support students’ mathematical learning and is common in mathematics assessment. However, MW is known to be particularly challenging for students with learning disabilities. While the use of model compositions of both high- and low-quality writing and the act of revision are evidence-based practices in writing instruction, models of MW are not readily available in the curriculum, and many teachers struggle to compose high-quality MW themselves. Artificial intelligence (AI) chatbots are increasingly accessible for teachers and provide one avenue by which MW models can be readily generated. This column guides educators on utilizing AI chatbots to produce MW models to support MW instruction for students with learning disabilities.

Jerónimo Muñoz’s Reception of Proclus’ In Euclidem: Philosophy of Mathematics and an Attempt to Prove the Parallel Postulate

Abstract The goal of this paper is to show – by way of a case study – how the contents of Proclus’ Commentary on the First Book of Euclid’s Elements were incorporated into university teaching in the sixteenth century. I analyse the impact of Proclus on the works of the Spanish mathematician and university professor Jerónimo Muñoz (ca. 1520–1591). In order to do so, I examine two manuscripts: Adnotationes in commentaria Procli super Euclidem (MS Vat. Lat. 6996), and Astrologicarum et geographicarum institutionum libri sex (MS Vat. Lat. 6998). I show that the contents of Proclus’ commentary pervade Muñoz’s mathematical writings and influence his mathematical ontology, his classification of mathematical disciplines, and the history and terminology of geometry that he adopts. Moreover, I expound on how Proclus’ text inspired Muñoz to maintain that the fifth postulate was a theorem, leading him to attempt a demonstration of it which pre-dates knowledge in the Latin West of Naṣīr ad-Dīn’s (1201–1274) previous attempt.

Exploring Primary School Mathematics Teachers' Strategies for Enhancing Students' Mathematical Writing Skills

This study aimed to determine female mathematics teachers’ level of performance in employing the teaching practices necessary to develop mathematical writing among female primary school students. It used the descriptive survey approach and collected data through observation. The study sample comprised 48 female teachers. The study generated several interesting results, most notably that the mathematics teachers’ level of performance was average, with overall means of 1.92–3, and there were statistically significant differences at the level of ? < .05 in the level of teaching practices employed attributable to teaching experience in favor of the group with fewer than 10 years’ experience. Based on these results, the study makes several recommendations. Primarily, it proposes that training programs for in-service female mathematics teachers should be strengthened, ensuring they cover the teaching practices necessary to develop mathematical writing skills.
 
 Received: 10 May 2023 / Accepted: 22 June 2023 / Published: 5 July 2023

Numbers and Narratives — or : When Russell meets Zhu Shijie to discuss Philosophy of Mathematics

Even if no explicit meta-discourse on mathematics is found in pre-modern China outside of mathematical writings, reflections upon objects of mathematical inquiry and the mathematician’s toolbox existed. They are shown to be built into the corpus of Chinese mathematics itself. As illustrated in particular through one specific mathematical domain that evolved from the first to the 19th century, such philosophical reflections are dispersed between texts, paratexts and images, thereby borrowing concepts and iconic images from other Chinese contexts of philosophical nature.

수학교육에서 수학 쓰기에 대한 문헌연구

In the future, mathematical thinking will occur in an extremely digitalized environment, and mathematics writing (MW), a basic competency that students must acquire through brain activity, will still be important. In this study, 26 papers in Korea were classified into evaluation, intervention program, and survey, focusing on the registered or candidate journals of the Korea Research Foundations. Regarding the results, first, most studies that measured the evaluation used descriptive, essay, or process-oriented MW types, and the majority of them evaluated core competences, such as problem-solving ability, communication ability, or affective ability, rather than students’ MW ability itself. Second, the studies using the intervention program revealed that most students’ cognitive or affective domains improved through journal writing. Third, in the surveys, it was difficult to grasp the perception of teachers and students regarding MW itself, as most of the said surveys pertained to narrative and essay-type assessments.

Understanding Rural Students Perceptions of their Online Learning by Analysing their Mathematical Writing

Understanding Rural Students Perceptions of their Online Learning by Analysing their Mathematical Writing

Mathematics and its Ancient Classics Worldwide: Translations, Appropriations, Reconstructions, Roles

The workshop analyzes the constitution, recovery, and role of the classical texts in mathematical practice throughout history. It aims at problematizing the notion of “classic”, to make it a historical category and to study the rhetorical, pedagogical, and institutional mechanisms that contribute to secure the status of classic to specific texts. So far, the focus of the historiography has dealt mostly with Greek classics and their impact on Western European societies. We aim to expand the focus of our enquiry culturally and chronologically in two ways. We want to address the reception and transformation of these “classics” outside Europe in different historical periods. We are particularly interested in the roles played by this classical tradition within Islamicate societies, South-East and East Asia. Secondly, we are interested in the ancient mathematical writings in Arabic, Chinese, Sanskrit and other languages that, at certain time periods in these other parts of the world and elsewhere, were perceived as classics. Widening the focus should allow us to inquire into questions such as: what did classical texts mean for various types of actors? How were they available to them? How did they read them? In the contexts of which institutions and with which expectations? The important role classical works have played in mathematical history pose deep methodological questions with far-reaching implications for the history and philosophy of mathematics. In mathematics conceptual and methodological innovations are thought to be legitimized only by appeal to mathematical arguments and consistency. Yet, legitimation has involved in many crucial episodes giving a prominent role to classical works. The mathematical classics have repeatedly been the source and grounds for new ideas and techniques. There is therefore a deep, complex tension between innovation and tradition. We are interested in how innovation has often been legitimized by re-reading old texts, concepts, and methods-old texts whose principles and methods were utterly different from the ones they contributed to sustain. What can this teach us about the nature of mathematical argument, and mathematical practice?

Maximizing the Potential of Mathematical Writing Prompts

Learn how to identify, adapt, and create writing prompts to capitalize on the insights you gain about each of your student’s thinking.

The Effect of ARIAS Model Learning on Mathematical Writing Skills Reviewed from Self-Efficacy

This study aimed to determine the influence of Assurance, Relevance, Interest, Assessment, Satisfaction (ARIAS) learning models on students' mathematical writing skills reviewed from self-efficacy. The type of research conducted in this study is a quasi-experimental research with a post-test nonequivalent control group design. The population in this study was students majoring in mathematics education at Bina Bangsa University, then two classes are selected at random as research subjects. The data was obtained from mathematical writing ability tests and self-efficacy questionnaires, then processed with ANOVA (Analysis of Variance) tests. The results showed significant differences in mathematical writing skills between students who obtained ARIAS learning models with students who received regular learning, and there were significant differences in students' mathematical writing skills reviewed on their self-efficacy. The implication is known that students with high self-confidence have better writing skills than students whose confidence is low.

On Newton's Mathematical Writings: Disciplinary Boundaries and Circulation

On Newton's Mathematical Writings: Disciplinary Boundaries and Circulation

Sourcebook in the Mathematics of Medieval Europe and North Africa edited by Victor Katz

The Sourcebook in the Mathematics of Medieval Europe and North Africa brings together a selection of mathematical writings in Latin, Hebrew, and Arabic from medieval Europe and North Africa (the Maghreb). At the very outset, it offers its readers an opportunity to survey briefly the mathematical contributions of scholars writing in different languages, at different times, and in different places across the intellectual geography of the medieval West. Reviewed by: Anuj Misra, Published Online (2021-08-31)Copyright © 2021 by Anuj MisraThis open access publication is distributed under a Creative Commons Attribution-NonCommercial-NoDerivatives License (CC BY-NC-ND) Article PDF Link: https://jps.library.utoronto.ca/index.php/aestimatio/article/view/37720/28724 Corresponding Author: Anuj Misra,University of CopenhagenE-Mail: anuj.misra@hum.ku.dk

3. Practical Suggestions for Mathematical Writing by Renee Bell, Borys Kadets, Padmavathi Srinivasan, Nicholas Triantafillou, and Isabel Vogt

3. Practical Suggestions for Mathematical Writing by Renee Bell, Borys Kadets, Padmavathi Srinivasan, Nicholas Triantafillou, and Isabel Vogt

Collecting to the Core — Writing in Mathematics

Collecting to the Core — Writing in Mathematics

Beckett, Lacan, and the Mathematical Writing of the Real by Arka Chattopadhyay

Reviewed by: Beckett, Lacan, and the Mathematical Writing of the Real by Arka Chattopadhyay Fernanda Negrete Beckett, Lacan, and the Mathematical Writing of the Real. Arka Chattopadhyay. New York: Bloomsbury, 2019. Pp. 224. $135.00 (cloth); $39.95 (paper); $35.95 (eBook). How might the writings of Samuel Beckett and Jacques Lacan respond to each other? Arka Chattopadhyay pursues this question in a cogent project that foregrounds mathematics as a common terrain for these two contemporary authors, whose work developed in separate fields despite various relevant points of intersection. Beckett, Lacan, and the Mathematical Writing of the Real begins by acknowledging the missed encounters between Beckett and Lacan, given their shared context in postwar Paris among avant-garde writers, their awareness of each other, and even the coincidence of their birthday. The book demonstrates a psychoanalytic sensibility in remarking on the missed encounters, and above all in allowing them to promptly place the investigation on the path of the textual unconscious in terms of the mathematical letter. The author offers an attentive ear to only seemingly passing comments the writers in question made about each other: Beckett mentions that Lacan's "later work tends to become unreadable" (4), and Lacan in his 1970 text "Lituraterre" invokes Beckett's "dustbins" (5), while discussing the materiality of the letter and the litter of the unconscious. Chattopadhyay follows these traces to reveal the uniqueness of what he calls mathematical writing, which is crucial to both Beckett and Lacan's creativity. Through the term mathematical writing, Chattopadhyay brings into focus the two authors' use of concepts from mathematics as well as a formal dimension of writing that is concerned with a kind of transmission that leaves behind the interest in sharing meaning. Chattopadhyay reminds us that as long as writing is understood as a technology subordinated to speech and meaning, the relation between literature and psychoanalysis remains unidirectional. In this relation, psychoanalysis is an interpretive device applied to literature. There are many critical works that establish such relations between the fields, through applied psychoanalysis that attempts to interpret—that is to say, to explain away—literary texts, or even more often, their authors. But it is fair to say that Beckett's texts refuse this sort of treatment. Attempts at enforcing it can only yield a partial grasp of what Beckett's texts put to work. While his writing stands beyond Oedipal concerns, its modes and gestures remain highly relevant to analytic thinking, especially the kind that also ventures out beyond Oedipus, as it did in Lacan's teaching. Chattopadhyay's book introduces the Lacanian register of the Real in order to approach writing from a perspective suitable to Beckett's experiments. From the perspective of the Real, Chattopadhyay demonstrates that Beckett's texts in fact contribute to better understanding the [End Page 806] relevance of the Real. The latter operates outside realist ideals and norms in literature, especially. The Real also places the psychoanalytic clinic outside normative and adaptive goals; this aspect, however, is only discussed to the extent that Lacan presents it as a logical process that seeks the end of analysis with the construction of a sinthome and the analysand's becoming analyst. In an exposition of existing commentaries on the role of mathematics in Beckett's work, Chattopadhyay declares his interest in adding to this investigation psychoanalysis, whose function he describes "as a bridge of Real inscription between mathematics and literature" (17). In his foreword to the book, Anthony Ullman instead sees the mathematical as the original bridging element between Beckett and Lacan (ix). In fact, mathematics, psychoanalysis, and literature are each set forth in chapter one to operate as bridges that enable a discussion between the two other terms, in a triad the author extracts from multiple texts by Beckett and Lacan throughout the book's other chapters. Contributing to this ambitious bridging or knotting of fields are the admirable breadth and depth with which both figures' work is embraced in the book. Its engagement with Beckett offers to Lacanian readers useful examples of the logical implications of the French psychoanalyst's related concepts of the letter, sinthome, jouissance, lalangue, the One, and above all the Real, or of...

Logic of Missed Encounters: A Review of Arka Chattopadhyay's <em>Beckett, Lacan, and the Mathematical Writing of the Real</em>

Beckett, Lacan, and the Mathematical Writing of the Real explores the essential connections between modernist literature, mathematics, and psychoanalysis through a double reading of Beckett's work through Lacan's oeuvre and vice-versa. Utilizing Lacanian key concepts and notions, Chattopadhyay deftly explains and questions them through close analyses of Beckett's works, ultimately showing how the relation between literary modernism and modern mathematics has two crucial embodiments in Beckett and Lacan. He ultimately presents us with a map of European twentieth-century thought, examining the problems of language, singularity, collectivity, sexuality, and love through two of its key figures. Proving thus the impossibility to think literary modernism without psychoanalysis (and vice-versa), Chattopadhyay leaves the readers intrigued, with a desire to further explore Beckettian analysis and Lacan's literature.

Basics and Structure of Project Writing in Mathematics

In this article various components of undergraduate project writing in mathematics are listed and discussed. We focus on the basics of a mathematical project writing in which we describe the necessity and usefulness of project writing. We then describe the structure of the project stating its various com- ponents. Finally we give some sample project topics. This article is intended for the students of bachelor level and faculties of mathematics among various universities in Nepal.

On C. S. Peirce´s primary arithmetic

his paper presents the initial studies on Peirce´s Primary Arithmetic, a set of manuscripts, never published by the author, written at the end of the XIX century. The originals – organized and published by Carolyn Eisele in 1976 – was translated to Portuguese and some initial studies are being developed focusing on the possibility that some features of Peirce´s Philosophy could be pragmatically – but implicitly – present in such manuscripts. Our partial conclusions, now, show that Peirce´s life circumstances, more than his Philosophy, characterize the texts under examination. Keywords: Charles S. Peirce; Primary Arithmetic; Mathematics Education; History; Philosophy; Peirce´s Mathematical Writings.