Mathematical Writings Research Articles

Beckett, Lacan and the Mathematical Writing of the Real. By Arka Chattopadhyay

Beckett, Lacan and the Mathematical Writing of the Real. By Arka Chattopadhyay

Arka Chattopadhyay. Beckett, Lacan and the Mathematical Writing of the Real. Bloomsbury Academic, 2019.

Arka Chattopadhyay. Beckett, Lacan and the Mathematical Writing of the Real. Bloomsbury Academic, 2019.

Counting with Alice

There are many mathematical references in Lewis Carroll’s two tales for children: Alice’s Adventures in Wonderland (1865) and Through the Looking-Glass (1872). Many critics suggested that Carroll inserted hidden meanings in those passages. We rather consider them as part of the story’s setting and narrative. Yet, those passages may be interpreted and used as convenient to illustrate mathematical ideas. In this paper, we consider two passages from the Alice tales that relate to arithmetic, and we discuss them in relation to issues of personal identity, mathematical certainty, the role of notations and the processes of composition and decomposition in mental calculation. Hence, we show how literary texts can be used to convey ideas related to mathematics, mathematical culture and mathematical education. We conclude on the importance of mathematical writings as literary texts.

Use Mathematical Writing as a Practical Approach to Increase Students’ Problem Solving Skills: A Case Study

Use Mathematical Writing as a Practical Approach to Increase Students’ Problem Solving Skills: A Case Study

Comparing and Validating Four Methods for Scoring Mathematics Writing

Current mathematics curricula and assessments emphasize students’ ability to communicate mathematical reasoning in writing. Limited research exists, however, on what mathematics writing (MW) is and how to assess the quality of MW. Therefore, based on our definition of MW construct, we explored 4 approaches to scoring MW: (a) holistic rubric scoring for overall quality of explanation; (b) analytical rubric scoring across 4 components (i.e., mathematics content, mathematics vocabulary, writing organization, writing grammar); (c) genre-based elements scoring (modified from the scoring form used for the Essay Composition subtest of the Wechsler Individualized Achievement Test); and (d) curriculum-based measurement mathematics-writing sequences (MWS) scoring, including rules for scoring numbers and symbols. Students from 6 classrooms in 3rd-grade, 4th grade, and 5th grade (2 classrooms at each grade level; N = 122) were recruited for the current study. Results indicated all 4 scoring methods were moderately correlated with measures of writing and mathematics. Holistic, analytic, and elements scoring were strongly correlated with each other, with slightly lower correlations for the MWS scoring. Confirmatory factor analysis further demonstrated adequate construct validity. All 4 scoring methods were reliable with an exception of lower reliability for writing components assessed by analytic scoring. Based on the validity, reliability, efficiency, and information provided by each scoring method, we recommend holistic scoring for summative assessments and elements scoring for formative assessments.

Effects of a Mathematical Writing Intervention on Middle School Students’ Performance

The benefits of content writing are widely recognized, yet there are still few studies that evaluate the benefits and challenges of mathematical writing (MW) for students. The National Council of Teachers of Mathematics and the Common Core State Standards for Mathematics have an emphasis on written communication of mathematical reasoning as an integral part of curriculum, peer-reviewed publications on this topic are lacking. This study evaluates the effects of self-regulated strategy development (SRSD) intervention on sixth-grade students’ MW. Findings indicate that the intervention had significant impact on MW outcomes. Additionally, the five predictors assessed prior to the intervention accounted for approximately 73.6% of variance in MW quality. Implications for the field and future research are discussed.

MATHEMATICAL WRITING OF INTERMEDIATE SCHOOL’S LEVEL THREE FEMALE STUDENTS IN RIYADH CITY AND ITS RELATION WITH MATHEMATICAL THINKING

Purpose of the Study: The study sought to discover the level of mathematical thinking in mathematical writing among the female students of the intermediate third-level in Riyadh, and thus determine the relationship between the levels of mathematical writing and mathematical thinking among the female intermediate students of the third level.
 Methodology: In this research, the descriptive and analytical method is used. The analytical descriptive method was used to analyze 68 books of mathematics textbooks. The study tools consist of the mathematical writing analysis card for the records of the students and to measure their mathematical thinking.
 Main Findings: The development of mathematical thinking in mathematics education is the main domain of this research. Through the paper, the researcher explains the students’ mistakes in their mathematical writing.
 Applications of this study: The results of this study may serve to guide teachers to take care of student writing, the importance of providing a track record for students' writing and their training in the integrity of mathematical writing, showing them understanding and teaching them to provide appropriate learning.
 Novelty/Originality of this Study: In light of the results of the study, the researcher suggests conducting studies such as: determining the relationship between the level of mathematical writing among students and other variables such as achievement, mental ability and problem-solving. The study may also be conducted on the relationship between the teaching practices of the mathematics teachers in the mathematical communication between the students and the construction of a training program to develop the written communication among the students.

Beginning Mathematical Writing Assignments

Writing assignments in any mathematics course always present several challenges, particularly in lower-level classes where the students are not expecting to write more than a few words at a time. Developed based on strategies from several sources, the two small writing assignments included in this paper represent a gentle introduction to the writing of mathematics and can be utilized in a variety of low-to-middle level courses in a mathematics major.

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

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

Piloting a Mathematics‐Writing Intervention with Late Elementary Students At‐Risk for Learning Difficulties

AbstractHigh‐stakes mathematics assessments require students to write about mathematics, although research suggests students exhibit limited proficiency on such assessments. Students with LD may have difficulties with writing, mathematics, or both. Researchers employed an intervention for teaching students how to organize mathematics writing (MW). Researchers randomly assigned participants (n = 61) in grades 3–5 to receive instruction in MW or information writing. Students receiving MW outperformed control students on a researcher‐developed measure of MW (d = 1.05). Component assessment revealed MW students improved in writing organization (d = 1.49) but not in mathematics content (d = 0.11 ns). Results also indicated MW students outperformed control on percentage of correct MW sequences (d = 0.82). Future directions for MW intervention development are discussed.

Mathematical Writing Profile of High Social Arithmetic Ability Student in Solving Social Arithmetic Problems

In solving problems, students need to communicate their ideas. One of the media is writing in written media. Social arithmetic is one of mathematics subject that close to daily live activities. Students’ understanding about social arithmetic and how students communicate their ideas in solving social arithmetic problems can be seen in their mathematical writing. This study aimed to describe how student with high social arithmetic ability mathematical writing in solving social arithmetic problems based on the use of precise mathematical language, explanation of the process, reasoning about the process to produce the right solution, connections between abstract mathematical procedures and the context of the problem. The analysis indicate that student clearly used accurate math vocabulary to communicate ideas, clearly provides the mathematical steps used to solve the problem, clearly described the reasoning used to solved the problem which includes connections between the numbers used in the strategy and the problem context, and then the final answer was clearly explained in the context of the problems. Through student mathematical writing, reader (teacher) will know that student understand the problem and the subject and also can clearly communicate their ideas.

New theories for new instruments: Fabrizio Mordente's proportional compass and the genesis of Giordano Bruno's atomist geometry

The aim of this article is to shed light on an understudied aspect of Giordano Bruno's intellectual biography, namely, his career as a mathematical practitioner. Early interpreters, especially, have criticized Bruno's mathematics for being “outdated” or too “concrete”. However, thanks to developments in the study of early modern mathematics and the rediscovery of Bruno's first mathematical writings (four dialogues on Fabrizio's Mordente proportional compass), we are in a position to better understand Bruno's mathematics. In particular, this article aims to reopen the question of whether Bruno anticipated the concept of infinitesimal quantity. It does so by providing an analysis of the dialogues on Mordente's compass and of the historical circumstances under which those dialogues were written.

ANALYSIS OF THE CURRENT STATE IN INNOVATIVE RESEARCH TRAINING OF PHD STUDENTS IN UKRAINE

The paper examines the challenges of curricular reforms aimed at updating Postgraduate study programmes of Ukrainian higher educational institutions in terms of specific innovative content and methodologies. By applying statistical methods to the data acquired from questioning first-year and second-year PhD students, the concept of PhD students’ training (comprising formal, content-based and methodological aspects) has been reconstructed from the point of view of its key beneficiaries. The research results show that the majority of postgraduate students consider research and innovation activities as an important part of their future professional activity; the level of innovative research training in Postgraduate Education is rated as higher than average, while their own level is viewed as average. The paper outlines main forms of research and innovation activities in which the students participated as well as difficulties which they encountered. As a result of the quantitative analysis, the author presents the rating of the most important modules, which should be included in the curriculum of Postgraduate studies (Foreign Language for Specific Purposes, Methodology of Scientific Research, Methods of Mathematical Statistics, Academic Writing and Academic Integrity, Critical Thinking Basics, Innovation basics, Intellectual Property and Technology Transfer, Project Activity Basics). The paper also outlines the most effective, in students’ opinion, forms and methods of innovative research training in the process of Postgraduate Studies, including preparation of scientific publications to be submitted to international journals; workshop conducting, organisation of thematic meetings with successful scientists and entrepreneurs; on-the-job training in leading research centres; participation in interdisciplinary discussion workshops; participation in youth contests of innovative ideas and projects; participation in scientific research conferences and workshops; realisation of scientific research and social projects. The obtained results can be used for the development of educational and scientific programmes for the third level of higher education and construction of a model for innovative research training of the future PhD candidates.

Evaluating Various Undergraduate Perspectives of Elementary-Level Mathematical Writing

Writing is recognized as a critical skill in science, technology, engineering, and mathematical fields, as it provides opportunities for individuals to think critically about learned information, integrate knowledge, communicate understanding, and contribute new information to the field. Requirements for applying mathematical knowledge to writing require a seamless blend of content-specific knowledge, domain-specific vocabulary, and an understanding of written expression. Relatively, little is known about how mathematics writing is currently being assessed in K-12 classrooms to promote the acquisition and growth of students’ writing. This exploratory survey research sought to evaluate how undergraduate students across various career majors, at a large university in the USA, perceive the writing quality of elementary mathematics writing samples. Research determined that respondents valued accuracy of the mathematics, logical explanation, effort of the response, as well as organization/mechanics of the writing. The extremes of mathematical writing had the most reliable scores, bringing attention to the need to develop quality assessments (e.g., rubrics) that address subjectivity of writing quality indicators and explicitly communicate expectations of mathematics writing. Implications for practice and future research are presented.

Intent and enactment: Writing in mathematics for conceptual understanding

ABSTRACTUsing a national sample of students’ writing from the National Study of Writing Instruction, this study examines the current state of writing in the mathematics classroom and the extent to which enactments align with the intentions established in the research base and curricula articulated by NCTM and the CCSS–M. Over 3,000 writing assignments from 138 students in grades, 6, 8, 10, and 12 were analyzed for functions of writing and epistemic complexity—the degree to which they explained or justified mathematical understanding. Additionally, shortanswer assignments were analyzed qualitatively for patterns in teacher-assigned prompts and student responses. Analyses reveal enactments of writing in the mathematics classroom do not align with the intent articulated by the CCSS-M. Mirroring techniques from the literacy field, a method for scaffolding students’ improved ability to write about conceptual understanding in mathematics is discussed.

BeyondDoingMathematics: Engaging Talented Students in Mathematically Creative Writing

With recent increased attention to engaging students in written mathematical communication, the Elementary Mathematical Writing Task Force has recommended specific types of and purposes for mathema...

Mathematical Writing Errors in Expository Writings of College Mathematics Students

<p>Despite the efforts to confirm the effectiveness of writing in learning mathematics, analysis on common errors in mathematical writings has not received sufficient attention. This study aimed to provide an account of the students’ procedural explanations in terms of their commonly committed errors in mathematical writing. Nine errors in mathematical writing were pre-defined namely, misuse of mathematical terms, misuse of mathematical symbols, incorrect notation, incorrect grammar, incorrect capitalization, no or incorrect punctuation, vague term, incorrect term, and lack of term or phrase. This study used qualitative method of research to keep a record of errors in mathematical writing. Conducted in the College of Education Arts and Sciences of De La Salle Lipa, the study involved twelve BS Mathematics students enrolled in Advanced Calculus 1 class as respondents. Results revealed that the most committed errors done in mathematical writing are incorrect grammar and misuse of mathematical symbols. Certainly, intervention programs on mathematics writing will bring favorable outcomes. Language courses in the students’ curriculum which tackle proper grammar usage may be integrated with writing about mathematics as part of the student activities. Such will provide the students with writing experiences fitted to their discipline.</p><p> </p>

Analyzing Diverse Learners' Writing in Mathematics: Systemic Functional Linguistics in Secondary Pre-Service Teacher Education

This article analyses the experiences of 55 secondary pre-service teachers (PSTs) in a mandated professional development course that used Halliday's systemic functional linguistics (SFL) and related pedagogical practices to support PSTs' development of disciplinary linguistic knowledge for working with linguistically diverse students in the United States. Of specific interest is how the course influenced the manner in which PSTs responded to a student's attempt at writing a mathematical explanation. We begin with a brief description of Halliday's theory of language and learning with particular reference to the semiotic demands of mathematics. Next, we provide a description of the professional development course and the mixed methods approach to analysing changes in PSTs' pre- and post-course responses to a student writing sample about linear equations. Third, we discuss findings that suggest PSTs' emerging understanding of the linguistic and multimodal demands of mathematical explanations supported them in providing more cogent and precise written feedback. We conclude by discussing the potential of SFL conceptual and pedagogical tools to support PSTs' professional development in the context of globalization.

A Synthesis of Mathematics Writing: Assessments, Interventions, and Surveys

A Synthesis of Mathematics Writing: Assessments, Interventions, and Surveys

Promoting Student Buy-in: Using Writing to Develop Mathematical Understanding

Writing in mathematics provides students with the opportunity to think critically about and reflect on their experiences while solving problems. While many studies have documented the benefit of writing in math, it is not clear which instructional methods should be used to help students learn how to use writing to support learning. In this study, we take a constructivist approach to building students understanding of effective writing by developing a series of active, student-centered lessons. The findings indicate that students wrote more effectively after the instructional sequence; in particular, they were better able to explain their reasoning and to make connections between abstract mathematics and the context of the problem. These results provide a pathway for improving both students’ conceptual understanding, and their performance on open-ended state assessment items.