Mathematical Texts Research Articles

Reading Mathematical Texts as a Problem-Solving Activity: The Case of the Principle of Mathematical Induction

Reading mathematical texts is closely related to the effort of the reader to understand its content; therefore, it is reasonable to consider such reading as a problem-solving activity. In this paper, the Principle of Mathematical Induction was given to secondary education students, and their effort to comprehend the text was examined in order to identify whether significant elements of problem solving are involved. The findings give evidence that while negotiating the content of the text, the students went through Polya’s four phases of problem solving. Moreover, this approach of reading the Principle of Mathematical Induction in the sense of a problem that must be solved seems a promising idea for the conceptual understanding of the notion of mathematical induction.

PENGARUH PEMAHAMAN WRITING MATHEMATICS MAHASISWA DALAM MENGKOMUNIKASIKAN SUATU BUKTI PERNYATAAN DALAM MATEMATIKA

The ability of writing and communicating Mathematics text are needed to get the whole understanding of specific topic in Mathematics. But so far, it is still can be found some meaningless statement that implies some misconceptions. The qualitative data analysis is conducted in this research to find out how big the change of the writing mathematics skill after conducting a technical guidance. The result of data analysis and some evaluation show that the skill of understanding the concept of writing mathematics takes effect in communicating or creating a proof of mathematical statement.

Exploring the process of learning mathematics by repeated reading: Eye tracking and heart rate measurement

This study aimed to investigate how the learners’ mathematics learning processes change with repeatedly reading mathematical text. As a way to teach and learn mathematics, we also wanted to examine the effect of repeated reading and to explore the implications for a more efficient teaching and learning strategy. To help us with this study, we mainly used eye tracking and heart rate (HR) measurement. There were four cycles in a cycle of repeated reading, and the number of repeated readings for all cycles was fixed to three times. In this study, eight prospective mathematics teachers in the Department of Mathematics Education of a National University in South Korea participated. Data were analyzed in five aspects: the total reading time per round, the total reading time per slide, the change trends of total reading time per round and slide, the order of slides read, and the change trends of HR per round. We found that most participants read in a similar pattern in the first reading, but the second and third reading patterns appeared more diverse for each learner. Also, the first reading required the most time regardless of the repeat cycle, and the time it took to repeatedly read afterward varied depending on the individual. Based on the findings of this study, the most primary conclusion is that self-directed mathematics learning by using repeated reading is effective regardless of cycle. In addition, we suggest four strategies to improve the efficiency of this teaching and learning method.

Content Teachers’ Perspectives of Student Challenges in Processing Science and Mathematics Texts in English at an Emirati University

There is a worldwide concern about science and engineering undergraduate students, particularly those who are English language learners, struggling with their entry-level content courses. From a teacher cognition perspective and drawing on semi-structured interviews with chemistry, mathematics and physics teachers at a university in the Middle East, we sought to gain insights into the extent to which language is seen as interfering with content learning and how this issue is being addressed. Focusing particularly on challenges students face with processing written text in English, since this emerged through thematic analysis as the investigated content teachers’ primary concern, we explore reported practices and highlight needs for in-service professional development. We suggest that science and mathematics instructors may need heightened syntactical and morphological awareness to prepare them to more effectively help their students to decode dense word problems. They may also need consciousness-raising, so that they can see themselves as language teachers too.

Onto-semiotic complexity of the Definite Integral

Teaching and learning Calculus concepts and procedures, particularly the definite integral concept, is a challenge to teachers and students in their academic careers. In order to develop an informed plan for improving instructional processes, it is necessary to pay attention to the nature and complexity of the mathematical features of the definite integral, that students are expected to understand and apply. In this research, we supplement the analysis made by different authors, applying the theoretical and methodological tools of the Onto-Semiotic Approach to mathematical knowledge and instruction. The goal is to understand the diverse meanings of the concept of the definite integral and potentials semiotic conflicts based on the given data. We focus attention on a first intuitive meaning, which involves mainly arithmetic knowledge, and the definite integral formal meaning as Riemann’s sums limit predominantly in the curricular guidelines. The recognition of the onto-semiotic complexity of mathematics objects is considered as a key factor in explaining the learning difficulties of concepts, procedures and its application for problem-solving, as well as to make grounded decisions on teaching. The methodology analysis of a mathematical text, which we exemplify in this work applying the tools of Onto-Semiotic Approach, provides a microscopic level of analysis that allows us to identify some semiotic-cognitive facts of didactic interest. This also allows for the identification of some epistemic strata, that is, institutional knowledge that should have been previously studied, which usually goes unnoticed in the teaching process.

On the correctness of problem solving in ancient mathematical procedure texts

It has been argued in relation to Old Babylonian mathematical procedure texts that their validity or correctness is self-evident. One “sees” that the procedure is correct without it having, or being accompanied by, any explicit arguments for the correctness of the procedure. Even when agreeing with this view, one might still ask about how is the correctness of a procedure articulated? In this work, we present an articulation of the correctness of ancient Egyptian and Old Babylonian mathematical procedure texts – mathematical texts presenting the solution of problems. We endeavor to make explicit and explain how and why the procedures are reliable over and above the fact that their correctness is intuitive.

Machine Translation of Mathematical Text

We have implemented a machine translation system, the PolyMath Translator, for LaTeX documents containing mathematical text. The current implementation translates English LaTeX to French LaTeX, attaining a BLEU score of 53.6 on a held-out test corpus of mathematical sentences. It produces LaTeX documents that can be compiled to PDF without further editing. The system first converts the body of an input LaTeX document into English sentences containing math tokens, using the pandoc universal document converter to parse LaTeX input. We have trained a Transformer-based translator model, using OpenNMT, on a combined corpus containing a small proportion of domain-specific sentences. Our full system uses this Transformer model and also Google Translate with a custom glossary, the latter being used as a backup to better handle linguistic features that do not appear in our training dataset. Google Translate is used when the Transformer model does not have confidence in its translation, as determined by a high perplexity score. Ablation testing demonstrates that the tokenization of symbolic expressions is essential to the high quality of translations produced by our system. We have published our test corpus of mathematical text. The PolyMath Translator is available as a web service at http://www.polymathtrans.ai.

O sposobach przedstawiania pojęć matematycznych w komunikacji specjalistycznej na przykładzie całki

The paper deals with the problem of various ways of representing concepts in specialist communication. In specialist communication in the field of mathematics we are dealing with a situation in which the concepts which are the basis of specialist knowledge are abstract. Therefore, in communication with the recipient, the problem of their representation arises. It turns out that they can be represented in a number of ways not seen outside the field of this science. In turn, the very choice of concrete representations may seem to be closely related to the communicative situation. Consequently, communication in mathematics turns out to be very complex in terms of the medium used to express content. This is because it can be represented by a word, a phrase or a metaphor, as well as by a symbol, a longer symbolic notation, or even a drawing. Such a wide range of various representations is a peculiar phenomenon in terminology, which is an important part of specialist communication, because it expands the understanding of a term as a sign, especially a linguistic one, with new, often non-literal material. The research touches upon an important problem of what unusual means a sender of a specialist text may use to present a term. The research material consists of popular representations of integrals, appearing in mathematical texts of varying levels of specialisation.

Quelques notes générales sur les textes scientifiques de Bessarion

About a fifth of the Greek manuscripts that belonged to Cardinal Bessarion refer to the mathematical sciences and the philosophy of nature. This article, which constitutes a general, modest and non-exhaustive presentation, attempts to present a classification of these texts in order to identify the interests of this important scholar of the Renaissance in the field that we call today "sciences" and through him, the interests of the Greek scholars of the Paleologian period. For this purpose, we have followed a classification by theme and by author, distinguishing ancient authors from Byzantine authors and indicating, if applicable, the number of copies of the same text that the cardinal possessed. Thus we can for example note the popularity of the arithmetic of Nicomachus of Gerasa, of the treatise of Philoponus on the astrolabe, of less known texts like the pseudo-Timaeus or more recent ones like the treatise on the astrolabe of Isaac Argyros and of course Bessarion’s personal interest in the Almagest. His penchant for astronomy (including astrology - four copies of the Tetrabiblos) is evident, but the number of mathematical texts is also very large. It is clear that the cardinal had little interest in exegetical texts on creation and the world (only two copies of the very popular Hexaemeron of Basil).

Автоматический подсчет сложности математических текстов

Developers of educational materials are expected to focus, inter alia, on the readability of information they include, including textual information. Readability is a measure of how easy a written text is to read. This indicator depends on several factors, such as sentence length, word choice, and text structure. Text metrics can be calculated with special formulas used to assess text readability. The reported study discusses some of the tools for calculating text complexity. It proposes methods of their modification and ways to improve the results. The study is based on the updated data for analyzing the complexity of certain words. Instead of traditional surveys, the data were obtained by comparing pre-selected texts. This significantly reduced the study time. The purpose of the reported study was to find a way to calculate the level of complexity of a mathematical text written in English using one of the “classic” readability formulas—the Dale–Chall formula. The article does not discuss modern methods of assessing text complexity with machine learning tools. The ability to determine the level of text readability solves the scientific issue of accurate assessment of accessibility and comprehensibility of a written text. This helps to ensure that written communication effectively reaches its target audience and conveys its intended message. Readability analysis is usually based on empirical research and mathematical algorithms that take into account various linguistic and cognitive factors to determine the level of complexity of a written text. Accurate assessment of readability makes it possible to improve the effectiveness of written communication in a variety of fields, including education, journalism, and marketing. The use of readability analysis also helps to promote literacy and ensure that written materials are accessible to individuals with different reading abilities.

Educational value of mathematical text problems while developing students' culture of thinking

Educational value of mathematical text problems while developing students' culture of thinking

ANALISIS STRATEGI PENERJEMAHAN TEKS BAHASA INGGRIS-BAHASA INDONESIA: STUDI KASUS MATA KULIAH BAHASA INGGRIS UNTUK PENGAJARAN MATEMATIKA

This study aims to analyze students' strategies in translating English-Indonesian mathematics texts. The study was conducted on students of the Mathematics Education study program in the English for Teaching Mathematics course. The research method is a qualitative descriptive method with data analysis units of text translation as many as 31 students. The translation strategy uses 2 stages, namely the comprehension strategies, referring to the analysis of the source text, and the production strategies, referring to the production of the translated text. The results of the study reveal that in general students have been able to carry out comprehension strategies well as evidenced by their good understanding of mathematics and mathematics learning vocabulary, while the production strategy stage is still lacking, i.e the results of the production of a full sentence translation text in paragraph form involving mathematical vocabulary still too 'stiff'. The conclusion of this study is that the factors of experience and student habituation in reading mathematics texts in English have an effect on the ability in understanding strategies and production strategies.

Kemampuan pemahaman membaca teks dan komunikasi matematik sebagai landasan dalam pemecahan masalah

This article is a review of international research articles that specifically emphasize the discussion of the ability to read mathematical texts and communicate mathematics as a basis for problem solving. The detailed descriptions include the criteria for understanding in reading a mathematical text; the effectiveness of language-based programs in school mathematics on student understanding; the use of learning approaches and media in building conceptual understanding and communication in solving mathematical problems; and strategies to build mathematical communication.

Printing the Bespoke Book

Abstract In 1482, Erhard Ratdolt, a prominent German printer in Venice, issued the editio princeps of Euclid’s Elements. Ratdolt experimented with the new technology of printing to overcome the difficulty in arranging geometric diagrams alongside the text. This article examines the materials and techniques that Ratdolt used in his edition of Elements including his use of vellum, gold printing, and illumination for special copies as well as his use of woodcuts, movable type, and metal-cast diagrams. Significantly, the legacy of Ratdolt’s innovations continued almost one hundred years later in subsequent editions of Elements. In 1572, Camillo Francischini printed Federico Commandino’s Latin translation and commentary, and today, there are at least two surviving copies of this edition printed on blue paper. Both printers, Ratdolt and Francischini, used the printing press to produce unique and bespoke books using material and visual cues from luxury objects like illuminated manuscripts. These case studies of Euclid’s Elements brings together the fields of art history, history of the book, and the history of geometry, and analyzes the myriad ways that printers employed the printing press in the early modern period to elevate and modernize ancient, mathematical texts.

Diversity of mathematical expression: the language of comparison in English and isiXhosa early grade mathematics texts

ABSTRACT The comparison of different languages in terms of specific mathematical ideas can provide insights into the nature of mathematics and into the learning and teaching of mathematics in both languages. This paper uses a typological perspective to contrast the language of comparison of isiXhosa and English, specifically when comparing countable quantities and numbers. Four canonical early grade mathematics texts in South Africa, written in English and translated into isiXhosa, were used as a source and were compared using interlinear morphemic glossing. An analysis of the texts exemplifies differences between isiXhosa and English. For example, in isiXhosa the word ngaphezulu can mean both “more” and “above”. This can cause a conflict when using representations such as the standard hundred chart where bigger numbers appear below smaller numbers. These and other findings may be of interest to instructional designers, teacher educators, and teachers of early grade mathematics in both isiXhosa and English.

History of Mathematics Education in China

China has a very long history of contributing to human civilisation, including its contribution to mathematics development. The Chinese had discovered many essential theories and concepts in mathematics long before the more famous Western mathematicians. Many of China's theories and concepts thousands of years ago have become references to many Western mathematicians. This paper traces the development of mathematics in China from all the dynasties in its history, including the development of mathematical theory, mathematical texts, and the famous mathematical figures of his time.

The Evolution of Mathematics in Ancient China: From the newly discovered 數 Shu and 算數書 Suan Shu Shu Bamboo Texts to the Nine Chapters on the Art of Mathematics

The history of ancient Chinese mathematics and its applications has been greatly stimulated in the past few decades by remarkable archaeological discoveries of texts from the pre-Qin and later periods that make it possible to study in detail mathematical material from the time at which it was written. By examining the recent Warring States, Qin and Han bamboo mathematical texts currently being conserved and studied at Tsinghua University and Peking University in Beijing, the Yuelu Academy in Changsha, and the Hubei Museum in Wuhan, it is possible to shed new light on the history of early mathematical thought and its applications in ancient China. Also discussed here are developments of new techniques and justifications given for the problems that were a significant part of the growing mathematical corpus, and which eventually culminated in the comprehensive Nine Chapters on the Art of Mathematics. What follows is a revised text of an invited plenary lecture given during the 10th National Seminar on the History of Mathematics at UNICAMP in Campinas, SP, Brazil, on March 27, 2013.

Counterexample to a Variant of a Conjecture of Ziegler Concerning a Simple Polytope and Its Dual

Problem 4.19 in Ziegler (Lectures on Polytopes. Graduate Texts in Mathematics, vol. 152. Springer, New York (1995)) asserts that every simple 3-dimensional polytope has the property that its dual can be constructed as the convex hull of points chosen from the facets of the original polytope. In this note we state a variant of this conjecture that requires the points to be a subset of the vertices of the original polytope, and provide a family of counterexamples for dimension $$d \ge 3$$ .

Mapping a university’s research outputs to the UN Sustainable Development Goals

The UN Sustainable Development Goals (SDGs) provide a framework to achieve sustainable development and fulfilling these Goals will take an unprecedented effort by all sectors in society. Many universities and businesses are using the Goals within their strategies and sustainability reporting. However, this is difficult as there is currently no standard methodology to map the 17 goals, 169 targets and 232 indicators. Work at the University of Leicester has focused on developing a robust methodology to map a higher education institution’s (HEI’s) research contribution to the Goals. We have integrated this unique methodology into an automated software tool to measure a university’s academic contribution to the Goals using mathematical text mining techniques. Our ability to quickly and effectively map institutions’ research contributions has boosted our ambitions and efforts to develop software to map the full operations of an HEI or business.

Mapping a university's research outputs to the UN Sustainable Development Goals

The UN Sustainable Development Goals (SDGs) provide a framework to achieve sustainable development and fulfilling these Goals will take an unprecedented effort by all sectors in society. Many universities and businesses are using the Goals within their strategies and sustainability reporting. However, this is difficult as there is currently no standard methodology to map the 17 goals, 169 targets and 232 indicators. Work at the University of Leicester has focused on developing a robust methodology to map a higher education institution's (HEI's) research contribution to the Goals. We have integrated this unique methodology into an automated software tool to measure a university's academic contribution to the Goals using mathematical text mining techniques. Our ability to quickly and effectively map institutions' research contributions has boosted our ambitions and efforts to develop software to map the full operations of an HEI or business.