Mathematical Language Research Articles

Developing a Mathematics Module in Support of Secondary School Reflective Learning

Reflective learning is a teaching method where active student learning is a core component of instructional design. In mathematical instructions, reflection and knowledge-construction take place in the language of mathematics. The development of mathematics module in the current study employs three computer-mediated communication (CMC) tools: Google Classroom, discussion forum and text messaging. This study seeks to determine the communication and learning forms which support reflective learning in the usage of CMC tools within the mathematics module. 30 Form 2 students with different mathematical abilities were selected as participants. Data collection include students’ online communication on Google Classroom (GC), forum discussion, and text messaging. A survey of students’ perception of communication using CMC tools and learning were also distributed. Google Classroom and text messaging were reported to have the highest frequency of communication among learners. The combined usage of the three CMC tools was found to be effective as it caters to learners’ preferred learning styles, encouraging collaboration and experiential learning. This study offers insights into group interaction in a reflective learning environment and its influence on the scaffolding of mathematics knowledge.

Визуализация задач начертательной геометрии посредством Wolfram Mathematica

The possibilities of Wolfram Mathematica (WM), which is a package of symbolic mathematics, are endless. In this paper are investigated the possibilities of WM software product contextualization in the process of geometric-graphic teaching of students; is considered the experience for using a set of WM computational algorithms in teaching practice. The source codes and output data of our own WOLFRAM projects are offered, which are illustrative, in the form of interactive graphs, visualization of the solution for one of DG course’s basic problems on construction of points A, B, C and D, given by coordinates in space; construction a plane of general position passing through points A, B and C; determining positions of these points and the constructed plane in space; and also on determining the point D belonging to this plane. Have been presented examples of several of the existing WOLFRAM projects in the form of interactive graphs used in teaching. The study of applied issues and the ability to translate a professional problem into mathematical language, working in WM, provides a student with an opportunity to assimilate the necessary competencies.
 Interactive visualization of solving DG problems, which can be carried out using WM, together with traditional problem solving, enriches the content of geometric education, introduces new opportunities in organization of the educational process, allows stimulate, maintain and increase students' interest in studying the discipline and further research in the area of DG. However, the ability to work in WM cannot replace the fundamental knowledge obtained by students of a technical high educational institute from the traditional course, but only complements the DG course by WM acquaintance.

Programming as Language and Manipulative for Second-Grade Mathematics

This article reports on an exploration of how second-graders can learn mathematics through programming. We started from the theory that a suitably designed programming language can serve children as a language for expressing and experimenting with mathematical ideas and processes in order to do mathematics and thereby, with appropriate tasks and teaching, learn and enjoy the subject. This is very different from using the computer as a teaching app or a digital medium for exploration. Children tackled genuine puzzles – problems for which they did not already have a pre-learned solution. So far, we have built four microworlds for second-graders and tested them with a diverse population of well over three hundred children. The microworlds focus on the most critical second-grade mathematical content (as mandated in state standards), let children pick up all key programming ideas in contexts that make them ‘obvious’ (to maintain focus on the mathematics) and suppress all other distractions to minimize overhead for teachers or students using the microworlds. Because children see the results of the actions they articulate (in the computer language, Snap!), they can evaluate their methods and solutions themselves. The feedback is purely the outcome, not happy or sad sounds from the computer. Notably, nearly all children showed intense engagement, some choosing microworlds even outside of mathematics time. Teachers spontaneously reported this as well, with special mention of children whom they found hard to engage in regular lessons. We report our experiments and observations in the spirit of sharing the ideas and promoting more research.

KEMAMPUAN MENGERJAKAN SOAL FISIKA MELALUI KONSEP MATEMATIKA AWAL PROSES PEMBELAJARAN FISIKA

In general basic laws in physical theory are expressed in mathematical language. Mathematical knowledge is an important prerequisite as initial knowledge that students must possess before studying physics. The purpose of this research is to know and improve students abilities in doing physics problems by using the application of mathematical concepts in the beginning of physics learning. This research is a quantitative descriptive study with test and interview methods. The results of the application of mathematical concepts can improve the ability of students of SMP Negeri 3 Tagulandang in working on physics problems especially on straight motion material. The types of questions used for test are questions that belong to the C1-C6 domain with the highest ability improvement found in C4 questions.

Analysis of Basic Students Learning Difficulties in Multiple Materials

<p><em>This study aims to obtain an overview of learning difficulties. This research was conducted in third class of SDN 2 Cintaraja. The research method used is descriptive qualitative. The data collection technique was carried out in two ways, namely by giving story questions and interviews. The story questions used in this study were three questions which refer to four characteristics of student learning difficulties according to Jamaris in 2014 (weakness in counting, difficulty in transferring knowledge, understanding of mathematical language, difficulty in visual operations) regarding the multiplication. The results showed that there were still many students who had learning difficulties in this multiplication material, of the six students who were sampled all of them were only able to master one characteristic of the four characteristics of learning difficulties, namely in terms of understanding the language of mathematics, while the other three learning difficulties had not able to be mastered by them, namely in terms of calculating weaknesses, difficulties in transferring data, and difficulties in visual operations of the multiplication material.</em></p>

Life tables and a physiologically based model application to Corcyra cephalonica (Stainton) populations

The rice moth Corcyra cephalonica is a harmful insect pest for grains stocked in storage systems. Its infestations represent a serious concern among producers, because of the non-marketability of the products affected by it and subsequent economic losses.New technologies are improving the supply chain of the stored grains, in line with the integrated pest management framework. However, a prompt control action also requires an in-depth knowledge of insect pests’ biology and their response to environmental parameters. If this information is available, it can also be translated into mathematical language. The modelling of insect pest populations is increasing in utility, particularly if the models are included in decision support systems.The aim of this work concerns two aspects of a model application and validation. Since physiologically based models require information about interactions between species and environment, C. cephalonica individuals were reared at different constant temperatures: 18, 21, 24,26, 28, 30,34 and 36 °C. This first part provided the life tables, whose data were used to estimate the parameters of the Logan, Briére, and Sharpe and De Michele development rate functions.The second part of the work concerns the application of a physiologically based model described by a first order partial differential equation. The validation of the simulations was conducted with a semi-field experimentation with three repetitions.Results showed that the life tables are well represented by the Sharpe and De Michele development rate function, and that the physiologically based model proposed is reliable in representing field populations.

Designing and enacting instruction that enhances language for mathematics learning: a review of the state of development and research

After four decades of research and development on language in mathematics classrooms, there is consensus that enhancing language is crucial for promoting students’ mathematics learning. After briefly sketching the theoretical contexts for work on this topic, in this paper we present six design principles for instruction that enhances language for mathematics learning. We then review the research that provides an empirical foundation for these principles, (a) concerning the design of learning environments to enhance language for mathematics learning and (b) on teaching practices (including teacher moves and classroom norms) involved in the enactment of those designed learning environments. Without claiming completeness, this review of the state of development and research shows that some aspects of design and instruction that enhance language for mathematics learning have been well researched, whereas research gaps for other aspects persist.

„Als der algoriſmus ſpricht…” – Indisch‐arabische Zahlen und der Algorismus in der Geometria Culmensis

AbstractThe Geometria Culmensis was written around 1400 and is one of the first known mathematical treatises in German. A textbook on land surveying, it not only uses the Hindu‐Arabic numerals throughout the text but also frequently refers to the most influential treatise on these new numbers, the Algorism. Roughly a hundred years before the first German arithmetic books, the Geometria Culmensis tries to educate laymen on the techniques found in the Algorism. This leads to some pertinent questions: How early did the Hindu‐Arabic numerals spread through the vernacular milieu in German‐speaking countries? How important was a mathematical education outside of a scholarly environment (the text refers to the necessity of teaching laymen how to measure and calculate correctly)? What does this early German mathematical language look like, knowing that the author of the Geometria Culmensis had no template from which to copy?

Mathematical Analysis of Uncertainty in Bangladesh Agricultural Sector

This study presents three different mathematical models for profit optimization of agricultural products in Bangladesh. The prime focus of the paper has been to develop a Mixed Integer Linear Programming (MILP) model and analyze this model for two situation of demand uncertainty. Considering demand will be known before and after production. For the mentions of above two cases, we investigate the change of solution applying least demand, maximum perhaps demand and extreme demand scenarios. I think this is real life problem and this analysis will be helpful for all types of agricultural producers. The proposed MILP model is to maximize the total profit and also to estimate the profitable production locations. The formulated MILP model were solved by A Mathematical Programming Language (AMPL) and results obtained by appropriate solver MINOS. Numerical example with the sensitivity of several parameters has been deployed to validate the models. Results show that maximum perhaps demand scenario gets better solution according to our expected value compare of other two scenarios.

Preface

Proceeding Young Scholar Symposium on Science Education and Environment (YSSSEE) 22-23 September 2020, Lampung, Indonesia Preface Young Scholar Symposium on Science Education and Environment (YSSSEE) is the annual conference held by Universitas Islam Negeri Raden Intan, Lampung, Indonesia. The theme of this conference is Science, Technology and Education for Sustainable Environment with the Focus and Scope of this research including (1) Physics; (2) Material Sciences; (3) Applied Physics; (4) Natural Sciences; (5) Sciences Education; (6) Mathematics; (7) Mathematics Education; and (8) Environmental Sciences.The keynote presentations are provided to talk the current issues in Education and Environment. The keynote speaker Prof. Konstantinos Ravanis, Ph.D., from Laboratory of Didactics of Sciences, University of Patras, Greece, presented the study of the physical sciences in early childhood education. Prof. Dr. Husin Alatas, M.Si., from Institut Pertanian Bogor, Indonesia, presented the study about Understanding complexity paradigm & sustainability of complex system. Jisun Park, Ph.D., Ewha Womans University, South Korea, presented the study about students’ unintended learning in elementary school practical science lessons. Korhan Cengiz, Ph.D., presented the study about novel energy efficient protocols for wireless sensor networks (WSNs). Prof. Cari, Ph.D., Sebelas Maret University, Surakarta, Indonesia, presented the study about physics and mathematics language as a physics learning tool. Dr. Achmad Samsudin, Universitas Pendidikan Indonesia, Indonesia, presented the study about measuring students’ conceptions on physics concepts: a case in Indonesia.We would like to thank to all of the participants attending this conference and also to committee for their contribution to this high-level conference and its overall success. We also would like to thank to the reviewers for their positive contribution to maintain the quality of the articles presented in this conference. We also appreciate the contribution of our sponsor supporting the conference.List of Executive Chair, Organizer, Co-Organized, Keynote Speaker, Advisory Board, Organizing Committee, Documentations of YSSSEE arein this pdf.

The dynamical landscape: phonological acquisition and the phonology–phonetics link

During acquisition children internalise adult-based phonological patterns and alternately adopt and discard child-specific patterns reflecting their unskilled production. The child-specific patterns are often assumed to be low-level phonetic effects, and so, in a classical modular feedforward grammar, they should not interfere with the higher-level adult-based phonology. This paper reports an interaction in which the application of a categorical adult-based process (Voice Assimilation) is conditioned by a gradient child-specific process (fricative devoicing). Acoustic analyses of longitudinal data from a Polish-speaking child reveal variable Voice Assimilation effects in target voiced fricative–stop/stop–fricative clusters (voicing and devoicing), correlated with the extent of voicing in fricatives in non-assimilatory contexts. I analyse this phonology–phonetics trade-off by appealing to symbol-like dynamical representations, expressed in the language of non-linear mathematics. Such representations offer a non-derivational link between the qualitative and quantitative aspects of speech. Variability ensues as a natural consequence of grammar change.

Possible causalities between malnutrition and academic performances among primary schoolchildren: a cross-sectional study in rural Madagascar

BackgroundThe importance of addressing malnutrition is increasing in the context of children’s health and their academic performances. Childhood malnutrition further could reduce a country’s economic productivity. No earlier study adequately...

Pre-service student teachers’ conceptions of the notion of limit

ABSTRACT The concept of the limit is often experienced as a very abstract concept. In this study we explore the understanding of the concept of the limit with 74 students who are prospective high school mathematics teachers. The study is located within the first of three calculus courses which they study as part of their bachelor’s degree in education at a university in South Africa. The students were asked to describe what they understood by the limit of a function at a certain point. The written responses were analysed inductively and six categories were identified as descriptors of the responses. Understanding the concept of the limit of a function requires the coordination of many processes, encompassing various constructs which must satisfy certain conditions for the limit to exist. The students in each category seemed to have differentiated between some constructs and conditions but struggled with others. Their responses also revealed differences in the way in which the language was used to describe the concept. This study strengthens existing research findings about students’ struggles with the formal mathematical language as well as their struggles with dealing with variation induced by the different constructs embedded in the concept.

Korean language math-to-speech rules for digital books for people with reading disabilities and their usability evaluation

Although Digital Accessible Information System, an international digital talking book standard, is conducting active research on upper level education for people with reading disabilities, special components like images or formulas are difficult to read aloud in Korean. Therefore, this paper defines Korean math-to-speech rules for Contents Mathematical Markup Language based on the formulas used in the Korean middle school and high school freshman curriculum. Based on the proposed rules, a program that turns formulas expressed in Contents Mathematical Markup Language into speech was also designed through Extensible Stylesheet Language Transformations. Finally, a performance test was conducted to determine both the accuracy of the transformed formulas and the clarity of formulas when read aloud.

HOTS study primary teacher education UNNES students based on self-regulated learning

This research aims to study students’ High Order Thinking Skills (HOTS) in Primary Teacher Education Department of Universitas Negeri Semarang (UNNES) viewed from their Self-Regulated Learning (SRL). The research method in this research is a mixed method of a sequential explanatory model. This research was conducted in the Department of Primary Teacher Education at UNNES for students of class 2020 in the Basic Mathematical Concept course. Data collection techniques using questionnaires, documentation, interviews. Analysis of quantitative data in the form of validity and reliability of the instrument was followed by descriptive analysis. Qualitative data analysis was performed by triangulation and descriptive statistical analysis. Analysis of quantitative data found two categories of the level of SRL, namely medium and high levels. The results of the analysis of student answers were obtained: (1) Students with moderate SRL category interpret the questions into Mathematical language, and the way they identified the problem is less communicative, while the students with high SRL category interpret the questions into Mathematical language communicatively; (2) Based on students’ ability to evaluate, students with moderate SRL category have not been fluent yet, while the students with high SRL category have been fluent in evaluating, and (3) Based on their creativity, students with moderate SRL still need more practices, while students with high SRL category have been fluent. The conclusion of this study is the ability to interpret problems and the habit of examining problem-solving carried out into the differences between the two categories.

Visual reasoning and the perception of forms

Whenever a new device enables our senses to access an uncharted sensible world, our experience needs to be widened to be able to embrace it. Many animals don’t recognize themselves in mirrors. Thus, mirrors found in ancient Egyptian tombs bear witness to a device that involved a widening of human experience. While by then reflectors were commonly believed to hold the spirit of their beholder, they also provided the motivating force for use of geometry as a logical framework, rather than the form of the outer world. Euclid of Alexandria conceived of geometric constructions and their rules as the connecting link between visual world and hypothetical-deductive reasoning. Yet, he didn’t have a clue about receivers. In our view the problem of linking received information in an image format to a mathematical space cannot be solved once and for all, but rather needs to be posed and understood afresh once in a while. All the more so in an information and telecommunication era, when the techniques of acquisition and rendering of visual information have been extended well beyond the domain of optical instruments, and the language of mathematics has advanced to a different level of proficiency.

Some Results of Stock Trading Strategy Based on Fuzzy System

In order to better study the stock trend and master the basic rules of stock trading, this paper uses the fuzzy system theory to transform the technology trading strategy in stock into the membership function in fuzzy mathematics, so as to study the trend change of technology trading rules in dynamic stock price with mathematical language. It can be seen from the experimental results that when only the moving average rule is adopted, the stock price trend is relatively flat, and the specific changes of the price cannot be accurately obtained. However, when the bull and bear rule is added, the stock price jumps greatly, so that the changes of the price can be easily captured, so as to make corresponding strategic adjustments to maximize the income.

On one approach to assessing the conflictological competence of a manager using the method of mathematical modeling

The article deals with the formulation of the problem of assessing conflictological competence by means of mathematical modeling. An analysis of existing definitions of this concept is provided. Conflictological competence as the most important feature of a manager’s professionalism is a complex concept that assumes the presence of theoretical knowledge about the possible ways to work with a conflict, a certain set of skills for their practical application and the necessary personal and professional qualities for effective conflict management in the interests of the organization. Conflictological competence of a leader can be defined as an integral assessment of the degree of achievement of goals at the stages of conflict management: the readiness of the leader to prevent conflict, conflict resolution and overcoming its negative consequences. The content model of the conflict is considered as the basis of modeling. To translate this model into mathematical language, the analitic hierarch process (AHP) by Thomas L. Saaty, which has its own software Super Decisions, is used. As a result of the use of AHP, the relative degree of interaction of elements in the hierarchy, the priorities of alternatives and the optimal solution are determined. In the article on the example of conflict in an organization, AHP is used to assess the conflictological competence of the leader. The proposed analytical toolkit can be effectively utilized by experts, managers and decision makers to assess conflictological competence.

A Study on Infant Learning Thinking Based on the Integration of Truth and Reality

This study focuses on the advertisement of children’s mathematical thinking. It analyses the scientific nature of the advertisement (curriculum system) and summarizes some methods to cultivate logical thinking. It also points out the limit of the course, such as: children’s action thinking has not been fully concerned, entity image thinking and mathematical language thinking is difficult to cultivate.

Optimal Design of a Fuzzy Controller Based on the Imperialist Competitive Algorithm for Fourth-order Nonlinear Systems

Nowadays, control and optimization of systems are two important and noticeable topics in all fields of science and engineering. One of the control methods, widely used because of its simplicity and accuracy, is the fuzzy control, which is based on the fuzzy logic theory. In the uncertainty conditions, this theory is able to formulate many inaccurate and vague implications, variables and systems in mathematical language, and provides requirements for reasoning, inference, control and decision making. This paper studies the stabilization of a Translation Oscillations with a Rotational Actuator (TORA) nonlinear fourth-order system by using a new fuzzy control technique which utilizes the small number of membership functions and rules. Besides, to determine the proper values for the controller parameters, the Imperialist Competitive Algorithm (ICA) is employed. Unlike the other optimization algorithms, ICA is not originated from evolutionary behavior of nature, but it is inspired by a human natural phenomenon called imperialism. In the optimization procedure, the objective function is defined as the sum of integrals of the rotor angle and the cart position. Finally, the comparison between the results obtained by the proposed strategy and some other researchers’ methods is provided, which shows the superiority of this work.