Mathematical Ideas Research Articles

Unpacking Elementary Preservice Teachers’ Ways of Reflecting on Conceptual Mistakes

ABSTRACT We know that making mistakes in mathematics is an inherent attribute of doing mathematics deeply. Yet, making mistakes is at the root of mathematical fear and anxiety for elementary preservice teachers (PSTs). Valuing mistakes in mathematics is an essential part of shifting from deficient views to asset views of mistakes and having better mathematical learning experiences. In two mathematics content courses at different universities, we implemented a project, “My Favorite Conceptual Mistake,” as a tool for supporting PSTs in reflecting on conceptual mistakes about mathematics. In this article, we describe the ways that the PSTs reflected on mistakes. The PSTs bravely made mistakes about mistakes, joyfully centered mathematical mistakes, and made connections beyond mathematical mistakes. The PSTs, for example, shared how they made mistakes about their mathematical identities or ideas of mathematical pedagogy. Unpacking the ways that PSTs reflected on mistakes expands what we know about supporting mathematical mistakes and enhances PSTs’ experiences with mathematics.

Comparison of the content in Palestinian Mathematical Textbooks for grades 3-5 with the Palestinian Document of Mathematics in light of the content standards of numbers and operations set by the National Council of Teachers of Mathematics (NCTM)

Objectives: The current study aims to identify the standards in the Palestinian mathematical textbooks for the third grade to the fifth grade and the Palestinian document of mathematics, to determine their compatibility in the light of the (NCTM) content standards of numbers and operations.
 Methods: To achieve the objectives of the study, the researcher used the analytical descriptive approach. The study sample consisted of 19 study units in the content of numbers and operations in textbooks and in the mathematics document issued by the Curriculum Center (2016). The researcher used a content analysis card derived from (NCTM, 2000) standards that students should fulfill in grades (3-5).
 Results: The study results showed that most of the sub-standards were found in both textbooks and the document. In addition, The compatibility level of the content of the Palestinian Mathematics textbooks for grades (3-5) with the Mathematics Document based on (NCTM) content standards of numbers and operations ranged from (high to excellent) in the light of the study scale.
 Conclusions: The study recommends enriching the new edition of mathematics books for grades (3-5) with paragraphs that considerate (NCTM) standards in the fields of numbers and operations as they were either not included in the document or the mathematics textbooks, or both. Furthermore, these books should contain paragraphs that help students understand mathematical ideas and operations conceptually by using estimation, mental arithmetic, visual models and diagrams, and activating the use of calculators in performing calculations on natural numbers, fractions and solving problems.

Analysis of Students' Mathematical Communication Ability With Relistic Mathematics Education

Communication skills are skills in conveying meaning in the form of ideas or information from one person to another through certain media and providing rational reasons for a statement, changing forms from verbal language into mathematical language, and illustrating mathematical ideas into descriptions. which is relevant.This study aims to describe students’ communication skills with Realistik Mathematic Education (RME). Data collection techniques are (1) validation, (2) RME, (3) pre-test and post-test of mathematics communication skills, (4) analysis of mathematics communication skills tests, and (5) observation of student activities. This research finally resulted in the identification of students’ communication skills based on indicators of mathematical communication skills, namely (a) Connecting real objects, pictures and diagrams into mathematical ideas, (b) Explaining ideas, situations and mathematical relations, in writing, (c) Stating everyday events. day in language or mathematical symbols. The identification stage is clarified in the category Very good, good, enough, not enough, not very bad. This research was conducted at SMP Negeri 1 Sipirok. To identify the increase in students’ mathematical communication skills in every aspect, the t test was carried out. Based on the students’ answers. The results showed that the students’ mathematical communication skills with RME increased significantly by the value of t = 3.896 while t table = 1.685 so it could be concluded that the students’ mathematical communication skills with RME were better.
 Keywords: Mathematical communication; RME; communication ability

Dynamic and Multipurpose Teaching Models at the First International Exhibition of Mathematics Teaching Material

The International Commission for the Study and Improvement of Mathematical Education (1950) was interested in updating and developing teaching resources to address the pedagogical problems of mathematics teaching in the mid-1950s. As a result of this concern, the First International Exhibition of Mathematical Teaching Material was held in Spain in 1957, an event that had great international repercussions. This work is situated in the field of the history of mathematics education, so the research method used is historical. The aim is to study those mathematical didactic models which, due to their dynamic and multipurpose nature, stood out at the Exhibition. The results show that these materials contributed favorably to the teaching of mathematics, as they made it possible to work on a wide variety of topics and provided numerous advantages over traditional material. The use of these models meant that the mathematical notions or ideas generally arose from the action that the child carried out with the material; they also made the student the main protagonist of their learning.

Analysis of Students' Analytical Thinking Ability and Mathematical Communication Using Online Group Investigation Learning Model

Analytical thinking and mathematical communication are abilities included in the learning process objectives. This study aims to describe students' analytical thinking skills and mathematical communication using the online group investigation cooperative learning model. The subjects of this research were 30 students of class VIII-C. The type of research used is descriptive qualitative. The data to determine the implementation of learning and the ability to think analytically and communicate mathematically are observations, documentation, and tests. The study results show that the online group investigation type cooperative learning model implementation takes place following the steps of group investigation learning. The results of the ability to think analytically and communicate mathematically meet all indicators. The distinguishing indicator of analytical thinking ability is the most widely achieved, and the one that has yet to be completed much is the attributing indicator. So that students' analytical thinking skills have an analytical category. The most widely conducted indicator of mathematical communication ability is the indicator of expressing mathematical ideas in writing. What has yet to be widely achieved is the indicator of analyzing and evaluating mathematical concepts. So that students' mathematical communication skills have a mathematical category.

Analysis of Mathematical Communication Ability in Solving Story Problems Based on Mathematical Ability and Gender

This study aims to test the written mathematical communication skills of students who st udy mathematics material about cubes and blocks at SMP 238 Jakarta. This study uses a qualitative descriptive methodology. Data collection using tests and interview. As a test of the v alidity of the data usin the triangulation technique was carried out by comparing the results of the subject’s mathematical communication ability test with the results of the interview. The subject of this study were students of class VIII SMP 238 Jakarta, totaling 6 students who were divide into 3 groups based on high, medium, and low level of mathematicl ability. This study uses 3 indicators, namely explaining mathematical ideas, situations and relationships/in writing, explaining mathematical ideas in the form of visual images/tables/diagrams, explaining ideas of problem situations picture or real objects into the language of symbols of mathematical models/mathematical expressions. This study revealed that students with high level of mathematical ability were able to answer questions on indicators 1, 2, and 3. Subjects with low level of mathematical ability were able to answer questions on indicators 1, 2, and 3 but still did not understand and were still in complete the method used in answering.

Teacher Moves and Knowledge in Preparing Students for General Certificate of Education Examination

This study investigated an experienced teacher’s moves in preparing high school students for an end of year certificate examination. Six consecutive lessons taught by this teacher were observed and videotaped in the second term of the 2020/2021 academic year. These lessons were transcribed and coded for teacher moves as well as teacher knowledge deployed in any of the moves. First, the two researchers coded teacher moves independently and agreed on them. Second, interviews were used to obtain justification for teacher moves used. Third, Ball, Thames and Phelps’s (2008) categorizations of mathematical knowledge for teaching was used to determine which teacher knowledge motivated the move. Results revealed that this teacher, Ngwa, a pseudonym, deployed the following moves: reading through all the topics to identify key concepts and determine connections between and among them, connecting ideas from one topic to another, returning to previous chapters or units for review of mathematical ideas, reinforce understanding by modifying problems, adoption/adaptations and extension of problems to generate the use of more ideas, withdrawal of the teacher and creation of space for interaction, announcing or advertising what will be learned in the next lesson, and learners designing their own questions for the class to engage with. The findings also revealed that understanding the structure of an examination might be a form of specialized content knowledge as it drives teaching. In addition, teaching and learning was found to be forward and backward to review concepts and reinforce learning in learners. Furthermore, teachers must intentionally create space for student-student interaction which provide opportunities for learners to make sense of what is being taught. The findings of this study might be beneficial to teacher educators and professional development experts to focus training on productive teaching moves. Classroom teachers can also use the outcome of this study for the improvement of their practice of teaching.

Deskripsi Kemampuan Representasi Matematis Siswa Kelas VIII SMP/MTs Ditinjau Dari Gaya Kognitif Visualizer Dan Verbalizer

Mathematical representation ability is one of the basic abilities that every student must have in examining, expressing, and exploring a mathematical idea in the form of a problem, information, definition, etc. to find an appropriate solution according to the results of the representation, whether in the form of pictures, words, tables, symbols, graphs, and patterns in mathematics. The biggest reason that hinders students' bright ideas from appearing is the weak ability of students' mathematical representations which hinders students in determining the completion of mathematical problems and even less careful in reading story problems, weak in problem analysis, inaccurate, and difficulty connecting between concepts. The subjects of this study were students of grade VIII in one of the MTs in the Angkona sub-district, which consisted of two students. The instrument used for this research is the Visualizer Verbalizer Questionnaire (VVQ). Mathematical representation ability test questions and interviews. This study used descriptive qualitative method. Based on the data analysis, it can be concluded that the students' representation abilities with the visualizer and verbalizer styles are quite good. There are several interesting things from the two research subjects, namely the Visualizer subject (SVi) in solving a problem prioritizing the visual aspect in examining each question and the information contained in the a simpler form in representing an image and illustration of a flat shape. Meanwhile, the subject verbalizer (SVe) is more likely to explore detailed and clear information in representing something related to the Pythagorean theorem.

Phenomenological Modeling of Deformation-Induced Anisotropic Hardening Behaviors: A Review

Numerous studies indicate that the hardening behaviors of materials are closely related to their deformation history. In the forming processes with loading path changes, such as sheet metal forming, anisotropic hardening behaviors are universally observed. In this situation, selecting or constructing a suitable anisotropic hardening model is essential. This paper presents a review of the phenomenological modeling of the deformation-induced anisotropic hardening behaviors. At the beginning, the deformation-induced hardening behaviors are introduced together with the relevant experiments. Different from other published review works, this paper is not laid out according to the description of a series of models. Instead, the modeling is emphasized by generalizing the main mathematical modeling ideas among various hardening models and sorting out the description methods for the decomposed anisotropic hardening behaviors. Some prospective development directions for the modeling of anisotropic hardening behaviors are suggested at the end of this work. This review work tries to provide the researchers with an instruction on how modeling for the anisotropic hardening behaviors according to the materials and forming processes.

Research on the integrated and innovative teaching mode of probability and statistics courses under the background of big data

Big data has become a buzzword in many industries, forums and economic exchanges, and its development is interrelated and permeated with mathematics, computers and mathematical statistics courses. Probability theory and statistics, as tools for big data analysis, often belong to different teaching departments, and teaching and research are separated, this paper is based on the Department of Economics and Statistics doing innovative reforms in the discipline foundation, course class connotation and talent training direction to achieve two This paper is based on an innovative reform of the Department of Economics and Statistics in terms of the foundations of the subject, the content of the course and the direction of personnel training. Vertically, realize the theoretical content integration of "high school probability statistics university probability theory and mathematical statistics university statistics big data and statistics"; In the horizontal expansion of the teaching process, grasp the context of "theoretical system interesting cases mathematical modeling ideas project-based embedded teaching competition participation guidance theory and practice review and strengthening"; Form a student-centered and output-oriented integrated and innovative teaching model.

Ability to Understand Mathematical Concepts of Students through Mind Mapping Method

The ability to understand students' mathematical concepts is the ability to absorb and understand mathematical ideas. Good concept understanding skills can help students in solving or providing solutions to a problem. This study aims to determine the ability to understand students' mathematical concepts with the mind mapping learning method and students who are not taught with the mind mapping method. The research method used is quantitative research with a quasi-experimental model designed in the form of non-equivalent control group design. The population in this study was all grade VIII students of SMP Negeri Liman and the research sample was taken in 2 classes with simple random sampling technique. The data collection technique and instrument used is a test in the form of a description question consisting of pre-test and post-test questions. The data analysis technique in this study used an independent t-sample test with prerequisite tests, namely the normality test and homogeneity test then continued with the gain score. Based on the results of the analysis, it was concluded that the ability to understand mathematical concepts of students who learn using the mind mapping learning method is better than students who learn without using the mind mapping learning method. The results showed that there was an increase in the ability to understand mathematical concepts of students in classes who received the mind mapping learning method in the high category with an average gain score of 0,74. Meanwhile, the ability to understand mathematical concepts of students in the control class is 0,29 which is a low category so that the improvement in the experimental class is better than the control class.

Promoting Equitable PST Participation in Mathematical Discourse: Rough Drafts on an Asynchronous Discussion Board

Issues of equity in mathematics classrooms existed prior to COVID-19. For many students, however, meaningful participation in mathematical discussions became nearly impossible in online settings during the pandemic. In this study, we note the diversity in and nature of participation in mathematical discourse in an online course for preservice teachers (PSTs). We investigate the influence of implementing two support strategies for discussion: (a) establishing a “rough-draft/revision” orientation to mathematical tasks; and (b) providing time and structure (tasks and prompts) in an online discussion board for PSTs to post their initial thoughts, react to peers’ solutions, and collectively revise their ideas. In this article, we highlight several benefits of these support strategies to equitable PST participation in a unit on number theory. For example, as compared with oral discussions where only a few PSTs offered their ideas, the written discussion format encouraged every PST to post their ideas. Using a rough-draft/revision stance in the prompts fostered sharing and revealed diverse mathematical approaches, perspectives, and ideas. We argue that giving students opportunities to interact with one another and the mathematics in a variety of ways promotes equitable participation.

Using Judicious Telling to Strengthen Literacy in Mathematics

Language is a conduit for communicating and understanding mathematical ideas. This article explores how we can use judicious telling to attend to students’ written and spoken literacy in mathematics.

LEVEL OF MATH ANXIETY AMONG THE STUDENTS OF THE 5TH – 9TH YEAR OF STUDY IN SLOVAKIA

Mathematics accompanies us throughout our lives. Difficulties in acquiring mathematical ideas can appear even without the presence of a math learning disability – developmental dyscalculia. Our lack of success can result from various external or endogenous causes. People who have a higher level of math anxiety often have difficulties in everyday life, wherever mathematics occurs in some way. Therefore, it is important to pay attention to this issue and look for possible solutions and qualitatively discuss questions related to math anxiety. Why and what level of anxiety do individual mathematical tasks cause in some people? Is it not only the fear and anxiety of failure in mathematics but also of failure in everyday life in solving everyday problems, such as counting up purchases, planning financial transactions, interest, discounts, etc.? These difficulties cause fear, stress and anxiety in individuals, and the impairment of mathematical skills is transferred into adulthood. Chinn (2020) reports that up to 22% of adults in the UK have difficulties with the mathematics that limit them in everyday life. The paper is aimed at finding out the level of math anxiety in a selected population of students and analyzing the questionnaire "How I feel about math" Chinn (2020) translated into Slovak. The research group consisted of 11-16-year-old Slovak students. The aim of the paper is to point out the importance of investigating mathematics anxiety in the diagnosis of a mathematical learning disability. At the same time, to draw attention to the fact that students with special educational needs experience a higher level of math anxiety than their peers. The authors point out that there are no significant gender differences in the experience of math anxiety in the Slovak sample of students and confirm, as stated by Chinn, that 4-6% of neuro-typical (normal) children experience a high level of math anxiety.

Profile of Mathematics Communication Ability of Seventh-Grade Students in Solving Set Problems Based on Cognitive Style

This study aims to describe the profile of students' mathematical communication ability in solving set problems in terms of field-dependent and field-independent cognitive styles. This research method includes qualitative descriptive research. In this study, the collected data was in the form of words so that it did not emphasize numbers. Participants in this study consisted of three students with a field-dependent cognitive style and three students with a field-independent cognitive style from class VII at one of the junior high schools in North Central Timor Regency. The instruments used are a mathematical communication ability test, Group Embedded Figure Test, and interviews. The results showed that students with a field-independent cognitive style have high mathematical communication abilities. This can be seen from the test results of the three field-independent students who are able to express mathematical ideas through oral, written, demonstration and describe in visual form, are able to analyze, interpret, and evaluate mathematical ideas through oral, written, and other visual forms, and are able to use terms, mathematical notations, and their structures to present ideas, describe relationships, and situation models when solving problems mathematical sets. Meanwhile, students with a field-dependent cognitive style have low mathematical communication abilities. This can be seen from the results of the mathematics communication ability test of the three field-dependent students who have not been able to meet all the indicators of mathematical communication.

STUDI LITERATUR ANALISIS PENINGKATAN KEMAMPUAN KOMUNIKASI MATEMATIS SISWA DENGAN PENDEKATAN PEMBELAJARAN MATEMATIKA REALISTIK

The purpose of this study is to describe the results of the analysis of improving students' mathematical communication skills with Realistic Mathematics Education approach. The type of this research is descriptive qualitative research using the library research method. The subject of this research is the most published articles in published journals about mathematical communication skills through Realistic Mathematics Education approach to junior high school students. Based on the findings from 5 journals, it was found that students' mathematical communication improved better in students who studied with Realistic Mathematics Education approach compared to students who studied with conventional learning. Realistic Mathematics Education approach can improve students' ability to describe, understand, and represent mathematical ideas contained in pictures, tables or diagrams. So, Realistic Mathematics Education approach is one approach that can improve students' mathematical communication skills at the junior high school level with effect size score of 1,158 in the large effect category.

The Students’ Representative Processes in Solving Mathematical Word Problems

Representation in mathematics is essential as a basis for students to be able to understand and apply mathematical ideas. This study aims to describe how students produce different representations in solving word problems. In solving word problems, students make verbal–written representations, image representations, and symbol representations. This research uses a qualitative descriptive study involving 75 fifth-grade students at one of the private schools in Makassar, Indonesia. Setting and Participants: two subjects were chosen from 75 participants based on the completion of word problems that resulted in different representations, including verbal–written representations, picture representations, and symbol representations. The instruments used were word problems and interview sheets, although some other students only used one or two forms of mathematical representation. The results of this study indicate that, from the different representations produced that include verbal–written representations, image representations, and symbol representations, students carry out the process of translation, integration, solution, and evaluation until finding answers. In addition, other findings were students’ ‘mathematical literacy which immensely helped the students’ representation process in solving word problems. three forms of representation were found to be produced by students: verbal–written, image representation, and symbol representation. Furthermore, the three forms of representation were created through carrying out four representation processes, namely the processes of translation, integration, solution, and evaluation.

Students Mathematical Communication Ability On Transformation Geometry

The purpose of this study was to determine the level of mathematical communication ability of high school students in the subject of transformational geometry. The population in this study were students of class XI at one of senior high school in Karawang. The sample selection was carried out by means of purposive sampling. This study uses a qualitative descriptive approach, with analytical techniques: (1) data reduction, (2) data presentation, (3) drawing conclusions. The results of this study are that students' mathematical communication abilities on transformation geometry material in one of the high school schools in Karawang district are in the sufficient category with an average value of 49%. One indicator of communication skills that should get more attention is the ability of students to connect real events or the application of mathematics to everyday life in the form of mathematical ideas.

Development of Grade 11 student Learning Achievements on Quadratic Functions Using Brain-Based Learning (BBL) Management

Integrating the knowledge of neurology in teaching has been an idea for learning management design for decades. The current study found the potential of brain-based learning (BBL) for developing high school students’ mathematics learning achievement. The purposes of the study were to investigate the effects of BBL learning management on grade 11 students’ learning achievement of quadratic functions and to examine students’ satisfaction with the BBL as the main principle of learning activities design. The participants were 36 grade 11 students selected by the cluster sampling method. The instruments were brain-based learning management, a learning achievement test, and a satisfaction questionnaire. The statistics used in data analysis were percentage, mean score, standard deviation, a paired t-test, and the index of effectiveness with the determining criteria of 75/75. The findings indicate the benefits of the BBL on mathematics education. They illustrate how learners nearing the end of high school could understand a complex mathematical idea using the BBL instructional strategy.

Student Representation of Mathematical Thinking In Mathematical Problem Solving

The way students who want to become teachers represent their mathematical reasoning when they solve mathematical problems—using case studies and qualitative techniques. Data were gathered from the vignette results of student work. They are using snowball sampling for subject selection. Three third-semester mathematics education program participants served as the study's research subjects—ways for gathering data, such as interviewing and recording. Three steps of the analysis were completed: presentation of data, elaboration of conclusions and verification. As a consequence of meeting all markers of mathematical thinking representation, the S1 and S2 subjects with high and moderate academic talents had good mathematical thinking representation abilities. Because S3 students with limited intellectual skills cannot still represent mathematical ideas.