General Mathematics Research Articles

Impacts of classroom teaching practices on students’ mathematics learning interest, mathematics self-efficacy and mathematics test achievements: a secondary analysis of Shanghai data from the international video study Global Teaching InSights

Teaching effectiveness is a core issue in educational research; however, there is little consensus about the most important results of classroom teaching from an international perspective. The effectiveness of teaching has remained a ‘black box’ for a long time. In the secondary study described in this paper we used empirical data for Shanghai taken from the international Organization for Economic Co-operation and Development (OECD) study Global Teaching InSights (GTI)—initially the Teaching and Learning International Survey (TALIS) Video Study—which was based on videotaped direct observations of classroom teaching. Eighty-five junior high school mathematics teachers and their students in Shanghai were observed to explore the impact of specific teaching practices on students’ interest, self-efficacy, and mathematics achievement scores. The results revealed that social-emotional support and instruction quality were the key dimensions relating to the characteristics and differences of mathematics lessons in Shanghai. While the former had a significantly positive impact on students’ general mathematics self-efficacy, the latter had a significantly positive impact on students’ mathematics interest. Although specific teaching practices had no significant direct impact on students’ mathematics achievement scores, social-emotional support and instruction quality considerably influenced students’ academic performance in an indirect way via general self-efficacy.

MATH ANXIETY, LEARNING ENGAGEMENT AND PERCEIVED USEFULNESS OF TECHNOLOGY AS PREDICTORS TO PERFORMANCE OF STUDENTS IN MATHEMATICS

The focus of this research was to verify if there was a link among anx-iety toward mathematics, learning engagement, and their perception of technology’s usefulness in mathematics. This ex-post research looked into the relationship and predictive degree of students’ math anxiety, learning engagement, and perceived usefulness of technology to their mathematics achievement. Both math anxiety and students’ perceptions of the utility of technology in learning have a significant impact on students’ mathematics performance, but not on their engagement. The findings showed the impor-tance of a high level of anxiety in improving student math performance. Additionally, math anxiety and the perceived usefulness of technology were discovered to be predictors of student mathematics performance. The findings suggest that anxiety, engagement, and perceptions of technology’s usefulness should all be considered when improving students’ general math-ematics performance.

Online Collaborative Learning and the Enhancement of Most Essential Learning Competencies in General Mathematics among Grade Eleven Senior High School Students

Making collaborative learning happen during a pandemic raised concerns and doubts among educators, given that learning during these trying times emphasized the importance of cooperating, corroborating, and interacting, particularly on subjects that were thought to be difficult, such as mathematics. The uncertainty stems from the question of how collaborative learning affects competency learning. Teaching students to acquire mathematical competencies is difficult in and of itself in a face-to-face setting; thus, peer-teaching and collaborative learning are always on the list to help below-average learners cope easily. This study determined the effect of online collaborative learning on the enhancement of most essential learning competencies (MELC) in General Mathematics. The study focused on thirty-five (35) respondents who were enrolled in online classes in the aforementioned subject during the academic year 2020-2021. The results revealed a significant difference between the pre-test and post-test scores, indicating that the OCL aided the students in mastering General Mathematics competencies. It was suggested that Mathematics Supervisors, Coordinators, Master Teachers, and Teachers propose in-service training or a learning action cell (LAC) that covers teaching and training of ways and means for teachers to make collaborative learning possible through the use of various modern-day applications such as Google Breakout Rooms, Open Broadcaster Software (OBS), and other platforms to ensure learners can still interact and learn with peers amid tumultuous times.

The Algebraic Sets in the General Mathematics and Teaching Them

Most of the pictures in general mathematics are algebraic sets. Indeed, even the first figures taught in class 1 of elementary school are already algebraic sets or part of algebraic sets, such as lines and segments. Therefore, knowing with certainty the properties of algebraic sets is very important for good teaching of high school mathematics, and it is essential to teach them better. To give suggestions and help teachers teach mathematics more effectively, in this report, we will present the Zariski topology, some of their most important properties and the methods to teach algebraic sets.

Proposal for developing mathematics self-study capabilities in Vietnam highschool

In terms of general learning and Mathematics study, in particular, self-study ability is a fundamental element to promote learning efficiency. The research objective focuses on Proposing specific measures for developing the math self-study ability of high school students. Secondly, the research result reveals 5 methods for developing math self-study ability of high school students in Vietnam, including (1) Fostering motivation, attitude, sense of self-study, nurturing passion and forming knowledge about Math self-studying for students through field trips or extra-curricular activities; (2) Applying objective tests as a tool to examine and evaluate students' self-study at home; (3) Training and developing students' self-instructed math skills in terms of finding and reading documents of the specific content of Mathematics and skills in listening, communicating and taking notes in class; (4) Designing and organizing for students learning activities in the direction of practising scientific research; (5) Fostering and improving student’s self-assessment skills, mistakes correction after each process of studying a specific content. The final part of the study will discuss several issues and solutions that need to be considered when putting these teaching Mathematics measures into practice at Vietnamese high schools.

Pre-Service Teachers’ Classroom Management Styles And Senior Secondary Students’ Performance In General Mathematics In Rivers State, Nigeria

Pre-Service Teachers’ Classroom Management Styles And Senior Secondary Students’ Performance In General Mathematics In Rivers State, Nigeria

Visually impaired student-teachers’ knowledge and use of basic assistive technology tools for mathematics

Studies show that assistive technology tools have provided opportunities for the visually impaired in some developed countries to pursue mathematics programmes and foster inclusive education. However, their counterparts in developing countries sparingly participate in any mathematical activity due to low knowledge and use of these tools. The main purpose of this study was to expose student-teachers with visual impairments to basic assistive technology tools. The knowledge and use of the tools helped to convert, convey and interpret basic mathematical equations. The design was a case study involving five student-teachers who were admitted to the Department of Basic Education, University of Education, Winneba to pursue a Post Diploma in Mathematics programme. A semi-structured interview guide was used to collect the data whose items contained tools for general administration, additional support, STEM, mathematics instruction, polynomials and assessment. These served as the cases of the study and data analysis. The analysis was undertaken in two stages. The first stage explored their knowledge and use of the assistive technology tools. The second stage analysed transcriptions of statements. The two stages helped to corroborate the findings. To ensure the validity and reliability of the findings, the interview guide was validated by post-graduate students of the Department of Special Education and Basic Education. The findings showed that the student-teachers had little knowledge and use of the basic assistive technology tools. However, they were still desirous to learn and use the basic assistive technology tools for mathematics teaching and learning. It was therefore recommended that stakeholders make available and accessible common basic assistive technology tools to schools, and restructure the mathematics curriculum to suit the integration of assistive technology tools.

Topological Essence of the Concept “Limit of a Numerical Sequence” in the General Mathematics

High school mathematics includes a number of extremely important concepts, including the concept of the limit of the number sequence. However, most students when learning it do not understand it with certainty, but only accept it to apply it to solve exercises. This paper aims to give a topological essence of the concept of limit of a sequence and present some methods for teaching this concept in general school in Viet Nam. The Paper consists of four parts. Part 1 presents an introduction to the definition of “Limit of a sequence”, part 2 deals with Some properties derived from definitions and notes in teaching, part 3 covers the Mathematical essence of the concept limit of a number sequence and part 4 talks about Defining topology on the set of real numbers. In each section, we include comments to help teach these notions and concepts. In each section, we make comments and observations to teach these concepts better.

Topological Essence of the Concept “Limit of a Function” in the General Mathematics

The limit of a function is one of the most important concepts in high school mathematics. But unfortunately, not many students understand the essence of this concept. They had to accept it. This paper presents the topological essence of a limit of a function and discusses methods for teaching this concept in general education in Viet Nam. It consists of four parts. Part 1 talks about the definition of “Limit of a function”, part 2 covers the Mathematical essence of the concept limit of a function, part 3 deals with Defining the limit of a function in a topological space of real numbers and part 4 presents Adding a topology on the set of real numbers and limit of a function. In each section, we include comments to help teach these notions and concepts.

Topological Essence of the Concept "Limit of a Numerical Sequence" in the General Mathematics

Topological Essence of the Concept "Limit of a Numerical Sequence" in the General Mathematics

Comparison on the Effectiveness of Modular Learning in General Mathematics among the Senior High School Strands

This study aimed to compare the effectiveness of modular learning among senior high school strands and investigate the influence of students’ demographic profiles on their academic performances. Using One Way ANOVA, results showed a significant difference in the test scores obtained from the different strands. Results with Tukey HSD revealed that ABM performed best under modular learning, followed by STEM, GAS, ATS, and EIM, respectively. Pearson’s r revealed a significant correlation between student’s sex, monthly income, and parents’ employment status to students’ academic performance. Furthermore, the z test for two means determined that there was a significant difference in the scores of males and females. From these results, the researcher suggests that teachers handling TVL tracks must exert extra effort in delivering their mathematics lessons to close the gap in academic performance with the students from academic tracks.

Math anxiety differentially impairs symbolic, but not nonsymbolic, fraction skills across development.

Although important for the acquisition of later math skills, fractions are notoriously difficult. Previous studies have shown that higher math anxiety (MA) is associated with lower performance in symbolic fraction tasks in adults and have suggested that MA may negatively impact the acquisition of fractions in children. However, the effects of MA on fraction skills in school-aged children remain underexplored. We, therefore, investigated the impact of MA on the performance of younger (second and third graders) and older (fifth and sixth graders) children in math fluency (MF), written calculation, fraction knowledge (FK), and symbolic fraction and nonsymbolic ratio processing. On the basis of our prior work suggesting a perceptual foundation for fraction processing, we predicted that symbolic, but not nonsymbolic, math skills (especially fractions) would be impaired by MA. As predicted, higher MA was associated with lower performance in general mathematics achievement and symbolic fraction tasks, but nonsymbolic ratio processing was not affected by MA in either age group. Furthermore, working memory capacity partially mediated the effects of MA on general mathematics achievement, FK, and symbolic fraction processing. These results suggest that understanding the bidirectional interactions between MA and fractions may be important for helping children acquire these critical skills.

A study on the improvement of basic general mathematics according to changes in the basic mathematical ability of first-year college students in the fields of science and engineering

The objective of this study is to examine changes in the Mathematics Curriculum and the College Scholastic Ability Test that affect the changes in the Basic Mathematical Ability of students enrolled in Science and Engineering departments and to compare and analyze the educational contents of basic general mathematics completed by first-year students in science and engineering fields in order to provide improvement plans for basic general mathematics. In Korea, whenever the mathematics curriculum is revised, the content covered in the previous curriculum is deleted or weakened in order to optimize the educational content, and ‘Calculus’ and ‘Geometry’ are required for science and engineering students to choose in the college scholastic ability test. Thus, the basic academic ability of mathematics is lowered, and it is difficult to complete the basic general mathematics taught in the first year of university. In order to solve this problem, it is necessary to analyze the mathematics and curriculum to include deleted or weakened contents in the university's basic general mathematics, to understand the students' basic academic ability in mathematics, and to operate basic general mathematics by level or operate basic mathematics courses. In addition, when revising the mathematics both in curriculum and the university scholastic ability test, the opinions of professors in charge of basic general mathematics education at universities should be sufficiently reflected to minimize changes in key factors for students to complete basic general mathematics, and it is necessary to provide policy support at the national level for the development and operation of the curriculum for general mathematics education at a college level.

Getting into Learners’ Pace: QR Coded Supplemental Materials for SHS Learners in the Division of Laguna, Philippines

“QR” stands for “Quick Response”, which refers to the instant access to the information hidden in the Code. It is a two-dimensional version of the barcode, typically made up of black and white pixel patterns. Now, it has found its way into mobile marketing with the widespread adoption of smartphones. This study explored the use of QR Codes in educational setting. The QR-coded supplemental materials were used both in modular and online distance learning since both modality use weekly home-learning plan (WHLP) being distributed to students in a regular basis. They were attached to WHLP beside the General Mathematics subject for the students to scan using their smartphones. If they don’t have the scanning application in their phones, they could just encode the affixed link in WHLP through Google engines and the teacher-made brochure will automatically pop out. Upon scanning or encoding the affixed link, the learners were able to have a glance of the supplemental material. Fifteen schools, from the Department of Education, Division of Laguna, Philippines, including the home school of the author, participated. The study made use of explanatory sequential mixed method of quantitative and qualitative approaches. Findings revealed that there is a significant increase in the academic performance of Grade 11 learners in the General Mathematics when QR-coded supplemental materials were used. Both learners and teachers highly agree that QR-coded supplemental materials have various benefits in lesson preparation and understanding of key concepts and competency in General Mathematics. Themes developed are (1) Easy access is a key to understanding and learning, and (2) Less time to browse, more time to help and teach. Reflection and challenge on continuing to make ways for knowledge to be accessible was given at the end of the study.

Exploration of Mathematics Culture and Stimulation of Ethnic Students’ Interest in Learning Mathematics

The interest, attitude, habit and ability of ethnic students in primary and secondary schools in Western China are not optimistic. In the mathematics classroom teaching of primary and secondary schools, appropriate infiltration of relevant mathematical cultural knowledge can enhance students’ self-confidence in learning mathematics, and stimulate students’ interest in mathematics learning, in order to promote students to understand and master mathematical knowledge and its ideological methods, and produce correct views on Mathematics and mathematics learning, which can promote the improvement of students’ mathematical achievements and the development of teachers themselves. The western region has many ancient cities, small border villages, classical culture, human geography, overview of natural scenery, unspoiled ecological environment, legends, wind washing dust, weddings and funerals, etc., all these are materials that can be used for mathematics classroom teaching in primary and secondary schools, which are of great educational significance to students’ mathematics development. According to the requirements of mathematics curriculum standards, primary and secondary school mathematics teachers should fully explore the rich and colorful traditional mathematics culture curriculum material resources in ethnic minority areas, reorganize the content of national general mathematics teaching materials, and design classroom teaching, as well as compile teaching plans for primary and secondary school mathematics classroom teaching according to the reality of students in the western region. It can improve the mathematics learning achievement of ethnic students in primary and secondary schools in the western region, so as to improve the quality of science teaching in the western region.

일반강의식 수업에서 교수·학습 방법에 관한 연구

From the past to the present, general mathematics classes have pursued changes in the educational environment. However, due to the actual college education conditions, general lecture classes are taking place. In this study, we wanted to find teaching and learning methods that would help students in general lecture classes. As a result, one group that took notes about class content and provided feedback on individual tasks was more effective in math achievement than the group that provided feedback on the same task. In addition, one group who took notes on class content and provided feedback on individual assignments was more effective in math achievement than the group who took notes on class content and provided feedback on the same task.

Pre-Examination Study Preparation and Its Effect on the Summative Test Score in General Mathematics of Grade 11 Senior High School Students of Dr. Carlos S. Lanting College

Examination weeks are the peaks of an academic year. The paper-and-pen test determines whether the learners are able to attain the specific educational standards set by the pedagogical curriculum they follow. The study wants to determine the pre-examination study preparation and its effect on the summative test score in general mathematics of grade 11 senior high school students of Dr. Carlos S. Lanting College. This study centers on two factors, the frequency and strategy of the student used on their pre-examination preparation. The descriptive and quantitative method of research is used in this study. As a results and conclusions in terms of pre- examination frequency, majority of the grade 11 senior high school students allotted one day (69.30%) before the examination 30 minutes to one hour (52.60%) as review time. The most preferred pre-examination study strategy of the respondents is rereading their textbooks and/or lecture notes (3.37 frequently). There is no significant positive correlation between the pre-examination study frequency and the summative test results, there is a significant positive correlation between Tracks and the summative test results and between the study strategy (rereading textbooks/lecture notes, and seeking assistance to parents) and the summative test results of the Grade 11 senior high school students of Dr. Carlos S. Lanting College. Lastly, avoid cramming, students spend at least three days of review before the examination for a better learning in a well managed time and engage their selves to the most significant favored review strategies that will give an impressive test results.

Mathematics vocabulary differentially predicts mathematics achievement in eighth grade higher- versus lower- achieving students: Comparisons across two countries

This study explored the relationship between mathematics vocabulary and mathematics achievement, controlling general vocabulary, for eighth graders (ages 13 to 14) from the United States (US; n = 89) and Turkey (n = 188). The mathematics achievement of Turkish students fell into higher- and lower-achieving groups, with students in the higher-achieving group showing achievement levels like their US peers. For US students and the corresponding higher-achieving Turkish students, mathematics vocabulary predicted mathematics achievement and mediated the relation between general vocabulary and mathematics achievement. For the lower-achieving Turkish students, only general vocabulary predicted mathematics achievement. The pattern of results extends findings from studies of younger students and is interpreted in terms of the domain-general and domain-specific contributions to mathematics achievement.

Language Skills of Children With and Without Mathematics Difficulty.

Purpose Language is an important skill required for children to succeed in school. Higher language skills are associated with school readiness in young children and general mathematics performance. However, many students with mathematics difficulty (MD) may be more likely to present difficulties with language skills than their peers. The purpose of this report was to compare the language performance of children with and without MD. Method We compared child vocabulary, morphology, and syntax between first- and second-grade children (N = 247) classified as with or without MD, controlling for child working memory. Results Children with MD (n = 119) significantly underperformed compared with their peers (n = 155) on all language measures. The largest difference between children with and without MD was in syntax. Conclusions Children with MD present poorer language skills than their peers, which aligns with previous research linking the importance of syntax with mathematics learning. More research is needed to better understand the complex links between language skills and mathematical development.

ELEMENTARY METHOD OF SUBSTANTIATION AND IDEOLOGICAL MEANING OF THE THEORY OF THE SECOND ORDER LINEAR DIFFERENTIAL EQUATIONS WITH CONSTANT COEFFICIENTS AND TRIGONOMETRIC FREE TERMS

In the article, adapted to the school course, the second order linear differential equations with constant coefficients and trigonometric free terms are investigated. The basic elementary methodological approaches to solving the equation are given. The solutions of the second order linear differential equation with constant coefficients and trigonometric free terms are investigated, which is a model of many phenomena. In addition, the applied values of the equation and its solutions were noted. The results obtained are presented in the form of theorems. The main novelty of the study is that these results are proved and generalized by elementary methods. These conclusions are proved in the framework of the methods of high school mathematics. This theory, known in general mathematics, is fully adapted to the implementation in secondary school mathematics and developed with the help of new elementary techniques that are understandable to the student. The main purpose of the research is to develop methods for solving a non-uniform linear differential equation of the second order with a constant coefficient at a level that a schoolboy can master. The result will be the creation of a special course program on the basics of ordinary differential equations in secondary schools of the natural-mathematical direction, the preparation of appropriate content material and providing them with a simple teaching method.