Mathematical Understanding Research Articles

Struggling as part of success: International Baccalaureate students’ productive struggle is strongly correlated to mathematical achievement

Productive struggle is an effective mathematics teaching practice that provides students opportunities to grapple with challenging mathematical concepts, connect prior knowledge, discover new ideas, and develop their critical thinking skills. Research has documented the benefits of secondary mathematics students engaging in productive struggle. Additional work is needed to detail how productive struggle relates to students’ mathematical achievement, specifically in the International Baccalaureate (IB) classroom. This study examined what correlation existed between 68 U.S. grade 11 and 12 IB mathematics students’ level of productive struggle exhibited during tasks of varying levels of cognitive demand and their mathematical achievement based on 10 IB established markschemes and a summative assessment. A strong, positive correlation was found between the level of productive struggle and mathematical achievement across all cognitive demand levels. These results support prior work emphasizing the importance of teachers making productive struggle a consistent, pervasive practice in their classrooms to foster student mathematical achievement and understanding.

The Use of Mother Tongue in Communicating Mathematics: Implication for Teaching and Learning of Mathematics

Mathematics as a school subject is designed to solve the everyday problem created by human activities; these problems are domesticated in the different cultures of man all over the world. However, the performance of students keeps dwindling due to the westernize approach of teaching and learning mathematics. In other to solve this precarious situation this paper advocated the use of mother tongue in the teaching of mathematics. Mother tongue approach here refers to first-language education as a medium of instruction. The use of mother tongue in the teaching and learning of mathematics is meant to address the high functional illiteracy of Nigeria where language plays a significant factor. Using mother tongue to teach the basic concepts of numbers, operations and other concepts of mathematics helps build a strong foundation for the understanding and learning of higher mathematics. This approach is effective not only in getting the interest of students in the lesson but as a springboard in teaching new mathematical concepts, principles and in deepening student understanding on how mathematical operations or processes work. The mother tongue concepts of teaching and learning mathematics in this work shall be based on the following sub-topics: Numeration/Counting System, Basic Arithmetic Operations, Rhymes and Geometric Concepts. The paper completely reduced the Eurocentric mathematics beliefs of students and make them discover how best mathematics can be learning from their mother tongue. The paper recommended amongst others that teachers of mathematics should adopt the use of mother tongue in teaching mathematics in order to improve students understanding of the subject.

ChatGPT in didactical tetrahedron, does it make an exception? A case study in mathematics teaching and learning

The didactical tetrahedron model proposes a framework for integrating technology into the previous didactical triangle. This study addresses this issue through examining the role of ChatGPT in educational settings. This quantitative and qualitative study reveals differences among three groups. We observed that students relying solely on ChatGPT for learning resulted in lower performance compared to those receiving instruction from teachers, either alone or supported by ChatGPT. The findings highlight the potential of ChatGPT in enhancing mathematical understanding, yet also underscore the indispensable role of instructors. While students generally perceive ChatGPT as a beneficial tool for learning mathematical concepts, there are concerns regarding over-reliance and the ethical implications of its use. The integration of ChatGPT into educational frameworks remains questionable within a didactic context, particularly due to its limitations in fostering deep information comprehension, stimulating critical thinking, and providing human-like guidance. The study advocates for a balanced approach, suggesting that ChatGPT can augment the learning process effectively when used in conjunction with guidance. Thus, positioning technology as an independent focal point in transforming the didactic triangle into a didactical tetrahedron is not appropriate, even when represented by ChatGPT.

Eksplorasi Validitas dan Reliabilitas Soal Pemahaman Konsep Dalam Asesmen Pembelajaran

Students’ understanding of concept can be measured and assessed using mathematical concept understanding test instruments. The instrument to be used must be prepared to meet the criteria for a good instrument. Therefore, the aim of this research is to determine the validity and reliability of students' conceptual understanding questions in learning assessments. This type of research is qualitative research using descriptive methods. Data was obtained through tests and interviews with mathematics subject teachers. The subjects in this research were class IX students at MTsN 2 Kerinci, totaling 22 students in 1 class. Based on the results of validity calculations using the Pearson Product Moment formula and t test, as well as calculations of question reliability using the Cronbach's Alpha formula, it was found that each question item was valid and reliable, so this test instrument can be used to measure students' ability to understand mathematical concepts.

Integration of Ethnomathematics Teaching Materials in Mathematics Learning in Elementary School

Objective: This research serves as a preliminary study to outline the framework and projection of ethnomathematics studies, particularly concerning the integration of ethnomathematics into mathematics curriculum and the development of mathematics learning objectives using an ethnomathematical approach. Method: The research employs a Systematic Literature Review (SLR) methodology involving identifying, evaluating, and interpreting relevant literature on the research topic. Results: The findings reveal that the ethnomathematical approach effectively enhances students' understanding of mathematics. Students exhibit higher motivation and satisfaction with mathematics learning when connected to their local culture. Novelty: This research shows that the ethnomathematics approach facilitates the development of teachers' competencies in integrating cultural elements into mathematics education. Both teachers' recommendations and research findings support the inclusion of ethnomathematics in mathematics curricula both directly in developing learning tools and materials and in curriculum policies. Additionally, there is potential for technology applications to support ethnomathematics learning, enabling students to study mathematics independently. In conclusion, integrating ethnomathematics holds significant potential in improving students' mathematical understanding, connecting mathematics with local culture, and motivating students to learn mathematics more enjoyable and relevantly.

KEMAMPUAN PEMAHAMAN KONSEP MATEMATIS SISWA PADA PEMBELAJARAN MODEL RME

This research aimed to produce a study of students' mathematical concept understanding abilities in classes with Realistic Mathematics Education (RME) model learning and classes that did not receive RME model learning. This research was a quantitative method of quasi experiment model designed in the form of non-equivalent control group design involving two research classes determined using purposive sampling technique. The instrument used was a test of students' mathematical concept understanding ability in the form of description questions. The data analysis technique in this study used an independent sample t-test and N-gain score. The results of the analysis showed that students' mathematical concept understanding ability in the class that received RME model learning was better than that of those who did not receive RME model learning. The increase in students' mathematical concept understanding ability in the class with RME model learning was in a low category with an average gain score of 0.025. The low increase is due to the limited learning time at school during the adaptation period of new habits, so that learning with the RME model does not run effectively.

Mathematical Understanding: Systematic Mapping Study Based on Bibliometric Analysis

This study aims to identify research trends related to mathematical understanding and research gaps using the Systematic Mapping Study (SMS) method of data collection through Publish or Perish (PoP) software to search the initial database on Scopus. Furthermore, the initial data obtained is analyzed using VOSviewer software. The number of published articles we selected according to research objectives is 23, and we reviewed them using VOSviewer. The level of education in the articles we have reviewed starts from elementary, junior high, high school, prospective teachers, and teachers. There are 4 clusters of research on mathematical understanding. In cluster 3, there is still space to conduct research related to the growth of mathematical understanding in junior high school students because, based on the results of the bibliometric analysis, there has not been much research related to the growth of mathematical understanding in junior high school students.

The Relation Between Mathematics Philosophy And Culture-Based Learning Model

The aim of this study is to study the correlation of mathematical philosophy with cultural-based learning models. The method of research used is the method of library research, i.e. conducting studies related to mathematical philosophy, philosophical mathematics learning, culture-based mathematic learning, the connection of mathematically philosopher with ethnomatematics, the relationship of mathematic philosophies with cultural-based learning models. The results of the research have been obtained that the philosofy of maths, the model of learning based on culture, and ethnomathematics have close connections in the context of understanding and teaching of Mathematics. Mathematical philosophy deals with the foundations of mathematical epistemology and ontology, while a culture-based learning model emphasizes the integration of values and cultural contexts in mathematics learning. Ethnomatematics refers to the study of mathematical ways of thinking in a particular culture. By understanding the cultures, traditions, and world views of a particular society, ethnomathematics can help develop more culturally relevant and meaningful learning models. Therefore, the interrelationship between mathematical philosophy, culture-based learning models, and ethnomathematics can create a more holistic and contextual approach to mathematics learning.
 Keywords: Mathematical Philosophy, Cultural Based Learning Model, Ethnomathematics

DEVELOPING MATHEMATICAL COMMUNICATION ABILITIES FOR VIETNAMESE PRIMARY SCHOOL STUDENTS

Mathematical communication is an essential component of math lessons. It facilitates the exchange of mathematical information between teachers and students. Moreover, effective mathematical communication can enhance students' understanding of Mathematics. However, both teachers and students face numerous challenges in this area. Therefore, developing mathematical communication skills in students is a critical responsibility for Vietnamese teachers under the 2018 General Education Program. This article examines the challenges related to mathematical communication faced by teachers and primary school students in Vietnam. Additionally, it proposes solutions to address these challenges while contributing to the development of mathematical communication skills among Vietnamese elementary school students.

Development and Usability of Games in Learning Mathematics

Game-based learning is important in helping teachers attract students’ interest in learning. Therefore, this study developed and investigated the usability of a game, namely Pirates Mathsdom, which was used to strengthen the students’ understanding of learning mathematics. The research design used is ADDIE model. A total of 30 pre-service mathematics teachers in Perak, Malaysia, were randomly selected. A questionnaire is developed to investigate the usability of Pirates Mathsdom and then analyzed using descriptive analysis and mean scores. Findings show that this game has a high validity and reliability value, with a Content Validity Index value of 1.00. Meanwhile, the level of usability is high, with the mean score values for each construct being 3.77 (design), 3.79 (ease of use), and 3.75 (satisfaction), respectively. The implication of the study is to promote games as one of the learning tools to attract students’ interest in mathematics.

The Mathematics-Language Proficiency: The Learners’ Perspecctive

Mathematics is considered a difficult school subject by majority of learners. For many learners, mathematics is a series of hurdles and challenges-a task made with continued failure and seeming irrelevance in spite of the value that mathematics plays in society. The effect of this has been unwilling class participation, disinterestedness, haphazard solving of mathematical tasks, plus low achievements and failure to communicate mathematics. The latter effect is important in application of mathematics in occupations such as building, construction, engineering and accounting. This state of affairs propagated the topic of the paper: “The Mathematics-Language Proficiency: The Learners’ Perspective”. The objective was to find out the nature of the relationship between proficiency in mathematics vocabulary and conceptual understanding of mathematics. The study drew on Vygotskian Socio-Cultural Theory (SCT) and used a multiple-case study design. The sample size of the study was 1353 participants comprising of 1339 form three learners and 14 mathematics teachers drawn from Sub-County Schools (SCS), County Schools (CS) and Extra-County Schools (ECS) in Bungoma South Sub- County. Data were collected by questionnaires, classroom observations and interviews. Analysis was done using Pearson correlation with two tailed tests for all the tests with a level of significance of 0.01. The study found out that there exists a strong positive relationship between mathematics vocabulary and conceptual understanding across all cases, that is, 0.798, 0.778 and 0.709 in SCS, CS and ECS respectively. Further learners were unable to interpret the meaning of some mathematics solutions after solving the question correctly. The study concluded that proficiency in mathematics vocabulary is necessary but not sufficient for conceptual understanding of mathematics. The study recommends learners to be supported in communicating mathematics ideas both verbally and in writing during mathematics lessons to broaden their conceptual understanding of mathematics.

Pedagogical and Content Knowledge (PCK) in Problem Solving of Pre-Service Teachers

This descriptive research aimed to determine the level of pedagogical and content knowledge (PCK) and the least-learned competencies in problem-solving Heuristics. The respondents were the pre-service teachers who have taught mathematics subjects during their practice teaching where purposive sampling was employed. The result showed that BSED math majors have low while the BEED have very low knowledge on problem – solving Heuristics. The most common strategy used by the pre-service teachers in solving problems were algebraic approach or using equation, making an organized list and drawing a diagram. In terms of Pedagogical Content Knowledge, the BSED has low pedagogical knowledge, high content knowledge and average pedagogical content knowledge while the BEED has low pedagogical knowledge, average content knowledge, and low pedagogical content knowledge. As a whole, the pre-service teachers have low pedagogical knowledge, average content knowledge, and low pedagogical content knowledge. Pre-service teachers need to be competent in their ability to teach mathematics subject to various classes of students specifically on problem solving. Knowledge on content and pedagogy has a significant role during the teaching and learning process. Thus, the pre-serve teachers must have deep mathematical understanding and adequate conceptual and procedural knowledge of the different problem-solving Heuristics so that they can transmit this to their students when they are in the field.

Penerapan Teori Belajar Behavioristik dalam Pembelajaran

Representation is a student’s ability to communicate mathematical ideas or thoughts learned in a certain way. Mathematical representation abilities can help students build concepts and express mathematical ideas, as well as make it easier for students to develop their abilities. Representation can help students to organize their thinking. Mathematical representation is learning that demands optimal mental activity of students in understanding a concept. The aim of this research is to find out how elementary school students use mathematical representation. Representation plays an important role in efforts to develop and optimize students’ mathematical abilities. The concept of mathematical representation learning is a concept that refers to an approach to students through emphasizing the importance of understanding and using various forms of representation to facilitate students’ understanding of mathematics.

Analysis of Students' Mathematical Understanding in Gradient Material Linear Function Graphics Class IX UPTD SMP Negeri 3 Pematang Siantar

This research aims to find out how to analyze students' mathematical understanding of gradient materials for linear function graphs for Class IX 7 UPTD SMP Negeri 3 Pematang Siantar. The research method used in this research is a qualitative method with descriptive data analysis. The subjects in this research are all students in class IX 7 of SMP Negeri 3 Pematang Siantar in the 2023/2024 academic year. The number of subjects in this research was 30 students. The instrument used in this research is a mathematical understanding test in the form of a description using 3 indicators, namely restating concepts that have been studied, presenting concepts in various forms of mathematical representation, applying concepts or problem-solving algorithms. These 3 indicators are used in 6 questions. Based on the data analysis carried out, the overall mathematical understanding ability of students is at a medium level, namely with a percentage of 47.8%. The indicators used are 1) restating mathematical concepts, 2) presenting mathematical representations, 3) applying concepts or problem-solving algorithms. Based on the previous explanation, it can be concluded that the mathematical understanding of students in class IX 7 UPTD SMP Negeri 3 Pematang Siantar as a whole is at a medium level.

Bimbingan Belajar Olimpiade Sains Nasional (OSN) Matematika Siswa di SMPN 3 Batusangkar

<p>The national mathematics science olympiads in junior high schools in the mathematics branch have an important role in the world of education by providing students with the ability to understand, apply and appreciate mathematical concepts in a scientific context. This includes developing a deeper understanding of mathematics, understanding of the scientific method, the ability to think logically, effective communication skills, and the ability to solve problems. This discussion details how the national science Olympiad helps students become individuals who are experts in mathematics and ready to play a role in science, technology and society.</p><p> </p>

PENINGKATAN KEMAMPUAN PEMAHAMAN MATEMATIS PESERTA DIDIK SD MELALUI MODEL PROBLEM BASED LEARNING BERBANTUAN MEDIA ARTICULATE STORYLINE

This research aims to determine the increase in mathematical understanding abilities in class II elementary school students through a problem based learning model assisted by articulate storyline media. The research method used is quasi-experimental research with a pre-test and post-test one group design research design. The research was aimed at class II students at SDN 066 Halimun, Bandung City. The population in this study was all class II students at SDN 066 Halimun. The research sample taken was class II-C as many as 20 people. The data collection techniques used in this research are mathematical ability description tests, observation and documentation. Researchers carried out data analysis by testing hypotheses using SPSS Statistics 26.0 for windows software. Based on the research results, an overview of the learning process using Articulate Storyline media with the problem based learning model is going well. From the results of the hypothesis test, it was concluded that there was a significant difference between the ability to understand mathematical concepts before and after using the problem based learning model assisted by articulate storyline media. There is an increase in students' mathematical understanding ability from the results of the normalized gain test, namely 0.45 with a moderate improvement category.

Penggunaan Representasi Matematika Siswa SD pada Pembelajaran Matematika

Representation is a student’s ability to communicate mathematical ideas or thoughts learned in a certain way. Mathematical representation abilities can help students build concepts and express mathematical ideas, as well as make it easier for students to develop their abilities. Representation can help students to organize their thinking. Mathematical representation is learning that demands optimal mental activity of students in understanding a concept. The aim of this research is to find out how elementary school students use mathematical representation. Representation plays an important role in efforts to develop and optimize students’ mathematical abilities. The concept of mathematical representation learning is a concept that refers to an approach to students through emphasizing the importance of understanding and using various forms of representation to facilitate students’ understanding of mathematics.

Improving Students' Mathematical Understanding Ability Through Canva Assisted Problem-Based Learning Model on Straight Line Equations

This study aims to determine whether there is an increase in students' mathematical understanding if learning is carried out using the scientific method compared to problem-based learning methods on straight line equations material. This research was conducted at SMP Negeri 5 Cimahi. This study uses a quantitative and descriptive qualitative approach. Learning outcomes data is used as a parameter to measure the increase in mathematical understanding ability. The results showed an increase in students' mathematical understanding abilities when learning using problem-based learning methods increased by 18% compared to scientific methods.

Relationships of Abstraction and Application Complexity in the Attainment between Mathematics and Electrical Engineering Modules in Diploma Courses of South Africa

In South Africa, universities are under pressure to meet increasing targets for student enrolment in engineering disciplines and fields. This has resulted in many students being enrolled in engineering programs without possessing the minimum required mathematical skills and understanding to tackle the challenging engineering disciplines. Hence, the engineering disciplines have a high student attrition and failure rate. This study aimed to evaluate the complex relationship of abstraction and application between mathematics attainment and principles of electrical engineering attainment by the students enrolled in diploma courses in technical universities of South Africa. A blend of quantitative and qualitative data was used. Legitimation code theory (LCT) was used to determine the complexity of higher learning levels. The relationships between six core courses in the Electrical Engineering curriculum were investigated to analyze the knowledge building from mathematics modules to principles of electrical engineering modules. The problem-solving, analytics, and abstract mathematical skills developed in these modules impact the overall progression into principles of electrical engineering courses at different levels for diverse students. The research examines the theoretical foundation, student performance, and practical application of mathematical ideas in electrical engineering using curriculum documents, student academic records, and interviews with electrical engineering lecturers. The study found a weak correlation between the two modules and examined how resources, cultural attitudes, and pedagogy affect student achievement. The results indicate an unexpected negative and fragile correlation between the lower mathematics and engineering modules at high levels. The LCT analysis showed the disconnect between the mathematics courses and the principles of electrical engineering in both the level of abstraction used in the studies and the extent of application principles taught.

An Overview of Mathematical Methods Applied in the Biomechanics of Foot and Ankle–Foot Orthosis Models

Ankle–foot orthoses (AFOs) constitute medical instruments designed for patients exhibiting pathological gait patterns, notably stemming from conditions such as stroke, with the primary objective of providing support and facilitating rehabilitation. The present research endeavors to conduct a comprehensive review of extant scholarly literature focusing on mathematical techniques employed for the examination of AFO models. The overarching aim is to gain deeper insights into the biomechanical intricacies underlying these ankle–foot orthosis models from a mathematical perspective, while concurrently aiming to advance novel models within the domain. Utilizing a specified set of keywords and their configurations, a systematic search was conducted across notable academic databases, including ISI Web of Knowledge, Google Scholar, Scopus, and PubMed. Subsequently, a total of 23 articles were meticulously selected for in-depth review. These scholarly contributions collectively shed light on the utilization of nonlinear optimization techniques within the context of ankle–foot orthoses (AFOs), specifically within the framework of fully Cartesian coordinates, encompassing both kinematic and dynamic dimensions. Furthermore, an exploration of a two-degree-of-freedom AFO design tailored for robotic rehabilitation, which takes into account the interplay between foot and orthosis models, is delineated. Notably, the review article underscores the incorporation of shape memory alloy (SMA) elements in AFOs and overviews the constitutive elastic, viscoelastic, and hyperelastic models. This comprehensive synthesis of research findings stands to provide valuable insights for orthotists and engineers, enabling them to gain a mathematical understanding of the biomechanical principles underpinning AFO models and fostering the development of innovative AFO designs.