Mathematics Instruction Research Articles

Student Teachers’ Knowledge of School-level Geometry: Implications for Teaching and Learning

<p style="text-align:justify">This study aimed to assess the geometric knowledge of student teachers from a university in the Eastern Cape province of South Africa. The study used a sample of 225 first-year student teachers who completed school mathematics baseline assessments on a computer- aided mathematics instruction (CAMI) software. The study adopted a descriptive cross-sectional research design, using quantitative data to measure student teachers’ geometry achievement level, and qualitative data to explain the challenges encountered. The results show that student teachers exhibited a low level of understanding of school-level geometry. The low achievement levels were linked to various factors, such as insufficient grasp of geometry concepts in their secondary school education, difficulty in remembering what was done years ago, low self-confidence, and lack of Information and Communications Technology (ICT) skills along with the limited time for the baseline tests. These results suggest that appropriate measures should be taken to ensure that student teachers acquire the necessary subject-matter knowledge to teach effectively in their future classrooms.</p>

Assessing the Utilization Level of Metaverse

The integration of metaverse technology within the educational domain is progressing swiftly, owing to its advanced technological features. This technology has the ability to captivate learners and empower teachers by offering unique learning opportunities and capabilities. Hence, the present study sought to identify the extent of Metaverse technology utilization in primary-level mathematics instruction, as perceived by both supervisors and teachers of Gifted Students. The study employed a descriptive survey method and utilized a questionnaire as the primary research tool. The study's results indicated that teachers of gifted students acknowledged and utilized Metaverse technology to a significant extent in the context of teaching mathematics at the primary level Perspectives of Supervisors and Teachers themselves. This suggests that Metaverse technology has been effectively integrated into their instructional practices, enabling them to provide enhanced learning experiences for their students.

Exploring group concepts in abstract algebra through ChatGPT

Traditional methods often struggle to engage students and effectively communicate the intricacies of abstract algebra. This study aims to explore the future of mathematics teaching, with a focus on integrating group theory concepts into Abstract Algebra using ChatGPT, an advanced language processing AI. Chat transcripts edited with ChatGPT were analyzed to gain insights into the evolving landscape of mathematics education, specifically concerning group theory. Group theory is a fundamental branch of Abstract Algebra poised to shape the future of mathematics instruction. ChatGPT facilitates interactive discussions and problem-solving tasks related to group operations, properties, and theorems, offering personalized explanations and guidance tailored to individual student needs. The study highlights the potential of AI-driven platforms like ChatGPT to revolutionize mathematics education by providing dynamic and engaging learning experiences centered around group theory. Furthermore, the study emphasizes the importance of incorporating group theory into mathematics curricula to foster critical thinking, problem-solving skills, and interdisciplinary connections. Educators are urged to leverage innovative tools like ChatGPT alongside traditional pedagogical approaches to ensure effective teaching and learning. Through thoughtful implementation and ongoing professional development, educators can harness AI's power to create inclusive, equitable, and enriching learning environments, empowering students in abstract mathematical reasoning and analysis.

ONLINE MATHEMATICS LEARNING STRATEGY APPROACH: TEACHING METHODS AND LEARNING ASSESSMENT

The primary focus of this research is to develop strategies aimed at identifying effective methods applicable to online mathematics instruction and assessment. Teaching through distance education has many challenges, requiring educators' adeptness in utilizing e-learning platforms for both instructional delivery and assessment purposes. This study adopts a literature review methodology, drawing upon various previous studies relevant to this subject matter. The research findings reveal several online mathematical strategies and assessment techniques envisioned to adequately measures students' capacity to discern complex issues and employ critical thinking to resolve mathematical problems. The important role of the educator as a facilitator is underscored in crafting learning materials synchronized to the needs of students navigating the online platform. In this context, online mathematics instructional strategies are intricately intertwined with pedagogical dimensions and the appropriateness of utilized media and assessment modalities. Emphasizing interactive, creative, and innovative learning emerges as a critically important characteristic, particularly within the realm of online mathematics instruction

Exploring the Integration of Artificial Intelligence-Based ChatGPT into Mathematics Instruction: Perceptions, Challenges, and Implications for Educators

This research investigates how secondary school mathematics educators in the Nsukka Education Zone, Enugu State, Nigeria, perceive the incorporation of artificial intelligence-based ChatGPT into teaching mathematics. The study employed a sequential exploratory mixed-methods strategy, starting with a systematic survey and followed by detailed interviews. The Mathematics Teachers’ Awareness and Perceptions of AI-based ChatGPT Questionnaire (MTAPACQ) used in this study was adapted from an existing online survey and administered to 80 mathematics teachers, who were selected using stratified random sampling to ensure varied representation across different local government areas. The survey explored teachers’ awareness, utilisation, and perceptions of ChatGPT. Following the quantitative phase, in-depth qualitative interviews were conducted with a subset of five teachers who were familiar with ChatGPT to gain deeper insights into their experiences. The findings indicate limited awareness of ChatGPT, with only 17% demonstrating familiarity with the technology. The infrequent utilisation of ChatGPT in mathematics teaching is mainly associated with this limited awareness. Teachers who integrate ChatGPT report positive outcomes, including improved teaching effectiveness, heightened student engagement, and enhanced comprehension of complex concepts. Nevertheless, the overall perceptions of the tool’s impact on mathematics teaching and learning are moderate. The identified challenges in relation to integration include technical adaptability, curriculum alignment, and the need for customisation to accommodate diverse learning styles. This study emphasises the significance of continuous professional development and ongoing support for teachers to integrate AI-based ChatGPT into mathematics instruction proficiently. The insights derived from the findings hold value for educators, policymakers, and technology developers aspiring to elevate the role of artificial intelligence in mathematics education.

Diagnosis, Remediation, and Error Correction for Mathematics: How to Teach Pre-Service Teachers

Mathematics is a core academic subject, regardless of grade level or setting. Everyone uses mathematics in their everyday life, so being competent in basic mathematics is critical to independent living. One thing teachers can do to ensure learners are learning the mathematics concepts being taught is to diagnose and remediate the errors they are seeing. This skill involves digging deeper into the work of the learners and looking for error patterns. Unfortunately, this skill is not a focus of mathematics instruction courses that pre-service teachers (PSTs) take in their program. This article is aimed at mathematics instruction faculty and describes three main error types as well as what to do when they are identified.

History of mathematical concepts and students’ cognitive understanding of mathematics: Effect of pedagogical content knowledge

This study aimed to explore the relationship between teachers’ pedagogical content knowledge (PCK), students’ interest and motivation in the history of mathematical (HoM) concepts, and students’ cognitive understanding (SCU) of mathematics. A five-level Likert scale questionnaire was used to collect quantitative data from 232 junior high school mathematics teachers. It was found that, on average, students have higher levels of interest, motivation, and cognitive understanding when they are taught utilizing HoM concepts as a pedagogy. The correlation analysis reveals that there is a positive relationship between each of the independent variables and the dependent variable. The regression analysis also shows that teachers’ PCK and students’ interest were strong predictors of SCU, while students’ motivation was a weaker predictor. Hence, it can be said that teachers’ PCK and students’ interest play crucial roles in promoting SCU of using HoM concepts. Further studies are recommended to explore how historical context impacts students’ confidence, enjoyment, and aspirations in mathematics-related fields, which would contribute to understanding the broader implications of incorporating history in mathematics instruction.

Learners' Spontaneous Gesture Before a Math Lesson Predicts the Efficacy of Seeing Versus Doing Gesture During the Lesson.

Gestures-hand movements that accompany speech and express ideas-can help children learn how to solve problems, flexibly generalize learning to novel problem-solving contexts, and retain what they have learned. But does it matter who is doing the gesturing? We know that producing gesture leads to better comprehension of a message than watching someone else produce gesture. But we do not know how producing versus observing gesture impacts deeper learning outcomes such as generalization and retention across time. Moreover, not all children benefit equally from gesture instruction, suggesting that there are individual differences that may play a role in who learns from gesture. Here, we consider two factors that might impact whether gesture leads to learning, generalization, and retention after mathematical instruction: (1) whether children see gesture or do gesture and (2) whether a child spontaneously gestures before instruction when explaining their problem-solving reasoning. For children who spontaneously gestured before instruction, both doing and seeing gesture led to better generalization and retention of the knowledge gained than a comparison manipulative action. For children who did not spontaneously gesture before instruction, doing gesture was less effective than the comparison action for learning, generalization, and retention. Importantly, this learning deficit was specific to gesture, as these children did benefit from doing the comparison manipulative action. Our findings are the first evidence that a child's use of a particular representational format for communication (gesture) directly predicts that child's propensity to learn from using the same representational format.

Exploring factors influencing 21<sup>st</sup> century mathematics in Thai secondary schools: A study in Lopburi Province

The objective of this study was to ascertain the elements that influence the effectiveness of mathematics instruction in the 21<sup>st</sup> century for secondary school students within the jurisdiction of the secondary educational service area office Lopburi (SEAOL). The research utilized survey methodology. The study population consisted of 400 secondary school students from SEAOL during the first semester of 2022. The participants were selected using a stratified random selection technique. The research tool utilized in this study was a questionnaire, which demonstrated a high level of reliability with a coefficient of .934. The research employed principal component analysis as the statistical analysis approach. The findings of the study indicate that there are various factors that influence the effectiveness of mathematics instruction in the 21<sup>st</sup> century for secondary school students in SEAOL. These factors include the level of technology support from schools, use of technology, ability to use basic technology, ability to use specialized technology, knowledge of content, math is crucial, and variety of teaching methods. Additionally, the study reveals that gender, program, and education level have a significant impact on knowledge and opinions regarding mathematics instruction, with statistical significance observed at a significance level of .05.

A systematic review of artificial intelligence in mathematics education: The emergence of 4IR

The integration of artificial intelligence (AI) in mathematics education, focusing on its implications in the 4<sup>th</sup> Industrial Revolution (4IR) era. Through a comprehensive analysis of 10 relevant studies in Scopus and Google Scholar from 2015 to 2023, this review identifies the research methods, research instruments, participants, and AI tools used in mathematics education. Some key ideas include using AI-driven personalized learning and enhanced mathematics instruction, real-time assessment and feedback, curriculum development, and empowering educators, which were highlighted. The study aligns with the preferred reporting items for systematic reviews and meta-analysis. Based on the analysis, most studies reviewed utilized qualitative research methods. The study indicates that questionnaires were mainly used to gather data from students and teachers who were the most significant participants in the reviewed papers. Further results revealed that ChatGPT were the primary AI tool used in mathematics education, among other AI tools, as identified in this review. Additionally, this review discusses the transformative potential of AI in addressing educational disparities and preparing learners for the demands of 4IR.

Integrating Computational Thinking into Mathematics Education: Its Effects On Achievement, Motivation, And Learning Strategies

This study aimed to explore the impact of mathematics instruction supplemented with CT activities on mathematics achievement, motivation, and learning techniques. A quasi-experimental research design involving a pretest-posttest control group was used for the present study. Research was carried out in a Turkish middle school with sixth-grade pupils in a mathematics class. The courses were provided via CT tasks to the experimental group. CT tasks were performed using a scratch-block-based coding tool. The results showed that the experimental group had much higher mathematical performance than the control group. Furthermore, substantial differences were discovered in favor of the experimental group in the motivation scale sub-dimension of learning control belief and the learning methods scale sub-dimension of time and study environment. The results of this research show that mathematics instruction supplemented with CT activities is effective in enhancing students' mathematical achievement. This helps students to organize their study time and environment effectively. This also reinforces the belief that learning objectives provide successful outcomes. Thus, computer laboratories should be considered essential alternatives for mathematical instruction.

Between Mathematics, Theology,And The City

These days, urban expansion and its associated social and ecological challenges are unavoidable. The clever yet morally upright people who create changes in this circumstance are one of the answers. I argued that a K–12 education can aid in the formation of morally upright and competent individuals. My argument is that, in order for students to eventually transform the city, a theological foundation for mathematics instruction can help them improve their character and cognitive abilities. Because of this, a theological perspective on mathematics education can help students grow as individuals and advance society by enhancing their knowledge. In line with the assertion, I think that the definition of mathematics and theology, their shared goal, and the ways in which they might help students become more morally upright constitute the intersection of these two fields. Trust, direction, and articulation are the end results. Trust is an invitation to consider and devise solutions for ecological and social issues. Direction is an invitation to map out the answer based on completed reflection. Finally, articulation is the attempt to carry out a decision in light of reflection.

Crossroads in Mathematics Games: Integrating Indigenous and Exotic Games

In numerous countries and higher education institutions, the significance of indigenous games in mathematics education is highly recognized. Nonetheless, the increasing preference for exotic games has placed indigenous mathematics teachers in a challenging position. This research aimed to examine the awareness and understanding of mathematics teachers regarding indigenous games amidst this competition. Initially, the study employed a phenomenological approach, targeting 200 teachers but randomly selecting a sample of 70 for the quantitative phase. Subsequently, the qualitative phase involved in-depth interviews and observation checklists with five teachers to explore the issue further. The collected data was systematically coded and thematically analyzed, focusing on teachers' knowledge, misconceptions, and potential solutions. The findings revealed that some teachers had greater knowledge of indigenous games than exotic ones. Conversely, other teachers believed that exotic games facilitated faster learning outcomes. This divergence created a significant dilemma in choosing indigenous games for mathematics instruction. Despite the popularity of games like draft, playing cards, snake-and-ladder, and Ludo, the teachers ultimately recognized that Indigenous games such as biloo, bilore, gollaa, and mullaa provided superior learning outcomes. Therefore, stakeholders were recommended to revamp mathematics curricula to incorporate indigenous games more effectively.

Innovative Strategies in Math Education: The Impact of PBL and TaRL on Concept Mastery and Classroom Dynamics

In scrutinizing the amalgamation of Problem-Based Learning (PBL) and Teaching at the Right Level (TaRL) approach within mathematics pedagogy, extant scholarship scarcely offers a holistic evaluation of their synergistic efficacy. Prior research predominantly accentuates scholastic outcomes, frequently neglecting the ramifications of these models on classroom dynamics, including the nuances of student-teacher interactions and student engagement and participation levels. This study probes the integration of PBL and TaRL models to augment students' comprehension of mathematical principles, employing a mixed-methods research design encompassing qualitative and quantitative methodologies. The investigation centered on seventh-grade students in junior high school, utilizing test instruments to evaluate mathematical comprehension and observational protocols to document student and teacher engagement for enriched insights. Comprehensive qualitative and quantitative data analyses were executed. The findings disclosed significant advancements in students' grasp of mathematical concepts, with observations revealing heightened student engagement and more favorable teacher-student interactions. Statistical analyses evidenced substantial disparities between pre-test and post-test scores (p < 0.05). The results proffer recommendations and pragmatic implications for enhancing mathematics education, underscoring the imperative for teacher professional development in deploying this integrative pedagogical model to elevate the quality of mathematics instruction at the secondary school echelon.

Pengembangan E-Modul Persamaan Lingkaran Kelas XI MA dengan Menggunakan Aplikasi Heyzine

Abstract This research aims to determine the validity, practicality, and effectiveness of using the Heyzine application in teaching circular equations to 11th-grade students in senior high school. The research method employed the Four-D (Define, Design, Develop, Disseminate) development model developed by S. Thiagarajan, Dorothy Semmel, and Melvyn I. Semmel. Data collection involved documentation and questionnaires, while data analysis used a descriptive qualitative approach. The results showed that the e-module for mathematics instruction was deemed highly valid by experts and practitioners. The validity percentages of the e-module were as follows: 82.5% for subject matter experts with the criteria "very valid," 89% for media experts with the criteria "very valid," 85% for language experts with the criteria "very valid," and 82.75% for practitioners with the criteria "very valid." Thus, the overall validity averaged 84.81% with the criteria "very valid." The mathematics e-module on circular equations was also evaluated to meet usability aspects. Student responses to the e-module's usability across 13 assessment aspects averaged 87.53%, indicating that the e-module fulfilled usability requirements in practice. The use of the Heyzine application in teaching circular equations was proven effective, as there was an increase in student learning interest after using the module. The increase in student interest in learning mathematics reached 37.679%. Therefore, this e-module can be considered an effective alternative for improving the teaching of circular equations to 11th-grade students in senior high school. Keywords: E-Module, Heyzine

Pre-Service Teachers’ Knowledge of and Beliefs About Direct and Indirect Proofs

ABSTRACT Teachers have difficulty integrating proof in their mathematics instruction due to both narrow beliefs about proofs and limited understanding of proofs. Indirect proofs seem to be a particular cause for concern. In this exploratory study, we contribute to the research area by reporting on an empirical study of Norwegian pre-service teachers’ knowledge of and beliefs about direct and indirect proofs. Inspired by situativity theory, we investigated pre-service teachers’ knowledge of and beliefs about proofs both professed generally and out-of-context and in situation-specific circumstances. Our initial findings are in line with much of the previous literature. First, for situation-specific beliefs and knowledge, we found that indirect proofs seem to be more challenging than direct proofs. Second, for general beliefs and knowledge, we found pre-service teachers’ views about proofs in general are narrow and rigid. However, we also investigated possible patterns between general and situation-specific beliefs and knowledge. We found that participants who empirically validated proofs also professed views that a good mathematical argument is an argument that is simply convincing, and not necessarily rigorous. Second, participants who professed preferences for direct proofs, also struggled with the logical conditions of indirect proofs. Implications are discussed.

What Mathematics Teachers’ Perceptions of The Integration of Educational Drama in Mathematics Instruction: A Mixed-Methods Study

This research aimed to explore mathematics teachers' perspectives on the integration of educational drama in mathematics instruction, specifically focusing on mathematical knowledge, classroom discourse and affective aspects. Using a mixed-methods approach and a sequential explanatory design, the study first employed a quantitative phase, applying a scale to gauge teachers’ views on incorporating educational drama into mathematics instruction. The questionnaire covered three key dimensions: the advancement of mathematical knowledge, facilitation of classroom discourse, and emotional elements. The framework was developed based on established theoretical models. Following this, interview protocols were designed, based on the quantitative outcomes, to explore the insights provided in greater depth. The results indicated a predominantly positive reception among mathematics educators for the use of drama in mathematics education, with consistent agreement observed across all aspects of the scale. The mean scores for the development of mathematical knowledge, classroom dialogue and emotional dimensions were notably high, reflecting substantial alignment among the participants. Qualitative analysis of the teacher interviews highlighted the beneficial aspects of employing drama in mathematics education. The teachers noted the role of drama in reinforcing concepts, enhancing specific mathematical skills and positively affecting student engagement. However, concerns were raised regarding the potential for students' focus to be diverted from core mathematical content. In terms of classroom discourse and emotional development, drama was acknowledged for its role in fostering interactive exchanges, refining students’ speaking abilities, and nurturing self-confidence and motivation. Nonetheless, there were caveats concerning the suitability of drama for all student cohorts, pointing to the need for tailored approaches.

Quantile regression model on how logical and rewarding is learning mathematics in the new normal

Learning mathematics through distance education can be challenging, with the “logical” and “rewarding” nature proving difficult to measure. This article aimed to articulate an argument explaining the “logical” and “rewarding” nature of online mathematics learning, elucidating their causal factors. Existing data from the literature that involving students at Visayas State University, Philippines, were utilized in this study. The study used statistical measures to capture descriptions from the data, and quantile regression analysis was employed to forecast the predictors of the logicality and rewarding nature of learning mathematics at a distance. Results indicate that learning mathematics in the new normal is perceived as “logical” and moderately “rewarding”. The regression and correlation analyses revealed a significant positive association between the perceived “logical” nature and the rewarding experience of learning mathematics. The constructed statistical models depicted that the determinants of logicality in learning mathematics include family income, money spent on the internet, learning environment, household size, social status, and health. Moreover, causal factors such as family income, money spent on the internet, learning environment, leisure activities, social status, and health significantly determine the rewarding nature of learning mathematics online. Conclusively, institution must support college students with their online learning needs. Furthermore, mathematics instructors should create lively and exciting online discussions that boost their logical thinking. Providing problem-solving task that are intrinsically rewarding can contribute to a more fulfilling learning experience.

Beginning to Implement Ambitious Mathematics Instruction: What Promising First-Year Elementary Teachers’ Lessons Can Teach Us

ABSTRACT Although teachers are expected to teach mathematics ambitiously, it is challenging for them to do so. Given that the first year represents a critical juncture between teacher preparation and inservice teaching, it may be particularly challenging to teach ambitiously. Understanding the nuanced characteristics in lessons taught by first-year elementary teachers identified as being generally ambitious can inform how mathematics teacher educators and school mentors support them. A thematic analysis of 15 transcribed lessons revealed instructional moves that were more and less prevalent. Task-level findings indicated that while first-year teachers solicited student input, encouraged them to participate in discussions, and had them attend to cognitively demanding tasks, they seldom assigned open-ended and non-procedural tasks. Students also had few opportunities to grapple with the mathematics. Turn-level findings indicated that first-year teachers maintained the task potential, facilitated student participation, and promoted student authority and perspectives. They further aimed to deepen students’ mathematical thinking, albeit the subtle ways they did so sometimes were apparent across lessons (e.g., encourage students to continue to problem solve) and other times were limited (e.g., provide an opportunity for students to agree or disagree).

Exploring how Teachers’ Gender Biases and Students’ Self-Efficacy Beliefs Impact Mathematics Instruction

The issue of gender biases among mathematics teachers and the self-efficacy beliefs of students is an intriguing subject. This study sought to explore how teachers' gender biases and students' self-efficacy beliefs impact mathematics instruction in the Adenta Municipality of the Greater Accra Region of Ghana. A sequential explanatory mixed method design was utilized in collecting data from 100 Basic school mathematics teachers and four hundred (400) Junior High School students through a closed-ended questionnaire and semi-structured interview guide. The study discovered that gender-related stereotypes and biases among teachers perpetuated gender-based misconceptions, affecting the self-efficacy of female students who were perceived to be weaker in mathematics. The study recommended comprehensive teacher training and awareness programs to help address gender-related stereotypes and biases in mathematics instruction.