Journal on Mathematics Education

Exploring the triad of mathematical engagement: Perceived abilities, interests, and teacher-student dynamics

Thu, 19 Sep 2024 00:00:00 +0000

This study investigates the relationships between students' perceptions, interests, and engagement in mathematics within the cultural framework of K-12 education in Kazakhstan. A diverse sample of K-12 students representing various grade levels and community settings was included in the research. The analysis proceeded in three distinct phases: first, a Confirmatory Factor Analysis (CFA) was conducted to evaluate the reliability of the instrument; second, a Structural Equation Modeling (SEM) approach was applied to examine relationships between variables and assess the overall model fit; and finally, descriptive and inferential statistical methods were employed. Students perceived mathematical abilities and interests were identified as significant predictors of their attitudes toward mathematics teachers, as revealed through SEM. Due to the nature of the data, nonparametric tests were utilized to explore group differences. The findings indicated a consistent pattern of negative student perceptions regarding their mathematical abilities and interests, juxtaposed with positive attitudes toward their mathematics teachers. These positive attitudes were more closely associated with students' personal rapport with teachers rather than their instructional effectiveness. Further analyses examined variations in perceptions across different grade levels and community settings, revealing the influence of contextual factors. Notably, no significant gender differences were observed, challenging existing literature on gender disparities in education. The study underscores the importance of adopting holistic educational strategies that account for cultural contexts and promote teacher-student solid relationships.

The effect of scaffolding-based digital instructional media on higher-order thinking skills

Wahyu Setyaningrum, Fransiskus Magnis Pastoriko, Khristin Fabian, Chiang Yi Ying — Fri, 20 Sep 2024 00:00:00 +0000

Higher-order thinking skills (HOTS) are widely recognized as an essential for addressing the challenges of modern life. As a result, numerous educational systems prioritize the development of students' HOTS. While previous studies have explored the impact of scaffolding on HOTS through either paper-based methods or gamified approaches, this experimental study seeks to examine the effects of scaffolding-based digital instructional media delivered via web-based instruction—specifically, the platform Madmatics—on students' HOTS. The participants in this study consisted of 64 junior high school students, with 32 students utilizing the scaffolding-based digital media for mathematics learning, while the remaining 32 students engaged in traditional paper-and-pencil exercises in a regular classroom setting. The findings reveal that students exposed to scaffolding-based digital instructional media demonstrated significantly greater improvements in HOTS compared to those in the conventional learning environment. Three key factors may explain this enhancement: the scaffolding guided students through problem-solving tasks, the media provided immediate feedback and explanations to facilitate learning, and the digital platform increased student engagement and motivation to solve mathematical problems.

Level of students' proportional reasoning in solving mathematical problems

Riska Novia Sari, Rizky Rosjanuardi, Ratri Isharyadi, Aat Nurhayati — Fri, 20 Sep 2024 00:00:00 +0000

This study aimed to evaluate the level of proportional reasoning among middle school students in their ability to solve mathematical problems involving proportions. Proportional reasoning is essential for understanding and mastering various mathematical concepts, serving as a fundamental skill for higher-level mathematics. A qualitative case study design was employed, involving 28 eighth-grade students from a school in Bandung, Indonesia. The participants were assessed using a set of proportion-related problems, including numerical comparison, non-proportional (additive), direct proportion, and inverse proportion tasks. The analysis focused on categorizing the students' problem-solving strategies into distinct levels of proportional reasoning, ranging from non-proportional to formal proportional reasoning. Additionally, three students representing high, moderate, and low mathematical performance were selected for in-depth interviews to explore their reasoning processes when addressing proportion problems. Data analysis included administering tests, reviewing students' problem-solving strategies, conducting in-depth interviews, and evaluating their proportional reasoning abilities. The findings revealed that students with high and moderate mathematical performance exhibited proportional reasoning levels ranging from 0 to 3, whereas low-performing students displayed levels ranging from 0 to 2. Moreover, students generally faced difficulties distinguishing between proportional and non-proportional problems. Even when correct answers were provided, many lacked a deep understanding of direct and inverse proportion concepts. The study also discusses several implications for enhancing students' proportional reasoning skills.

Which is better between gold and its share? A context for designing a financial mathematical task

M. Hasbi Ramadhan, Zulkardi, Ratu Ilma Indra Putri, Yulia Resti — Sun, 06 Oct 2024 00:00:00 +0000

Financial mathematics is a crucial discipline for students, mainly when taught using real-life contexts such as gold and its share. It can help students develop practical solutions to financial problems. This study aimed to design a financial mathematics task for Vocational High Schools (VHS) that is valid, practical, and demonstrates potential effects utilizing the Pendidikan Matematika Realistik Indonesia (PMRI) approach in the context of gold and its share. The research employed a design research methodology, specifically a development study involving two primary phases: preliminary and formative evaluation. The latter included multiple stages of prototype development, beginning with self-evaluation, then expert review, one-on-one sessions, small group trials, and culminating in a field test. The study was conducted with 44 eleventh-grade accounting students at VHS 1 Jambi City, consisting of 3 students for the one-to-one phase, 6 for the small group phase, and 35 for the field test phase. Data were collected through tests, interviews, documentation, and observations. The findings indicate that the financial mathematics task designed using the PMRI approach, contextualized in gold and its share, was valid, practical, and positively impacted student learning. Students not only developed a deeper understanding of real-world financial issues but also enhanced their decision-making abilities in financial contexts. Additionally, teachers expressed a greater willingness to adopt the PMRI approach in their instruction, suggesting that this context can effectively support the teaching of financial mathematics in vocational high schools.

Prospective secondary mathematics teachers’ use of inquiry-based teaching principles as conceptual tools when modifying mathematical tasks

Mar Moreno, Salvador Llinares, Paloma Santonja — Sun, 06 Oct 2024 00:00:00 +0000

The objective of this study was to investigate how prospective secondary mathematics teachers apply inquiry-based teaching principles to modify tasks that support students' engagement in specific mathematical practices. The research employed the theory of goal-oriented decision-making to describe and explain the use of inquiry-based teaching principles as a conceptual tool by these prospective teachers. The study involved two cohorts, comprising 43 prospective teachers (20 in one cohort and 23 in the other) enrolled in a Secondary Education Teaching program. Data were collected from written reports documenting the implementation of two professional tasks, where participants modified textbook assignments to promote exploratory teaching. An inductive analysis was conducted in two phases. The findings revealed that prospective teachers consistently applied inquiry-based teaching principles when they set specific mathematical practices as student learning objectives, such as analyzing particular cases, identifying patterns and relationships, and formulating conjectures and generalizations. However, when these mathematical practices were not established as learning objectives, teachers struggled to apply inquiry-based teaching principles consistently during task modification. These results suggest that inquiry-based teaching principles are an effective conceptual tool for prospective teachers' instructional reasoning. Nonetheless, for consistent application, it is crucial to establish a coherent network of logical connections between the conceptual tool and the intended learning objectives.

Learning fraction with vacation: Integrating Musi Rawas tourism in designing learning trajectory on fraction

Sukasno, Zulkardi, Ratu Ilma Indra Putri, Somakim — Sun, 27 Oct 2024 00:00:00 +0000

Fraction learning has gained significant attention in mathematics education research, with a growing body of literature addressing the instructional challenges inherent in teaching fractions effectively. Establishing a solid conceptual foundation in fractions is critical to fostering broader mathematical proficiency, yet many students continue to struggle with core fractional concepts. This study addresses these issues by integrating a real-world context—Musi Rawas tourism—into fraction instruction, targeting pre-service elementary teachers enrolled in an elementary mathematics education program. Adopting a design research methodology, specifically a validation study, the study progresses through three structured phases: preliminary design, design experiments (encompassing pilot and teaching experiments), and retrospective analysis. Data collection involved teaching materials, observational checklists, and documentation to capture the instructional dynamics and learning outcomes. The study’s primary contribution is a localized instructional theory for teaching fractions within a tourism context, organized across five progressive learning activities: problem identification in the Gegas Water Lake tourism setting, contextual model development, model-based problem-solving, context-specific solution formulation, and abstraction of mathematical conclusions. This framework offers an innovative pedagogical approach, illustrating the potential for enhancing fraction learning through contextualized instruction in tourism, with detailed insights into the methodology and outcomes presented in the full study.

Primary school teachers’ knowledge for teaching multiplicative thinking

Mayamiko Malola, Wee Tiong Seah — Sun, 27 Oct 2024 00:00:00 +0000

Multiplicative thinking is important for students’ learning of key topics in mathematics such as algebra, geometry, measurement, fractions, statistics, and probability. This study employed an embedded mixed-method approach to investigate primary school teachers’ pedagogical content knowledge for developing multiplicative thinking in students. The study participants (n = 62) were primary school teachers in Australia at different levels of teaching experience, from preservice teachers to novice, experienced, and expert teachers. Teachers completed a carefully designed questionnaire, and a model of Teacher Capacity was the framework for instrument design and data analysis. The investigation in this research focused on three key teaching stages for developing multiplicative thinking: transitional, multiplicative, and proportional reasoning. Estimated marginal means, pairwise comparison, and regression analysis statistical tests were conducted using SPSS 2.0. The results highlight specific areas requiring attention in teacher professional development and preparation programs to enhance teachers’ capacity to effectively support students’ learning and development around multiplicative thinking. For example, there is a need to enhance teachers’ capacity for multiplicative thinking during transitional teaching and the need to emphasize the development of teachers’ knowledge of students and the design of instruction.

Praxeological analysis in Indonesian and Singaporean mathematics textbooks: An understanding geometrical similarity by students

Krida Singgih Kuncoro, Didi Suryadi, Jarnawi Afgani Dahlan, Al Jupri — Sat, 16 Nov 2024 00:00:00 +0000

Mathematics textbooks are essential tools for facilitating the achievement of learning objectives, yet their use varies across classrooms, even when the same mathematical concepts are being taught. This study aims to investigate students' understanding of geometrical similarity through praxeological analysis within the framework of the Anthropological Theory of the Didactic (ATD). The analysis identifies differences in the structuring of geometrical similarity tasks between Indonesian and Singaporean textbooks. According to ATD praxeology, mathematical content is analyzed through the "praxis" and "logos" blocks, where praxis encompasses task types (T) and techniques (τ), while logos involves technology (θ) and theory (Θ). The findings highlight distinct priorities in how geometrical similarity is presented in textbooks from both countries, with implications for students’ conceptual and procedural understanding. Specifically, the absence of pantograph tasks in Singaporean textbooks and the lack of scale factor exercises in Indonesian textbooks reflect differences in knowledge construction and task emphasis. These variations impact students' ability to relate textbook knowledge to real-world applications. The study underscores the significance of incorporating a diverse range of task designs and practical experiences to enhance students' geometric reasoning abilities. A well-structured textbook not only supports students in achieving learning objectives but also fosters a continuous process of building, connecting, and deepening their mathematical understanding.

Factors shaping Indonesian preservice math teachers’ digital media adoption in online mathematics teaching practice: An instrument development and validation study

Sat, 16 Nov 2024 00:00:00 +0000

Numerous studies have examined the development of instruments to identify factors influencing preservice teachers' integration of technology in teaching practices. However, limited research has been dedicated to designing instruments specifically tailored to assess mathematics preservice teachers' integration of Digital Mathematics Learning Media (DMLM) during online teaching practice. This gap is particularly pertinent in the Indonesian context, where assessing future teachers' competencies is crucial. Addressing this gap, the present study endeavors to develop and validate an instrument to identify the factors influencing Indonesian Preservice Mathematics Teachers' (PSMTs) integration of DMLM in online teaching practice. The instrument's theoretical foundation is derived from the Technological Pedagogical Content Knowledge (TPACK) framework, with an emphasis on the Math-TPACK domain, and the Theory of Planned Behavior, focusing on beliefs related to DMLM and online learning. The research employed the ADDIE model for instrument development, combined with Exploratory Factor Analysis (EFA), involving a sample of 303 Indonesian preservice mathematics teachers. The study resulted in the development of a questionnaire comprising 59 indicators across four domains: Math-TPACK, Beliefs on Online Learning, Beliefs on DMLM, and the Use of DMLM. This instrument provides a robust tool for policymakers and educators to identify critical factors affecting PSMTs' effectiveness in online mathematics teaching. Additionally, it offers insights for designing targeted interventions to enhance the quality of online teaching practices.

Horizontal and vertical mathematization processes of 10th grade students: The case of Law of Sines

Quoc Ai Nguyen, Ngoc-Giang Nguyen — Wed, 20 Nov 2024 00:00:00 +0000

Realistic Mathematics Education (RME) has gained significant attention in Vietnam over the past decade due to its potential for enhancing mathematics instruction. This study investigates the process of mathematicization undertaken by students as they transition from solving a real-world contextual problem to discovering and applying the Law of Sines. The primary problem involves determining the angle formed by the crossbar and the hanging rope of a disco ball. Guided by the principles of RME, the mathematicization process encourages students to model this scenario as a triangle with two given side lengths and a specified angle between one side and the base. With teacher facilitation, students construct a general mathematical model and subsequently reinvent the Law of Sines. They apply this law to solve the initial problem and further extend their understanding by tackling a similar contextual scenario. The study involved 40 students, who engaged with worksheets designed to present relevant problems. Their problem-solving processes were documented and analyzed using qualitative methods. The findings contribute to the development of a teaching approach for introducing the Law of Sines within the framework of RME, specifically tailored to the Vietnamese educational context. This approach underscores the progression of students' understanding through the integration of contextual problem-solving and theoretical reinvention.

Integrating traditional food and technology in statistical learning: A learning trajectory

Rahmi Ramadhani, Rully Charitas Indra Prahmana, Soeharto, Alfa Saleh — Wed, 20 Nov 2024 00:00:00 +0000

In the 21st century, understanding variability and developing statistical investigation skills are crucial for enhancing students' data literacy. However, these essential skills are often overlooked, limiting students' growth in numeracy whereby statistical problems are frequently disconnected from real-world or cultural contexts, reducing student engagement. To address this issue, this study integrates the culturally relevant context of Lemang Batok, which enhances students' ability to understand, apply, and analyze data through appropriate statistical concepts. The research uses an ethno-flipped classroom model that promotes flexible, collaborative learning, aiming to design a learning trajectory for teaching descriptive statistics in this context to improve numeracy skills. Utilizing design research methodology, specifically a validation study, the research followed three phases: preliminary design, experimental design, and retrospective analysis. The subjects were junior high school students from Medan and Binjai Cities, North Sumatera-Indonesia. The results indicated that the learning trajectory developed through tiered discussions significantly improved students' numeracy skills in descriptive statistics, as evidenced by increased critical thinking and enhanced abilities to analyze variability.

Curriculum and teacher assessment practices in mathematics learning: Alignment with higher order thinking skills in Indonesian secondary schools

Wed, 20 Nov 2024 00:00:00 +0000

Higher-Order Thinking Skills (HOTS) are an essential element in education that must be integrated into curricula and classroom assessments. In Indonesia, educational initiatives have increasingly emphasized the incorporation of HOTS into both curriculum design and assessment practices. However, prior research has primarily focused on the challenges faced by teachers in developing HOTS-based assessments and aligning their teaching with curriculum demands. This study aims to investigate how the Indonesian mathematics curriculum integrates HOTS and evaluate the alignment between the curriculum objectives and teacher-developed assessments in fostering HOTS. The study employed a descriptive qualitative approach and was conducted in two Indonesian high schools, one located in an urban area and the other in a regional setting. A total of 15 mathematics teachers from grades ten, eleven, and twelve participated in the research. Data collection methods included focus group discussions, document analysis of mathematics assessments, and semi-structured interviews. The analysis employed Anderson and Krathwohl’s Taxonomy to categorize cognitive levels. Findings reveal that the Indonesian Mathematics Curriculum predominantly emphasizes Low-Order Thinking Skills (LOTS), and teacher-developed assessments are largely aligned with these LOTS-focused objectives. Furthermore, even when curriculum indicators aim to target HOTS, teachers often struggle to design assessments that effectively evaluate students’ higher-order cognitive abilities. These findings highlight a significant gap between curriculum goals and the practical implementation of HOTS in assessments. The results provide valuable insights for curriculum developers, suggesting the need for a curriculum redesign that places greater emphasis on HOTS. Additionally, the study underscores the importance of professional development initiatives to equip teachers with the skills necessary to design and implement HOTS-based assessments. This research contributes to advancing educational practices and policies that prioritize the integration of HOTS into teaching and assessment frameworks.

Statistical literacy in primary education: An analysis of Indonesian fifth-graders' data interpretation and analysis skills

Uswatun Hasanah, Susilahudin Putrawangsa, Farida Agus Setiawati, Edi Purwanta — Fri, 22 Nov 2024 00:00:00 +0000

Statistical literacy is an essential competency in today’s data-driven society. However, research in this field often overlooks primary-level students, focusing predominantly on those in higher education. To address this gap, the present study evaluated the statistical literacy of 50 fifth-grade students in Indonesia, with a focus on their abilities in data analysis and interpretation. Utilizing a descriptive cross-sectional design, the study employed a written test grounded in real-world data scenarios, adapted from established theoretical frameworks. The assessment included various data representations—pictograms, bar charts, tables, and line charts—designed to evaluate students’ skills in comprehension, comparison, and interpretation. The results indicate that the majority of students operated at an Idiosyncratic level, demonstrating limited capacity for data interpretation, while a smaller proportion reached the Transitional level; notably, no students attained Quantitative or Analytical proficiency. These findings underscore the urgent need for curriculum reforms to enhance both computational and analytical skills at an early stage, thereby equipping students with the foundational competencies required for advanced data reasoning. Future research should investigate pedagogical strategies that can bridge early-stage statistical literacy with the demands of higher-level statistical reasoning, ensuring students are better prepared for a data-intensive world.

Revealing the dominant metacognitive activities of high school students in solving central tendency and dispersion problems based on gender

Kiki Henra, I Ketut Budayasa, Ismail — Sun, 01 Dec 2024 00:00:00 +0000

Research on the relationship between gender and metacognition in mathematical problem-solving has yielded inconsistent findings. Some studies suggest that gender influences metacognitive activities, while others report no significant differences. This study seeks to explore metacognitive activities during each stage of statistical problem-solving among two 12th-grade students with contrasting gender expressions: a feminine-expressing female and a masculine-expressing male. The instruments utilized in this research include the Bem Sex Role Inventory (BSRI) gender questionnaire, a mathematical ability test, a statistical problem-solving task, and an interview guide. Data collection was conducted in two phases: the BSRI questionnaire and mathematical ability test were used to classify participants, followed by problem-solving tasks and semi-structured interviews to capture their metacognitive processes. Employing a descriptive exploratory design with a qualitative approach, the study applied thematic analysis to organize and interpret data from task performance and interview transcripts. These findings were further synthesized into hierarchical diagrams to illustrate the dominance of metacognitive components at different problem-solving stages. Results indicate that the feminine-expressing female predominantly utilized metacognitive knowledge, specifically declarative knowledge, during the problem-understanding phase. In contrast, the masculine-expressing male demonstrated more reliance on metacognitive regulation, particularly in planning and monitoring, during the problem-implementation stage. These findings underscore the importance of developing inclusive curricula and differentiated teaching strategies to enhance metacognitive skills across diverse student populations.

Exploring the link between cognitive load and brain activity during calculus learning through electroencephalogram (EEG): Insights from visualization and cluster analysis

Rina Oktaviyanthi, Ria Noviana Agus, Khotimah — Mon, 09 Dec 2024 00:00:00 +0000

Understanding the relationship between cognitive load and brain activity is essential for enhancing learning outcomes, particularly in complex subjects such as calculus. Despite its significance, empirical research examining the manifestation of cognitive load in brain activity patterns remains sparse, indicating a notable gap in the literature. This study aims to investigate the correlation between brain activity and cognitive load in a cohort of 30 mathematics education students enrolled in a calculus course, utilizing electroencephalogram (EEG) recordings. A quantitative descriptive research design was employed, integrating cluster analysis and data visualization techniques to facilitate an in-depth examination. EEG recordings of theta, alpha, and beta wave activity were collected during calculus sessions, followed by the administration of a cognitive load questionnaire. Descriptive statistics were utilized to analyze the distribution of cognitive load and brain activity, while correlation analysis was conducted to explore the relationships between cognitive load and EEG parameters across the different brainwave bands. The results revealed that higher cognitive load was positively correlated with increased frequency and amplitude in the alpha and beta bands, while a negative correlation was observed with theta frequency. Furthermore, cluster analysis effectively categorized participants based on distinct EEG signal patterns associated with varying levels of cognitive load. These findings offer valuable insights for the development of personalized learning interventions tailored to individual brain activity profiles, providing a foundation for future research on adaptive learning environments.

Predictive analysis of independent learning bearing on students’ mathematics performance in Davao de Oro, Philippines

Judiel B. Cabilan, Emerson D. Peteros — Wed, 11 Dec 2024 00:00:00 +0000

The abrupt transition from face-to-face to remote learning due to the COVID-19 pandemic has made independent learning the dominant pedagogical framework globally. As students return to in-person education, there is an increasing expectation for them to demonstrate autonomy in their learning and its impact on academic outcomes. This study aims to evaluate students' level of independent learning across cognitive, metacognitive, and motivational strategies, assess their mathematics performance, and identify which learning strategies predict their performance in mathematics. A descriptive correlational research design was employed to examine the independent learning levels and mathematics performance of secondary school students in Davao de Oro, Philippines. The findings revealed that the students exhibited high levels of independence in their mathematics learning, particularly in cognitive, metacognitive, and motivational strategies, with metacognitive strategies receiving the highest ratings. Additionally, students achieved very satisfactory results in their mathematics courses. A multiple linear regression analysis identified that only cognitive and motivational strategies significantly predicted mathematics performance, with motivational strategies emerging as the strongest predictors. In contrast, metacognitive strategies were found to be non-significant predictors, which contradicts existing literature. These findings provide valuable insights for educational stakeholders to enhance students' independent learning, specifically focusing on cognitive and motivational strategies, to further improve mathematics performance.

Constructing slope conceptualizations: Physical, geometrical, and algebraical

Aprilia Nur Utami, Maarten Dolk, Farida Nurhasanah, Triyanto — Wed, 11 Dec 2024 00:00:00 +0000

The concept of slope constitutes a fundamental component of the discourse surrounding linear equations. A subset of students frequently interprets slope merely as an algebraic ratio. This particular context fosters a superficial understanding of slope, as these students typically resort to mechanical memorization of the slope formula. The intent of this research endeavor is to enhance a holistic understanding of the slope concept: physically, geometrically, algebraically; through the deployment of realistic teaching activities. Two students are participants in this research endeavor. The research group initiated a series of questions aimed at assessing their comprehension by delivering a total of six activities, which were systematically designed using the emergent modeling framework central to the educational design principles of Realistic Mathematics Education (RME). These activities are structured to facilitate the students' understanding of the fundamental concept of slope, transitioning from physical properties, through geometric ratios, to algebraic ratios. Subsequent to the investigations and the interviews conducted, the researchers deduce that the utilization of realistic activities significantly enhances students' comprehension of the foundational concept of slope: physical, geometric, algebraic.