Journal on Mathematics Education

Learning numeracy using new Pempek mathematics

2024-10-24T22:36:49+00:00

This study addresses the challenges faced by students in comprehending and articulating the concepts of cost, selling price, and profit, despite their ability to perform related calculations. Contributing factors include a limited learning context and a didactic approach that often prioritizes rote memorization of formulas, thereby hindering a deeper understanding of these concepts. The objective of this research is to design a learning trajectory utilizing the context of New Pempek Mathematics, an innovative adaptation of the traditional Pempek dish, represented in geometric forms such as cones, trapezoidal prisms, cuboids, and cubes, to facilitate students' understanding of cost price, selling price, and profit. The study employs a design research methodology, consisting of three stages: preliminary design, experimental design, and retrospective analysis. The study involved 31 junior high school students from Belitang, Indonesia. Data collection was conducted using a variety of instruments, including student worksheets, video recordings of lessons, interviews with students, and photographs of their presentation work. The proposed learning trajectory, centered around the New Pempek Mathematics production project, emphasizes activities such as identifying cost prices, estimating selling prices, and calculating profit. The findings indicate that integrating mathematics with local cultural contexts, such as New Pempek Mathematics, enhances student engagement and makes the learning experience more relevant, thus improving students' understanding of these fundamental economic concepts.

Number sense of junior high school students based on learning speed: Slow, average, and fast learners

2024-10-24T00:49:28+00:00

Students’ learning speed and number sense are critical aspects of mathematics education, yet little is known about how these factors interrelate across different learner profiles. Addressing this gap, this research investigates the characteristics of students’ number sense in relation to their learning speed, providing a novel perspective on tailoring mathematics instruction. This qualitative case study involved 185 8^th and 9^th students from seven junior high schools across seven sub-districts in Sukabumi, Indonesia, who had previously studied fractions. The research was conducted in three stages: identifying learning speed through IQ scores, self-assessment, and teacher evaluations; administering a diagnostic test to assess number sense; and analyzing the number sense characteristics of representative students from each learning speed category. Findings reveal a comprehensive mapping of learning speeds, highlighting the role of factors such as conceptual understanding, study habits, and mathematical content processing in number sense achievement. Notably, differences were observed among slow, average, and fast learners, suggesting the need for differentiated instructional strategies. The implications of this study emphasize the importance of targeted approaches in mathematics teaching, enabling educators to foster inclusive environments that cater to diverse learning needs. This research contributes a unique methodology for integrating cognitive and practical assessments to better understand and support students’ mathematical development.

A proposed constructivism-based instructional model to enhance metacognition and mathematical problem-solving skills in Bhutanese grade nine students

2024-12-07T15:55:46+00:00

The enhancement of metacognitive abilities and problem-solving skills is essential for effective mathematics instruction. However, these critical components are frequently overlooked in traditional teaching practices. This study addresses the challenges and requirements faced by mathematics educators and explores the integration of constructivist activities in classroom settings. It aims to develop and evaluate the suitability of an instructional model designed to address these issues. Employing a mixed-method approach within a research and development framework, the study gathered data through semi-structured interviews with seven mathematics teachers in Bhutan to identify their instructional challenges. Additionally, two experts from Bhutan and one from Thailand were consulted to provide insights into constructivist teaching methodologies. The content analysis of teacher interviews revealed a predominant reliance on structured, teacher-centered instructional methods, with limited emphasis on fostering higher-order cognitive skills. To bridge this gap, an instructional model emphasizing the development of higher-order thinking was designed. This model incorporates active learning, problem-solving, collaboration, scaffolding, reflection, and self-monitoring, organized into six steps: prior knowledge activation, mediation, internalization, generalization, transfer, and evaluation. The model was evaluated using a 5-point Likert scale, achieving a mean score of 4.33 (SD = 0.70), indicating high levels of appropriateness and acceptability. Furthermore, a pilot test yielded an effective index (E.I. = 0.51), demonstrating the model's efficacy in fostering metacognitive and problem-solving skills.

Proportional reasoning in the artisan personality type: A case study of high school students in trigonometry ratios

2024-10-23T07:17:19+00:00

Proportional reasoning is a critical component of mathematical competence that should be developed at the senior high school level, as it fosters both foundational and advanced mathematical understanding. Educators frequently encounter variations in proportional reasoning abilities among students, often influenced by individual personality types. However, limited research has specifically investigated the proportional reasoning capabilities of high school students with artisan personality types. This study aims to examine the strategies and approaches utilized by students with Artisan Personality Types (APT) in solving trigonometric comparison problems. Employing a qualitative descriptive methodology within a case study design, the research focused on high school students identified as having APT. Data were collected using proportional reasoning tasks, the Keirsey Personality Type Questionnaire, and structured interviews. The analysis was conducted qualitatively, with findings categorized based on established indicators of proportional reasoning. Results indicate that APT students demonstrate the ability to address proportional reasoning problems related to covariation, ratios, and proportions, employing distinct strategies and logical reasoning. Nevertheless, instances of both correct and incorrect responses were observed, often stemming from misinterpretations of the problem context. These findings provide valuable insights for future studies aimed at designing targeted instructional strategies and developing learning tools to enhance the proportional reasoning skills of students with APT.

Numeracy skill development in prospective mathematics teachers: Challenges and opportunities in real-world contexts

2024-10-23T06:54:15+00:00

Numeracy skills are essential for prospective mathematics teachers as they bridge mathematical concepts with real-life applications. However, many prospective mathematics teachers face challenges in applying these concepts to practical situations. This study aims to analyze the conceptual and procedural errors made by prospective mathematics teachers when solving numeracy problems within the context of "Save Our Water." A descriptive research design was employed, utilizing a numeracy test adapted from the Minimum Competency Assessment (MCA) and semi-structured interviews as research instruments. The study involved 30 prospective mathematics teachers from the University of Jambi, Indonesia. The findings revealed that conceptual errors primarily stemmed from reliance on rote memorization of formulas without a deeper conceptual understanding. Procedural errors were attributed to difficulties in unit conversion, incorrect formula application, and improper manipulation of formulas. To address these issues, the study recommends incorporating contextual approaches, problem-based learning, and project-based learning strategies that connect mathematical concepts to real-world contexts. Additionally, the use of visual aids, such as diagrams and 3D models, is suggested to enhance conceptual understanding and strengthen the connection between abstract concepts and practical applications. Future research should investigate the effectiveness of these instructional approaches in improving numeracy skills and enhancing the teaching readiness of prospective mathematics teachers.

Analysis of pre-service mathematics teachers’ proof comprehension through Toulmin’s argumentation model

2024-12-28T07:46:28+00:00

The comprehension of mathematical proofs by preservice mathematics teachers is vital for their ability to effectively teach mathematical reasoning. Despite its importance, existing research reveals a significant gap in preservice teachers’ understanding and application of formal proof methods, especially in the context of mathematical argumentation. This study examined how preservice teachers construct mathematical proofs, using Toulmin’s argumentation model as a framework. A qualitative exploratory case study design was adopted, involving written proofs from 72 third-year preservice teachers at a South African university, supplemented by task-based interviews with nine participants. The findings indicate that 62.5% of the participants were able to construct correct direct proofs, and 61.1% applied the contraposition proof method correctly. However, only 30.6% produced valid proofs using the contradiction method. Further analysis uncovered notable gaps in essential components of proof construction, such as warrants, backing, and rebuttals, particularly when dealing with tasks requiring contraposition and contradiction methods. While many participants (62.5%) demonstrated procedural fluency in direct proofs, 31.9% failed to provide explicit definitions or logical precision, suggesting a superficial engagement with proof construction. These results highlight the need for teacher education programs to emphasize a deeper conceptual understanding of proof structures, which is crucial for preparing preservice mathematics teachers to foster reasoning and argumentation skills in their future classrooms.

Students’ financial literacy in math classroom: Insights into financial awareness

2024-10-24T22:29:15+00:00

The current generation of young people faces significant financial challenges in an increasingly volatile global economy, highlighting the need for enhanced financial literacy education. While the OECD has recommended the integration of financial literacy into school curricula, a notable gap exists in the development of age-appropriate financial literacy content that aligns with students’ cognitive and developmental stages. This study addresses this gap by evaluating students’ financial literacy knowledge, with a particular focus on integrating financial concepts into mathematics education. Specifically, the research targets financial topics that are accessible and relatable to upper elementary school students, exploring how these concepts can be integrated into existing mathematics curricula. The study involved students from grades 4, 5, and 6, with data collected through interviews that were transcribed and analyzed using NVIVO software. Findings indicate that topics such as exchange rates, foreign currencies, cash transactions, and digital payment systems resonate with students' existing knowledge and personal experiences. Furthermore, the study underscores the importance of introducing foundational personal financial management skills, such as distinguishing between needs and wants and promoting saving habits, from an early age. However, it also highlights that more complex financial concepts, including regulatory frameworks, consumer protection, and data security risks, are not developmentally appropriate for elementary students. The results of this research offer valuable insights into the practical integration of financial literacy into mathematics classrooms, with potential implications for curriculum development. These findings contribute to the growing body of knowledge on financial literacy education, providing a basis for selecting relevant financial topics for school curricula and fostering a more financially literate future generation.

Learning obstacles and the didactical design for teaching the limit of function in a Calculus course

2024-10-23T00:29:03+00:00

Students often face difficulties in understanding the concept of limits in functions, a challenge that arises due to the abstract nature and complexity of the topic. Despite being familiar with the procedural steps, students may fail to grasp the underlying meaning of limits. This gap in comprehension leads to significant learning obstacles. As such, there is a critical need for effective didactical designs that can enhance the teaching and learning of this concept. This study aims to address this issue through a Didactical Design Research (DDR) approach, which is structured into three phases. The first phase involves a preliminary didactical design analysis, followed by administering a diagnostic test on the limit of functions to 26 third-semester students (Group 1) who have already completed a differential calculus course. This diagnostic test helps identify the initial learning obstacles. In the second phase, a didactical design is developed to address these obstacles, and it is then implemented with 33 first-semester students (Group 2) enrolled in a Differential Calculus course to evaluate the impact of the design. Data analysis is conducted based on the scores from the written diagnostic test, categorizing them into three levels of ability. The findings reveal that the primary learning obstacle for students is the formal definition of limits, and the identified obstacles are epistemological, psychological ontogenic, instrumental ontogenic, and conceptual ontogenic. The results of implementing the didactical design demonstrate a significant improvement in students' understanding of limits, as evidenced by a reduction in the learning obstacles encountered. This research contributes to the development of more effective didactical approaches for teaching complex mathematical concepts, offering a potential model for addressing similar learning challenges in other abstract topics.

Rehabilitation of children with a cochlear implant: Overcoming difficulties in solving mathematical problems

2024-12-28T08:05:08+00:00

Children with cochlear implants face cognitive and linguistic challenges, particularly in the relationship between auditory perception and mathematical cognition. While auditory rehabilitation has advanced, there is a gap in understanding how integrating mathematical problem-solving with language rehabilitation can improve both cognitive and linguistic outcomes for these children. This study explores the potential of structured mathematical interventions to enhance cognitive flexibility, numerical reasoning, and verbal communication. The research was conducted in multiple phases, each increasing in complexity to assess cognitive and linguistic changes under various intervention conditions. Pre-intervention assessments compared cognitive and linguistic performance through auditory and verbal tests, quantitative evaluations, and real-time speech monitoring. The intervention involved structured mathematical modules combining arithmetic and logical reasoning with verbal learning, alongside multisensory approaches to integrate auditory and visual stimuli. Post-intervention analysis utilized statistical methods including χ² for categorical data, ANOVA for intra-subject variations, and t-tests for inter-group comparisons. Results revealed significant improvements in cognitive adaptability (χ² = 29.41, p ≤ 0.001) and numerical thinking, with enhanced logical sequencing, arithmetic operations, and spatial structuring. Speech comprehension showed a marked shift from predominantly gestural and visual communication (χ² = 12.36, p ≤ 0.01) to active verbal responses to abstract mathematical concepts (p ≤ 0.05, Cohen’s d = 0.82). Additionally, there was a 1.5-fold increase in multi-sentence responses (p ≤ 0.05), indicating improved linguistic processing skills. These findings emphasize the importance of incorporating mathematical thinking into auditory-verbal therapy, redefining problem-solving as a dual-mode intervention that enhances both cognitive and linguistic development. Educational programs for children with cochlear implants should integrate mathematical foundations, such as spatial arithmetic and logical reasoning, to support linguistic adaptation and bridge numerical abstraction with verbal comprehension in rehabilitation.

Javanese folklore with moral values: An impactful context in learning relations and functions

2024-12-19T14:57:21+00:00

Indonesia, particularly the Java region, is home to a wealth of folklore rich in moral teachings. Among these, the story of Rama and Sinta is one of the most prominent, and upon initial investigation, it reveals an underlying presence of mathematical concepts, particularly relations and functions. Despite this potential, there is a lack of research on integrating such cultural elements into the teaching of mathematics. This study aims to fill this gap by exploring the use of the Rama and Sinta narrative as a contextual tool for teaching relations and functions. Following the design research method within the Ethno-Realistic Mathematics Education (Ethno-RME) framework, we developed instructional materials for seventh-grade students at a public school in Magelang, Central Java, Indonesia. These materials, consisting of both student and teacher books, were designed to contextualize the mathematical concepts of relations and functions within the cultural narrative. The resulting learning trajectory, consisting of five interconnected activities, not only deepened students' understanding of the mathematical concepts but also reinforced the moral lessons embedded in the folklore. This paper details the development process, implementation, and outcomes of this culturally responsive approach, contributing valuable insights into the integration of local cultural narratives with core mathematical concepts to enhance the learning experience.

A praxeological analysis of linear equations in Indonesian mathematics textbooks: Focusing on systemic and epistemic aspect

2024-10-17T01:13:28+00:00

Educational research has consistently highlighted that learning obstacles stem not only from the design of learning situations but also from curriculum structures and textbooks, which are pivotal learning resources. Despite the growing body of literature, limited studies focus on the specific challenges posed by the design of learning materials, particularly in early algebra within the Indonesian context. This study addresses the gap by analyzing the grade VII mathematics textbook in the Merdeka Curriculum, with a focus on linear equations with one variable, to uncover learning obstacles in early algebra. Utilizing Didactical Design Research (DDR), a qualitative approach, the research examines the praxeological components of the textbook—tasks (T), techniques (τ), technology (θ), and theory (Θ). The findings indicate three primary categories of learning obstacles: ontogenic, epistemological, and didactic. Notably, the analysis reveals that the design of linear equation content in the textbook is non-systemic and lacks epistemic coherence, posing significant challenges for learners. This study contributes to the understanding of curriculum design by identifying specific obstacles in the Merdeka Curriculum's grade VII mathematics textbook and underscores the need for more systematic and epistemically aligned textbook development. Future research should extend this analysis to other textbooks across various grade levels to determine if these findings are consistent within the broader curriculum framework.

Pre-service teachers’ perspective toward problematic word problems

2024-11-05T01:58:59+00:00

Despite extensive research indicating that students often fail to apply real-world knowledge and common sense when solving word problems, the underlying causes remain underexplored. Teacher behavior and instructional methods are potential factors contributing to students' tendency to provide unrealistic answers to such problems. The current study aims to address this gap by examining the cognitive processes and perspectives of pre-service teachers when solving problematic word problems. A group of 146 pre-service teachers (97 females, 49 males) in Iran participated in the study, which consisted of two phases. In the first phase, participants were given three problematic word problems to solve and were subsequently asked to evaluate four different student responses. A significant correlation was found between the participants' responses in the initial test and their evaluations in the second phase. In the second phase, the study employed a phenomenographic approach to explore the thinking processes and perspectives of the pre-service teachers while solving the problems. The analysis of interview data led to the identification of two primary categories of unrealistic problem-solving: "inattention" and "ignoring." In the "inattention" category, the problem solver fails to recognize the relevance of real-world knowledge, while in the "ignoring" category, the solver acknowledges real-world factors but deliberately chooses not to integrate them into the solution. In the end, a model of unrealistic problem-solving is proposed and discussed, with implications for teacher training and pedagogical practices.

The potential problem to explore students’ functional thinking in mathematical problem-solving

2025-02-07T06:19:22+00:00

Many studies have reported that functional thinking plays a crucial role in mathematical problem-solving, particularly in fields requiring analytical reasoning, such as maritime studies. However, existing research has yet to comprehensively explore the specific task characteristics that effectively stimulate functional thinking in mathematical problem-solving, particularly among maritime students who must apply these skills in solving safety-of-life problems at sea. Addressing this gap, the present study investigates the potential of mathematical tasks in fostering functional thinking among second-semester students enrolled in the Deck Officer Program in Indonesia. The study involved three students with different mathematical abilities, who were given problem-solving tasks. Their responses were observed, recorded, and analyzed based on their written work. The findings reveal that non-routine problems involving functional situations—where students generalize relationships between varying quantities to determine function rules—effectively promote functional thinking. This is evidenced by the emergence of key functional thinking components, including problem identification, data representation, pattern recognition, covariational and correspondence relationships, and the evaluation of generalization rules. These results contribute to the development of research instruments in mathematics education and provide valuable insights for researchers and educators seeking to enhance functional thinking through task design.

Elementary school teachers’ experiences in engaging with digital technology in teacher professional development: The case of GeoGebra

2025-02-25T23:13:54+00:00

Technological advances require teachers to be competent in utilizing them in mathematics learning. Teachers' success in teaching mathematics using digital technology cannot be separated from their mathematical and didactic knowledge. This study aims to reveal elementary school teachers' knowledge during their experiences in engaging with digital technology, GeoGebra, in teacher professional development programs. Data was obtained from the implementation of the Professional Development (PD) program in two schools, one in a private school focusing on the design of mathematical learning instruction integrated with GeoGebra and another in a public school focusing on the experimental process of teaching mathematics with GeoGebra. The data were analyzed using the Anthropological Theory of the Didactic (ATD) framework, specifically praxeology. The findings of this study reveal that elementary school teachers are aware of the need for theoretical aspects of a praxeology when designing mathematics learning instruction using GeoGebra in a PD program. Meanwhile, it is challenging for elementary school teachers to make use of GeoGebra instruction to support students' mathematical praxeologies. Therefore, the use of digital technology in teaching mathematics in elementary schools is still a significant challenge due to the mismatch between available technology and teacher needs.

An enquiry approach to rediscovering sundials as a didactic tool for teaching time

2025-02-22T04:41:02+00:00

The ability to measure quantities is a fundamental component of primary mathematics education due to its relevance in both real-world applications and mathematical horizontality. However, the concept of time measurement remains one of the most challenging topics for students to grasp due to its abstract nature. Despite the recognized difficulties, there is a lack of effective instructional strategies that integrate constructivist approaches to enhance students' conceptual understanding of time. Addressing this gap, this study presents the design and implementation of a constructivist didactic sequence based on active learning within an Inquiry-Based Learning (IBL) framework. The study involved 31 pre-service teachers in their final year of training, aiming to enhance their pedagogical competence in teaching time measurement through the use of sundials. The research explores how these future educators conceptualize time and how they interpret sundials as a means to represent its passage. To evaluate their assimilation and comprehension of the topic, a phenomenographic analysis was conducted, comparing their depth of knowledge before and after the intervention. The findings indicate a significant improvement in both conceptual understanding and didactic application. The results underscore the effectiveness of sundials as instructional tools, not only for illustrating the passage of time and calendar cycles but also for highlighting the social and historical contexts associated with timekeeping. This study contributes to the field of mathematics education by providing empirical evidence supporting the integration of inquiry-based, constructivist methods in the teaching of time measurement, ultimately enhancing pre-service teachers’ instructional competencies and students’ conceptual grasp of temporal concepts.

Exploring three-dimensional geometry using praxeological analysis: Indonesian textbook insights

2025-02-20T06:14:24+00:00

The integration of three-dimensional geometry in secondary mathematics education plays a crucial role in developing students' spatial reasoning and problem-solving skills. However, textbooks often present limitations in structuring tasks, techniques, and justifications, which may lead to learning obstacles. Despite the importance of well-designed instructional materials, there is a lack of comprehensive studies analyzing Indonesian mathematics textbooks using both the praxeological framework and the learning obstacles perspective in didactic situations. Addressing this gap, this study examines a Grade XII mathematics textbook in Indonesia, focusing on three-dimensional geometry through a structured content analysis. The analysis categorizes tasks based on praxeological components, including types of tasks, solution techniques, technological justifications, and supporting theories, while also identifying potential learning obstacles related to the clarity of visual representations and contextual problem diversity. The findings reveal that the textbook includes 10 types of tasks, solved using 6 techniques, supported by 7 forms of technological reasoning, all grounded in three-dimensional geometry concepts. The presentation of tasks is systematically structured and balances conceptual and procedural aspects, minimizing significant didactic obstacles. However, epistemological obstacles were identified, primarily due to limited visualizations and a lack of diverse contextual tasks, which may hinder students’ flexibility in applying three-dimensional geometry concepts. These findings highlight the need for improved task design and enhanced visual representations to foster deeper conceptual understanding and adaptability in problem-solving. This study contributes to mathematics education research by providing empirical insights into textbook design and its impact on students' learning processes, offering recommendations for more effective instructional material development.

The ‘mound-hollow’ model for solving integer addition and subtraction problems

2025-02-25T23:07:10+00:00

Understanding integer operations is a fundamental yet challenging concept for elementary students, often requiring effective visual models to support their comprehension. Despite various instructional approaches, many students continue to struggle with integer addition and subtraction, particularly when negative numbers are involved. Addressing this gap, this study explores the potential of the mound-hollow model as an intuitive representation to facilitate students’ understanding of integer operations. This study aimed to examine how three sixth-grade students utilized the mound-hollow model to solve integer addition and subtraction problems. Data were collected from students' written tests and individual interviews conducted after a teaching experiment involving 25 sixth graders in Indonesia. The findings indicate that the mound-hollow model provides a meaningful analogy for solving addition problems of types $x + (- y)$ and $(- x) + y$ (where $x > y$ and $x, y$ are natural numbers) and subtraction problems of types $x - (- y)$ and $(- x) - y$ . All three students successfully employed the model for addition by neutralizing every mound-hollow pair and used diagrammatic representations to solve subtraction problems by forming corresponding pairs. Additionally, students demonstrated the ability to justify their solutions and correct errors through the mound-hollow representation. The use of a single mound or hollow to represent larger integers enhanced students’ proficiency in solving integer operations and reinforced their understanding of the relationship between addition and subtraction, such as $x - (- y) = x + y$ and $(- x) - y = (- x) + (- y)$ . These findings highlight the effectiveness of the mound-hollow model as an alternative instructional tool for teaching integer operations, providing students with an intuitive framework to construct abstract mathematical concepts. The implications of this study contribute to mathematics education by offering insights into the design of visual models that support conceptual understanding in integer arithmetic.