Journal on Mathematics Education

Corrigendum to “Developing mathematics teaching materials using maritime context for higher-order thinking in junior high school,” [Journal on Mathematics Education, Volume 15, No. 1, 2024, pp. 173-190]

2024-03-22T08:05:52+00:00

The authors express regret regarding the first author's affiliation with the Mathematics Education Department, Universitas Sriwijaya, Palembang, Indonesia. They extend their apologies for any inconvenience this may have caused.

How abstraction of a pre-service teacher in constructing relationships among quadrilaterals

2023-11-23T14:25:18+00:00

Abstraction is essential to learning mathematics because the mathematical concepts obtained through abstraction will be more meaningful than directly receiving these concepts. This study aims to describe the pre-service teachers' abstraction in constructing relationships among quadrilaterals. This research method was explorative qualitative research with a purposive sampling technique. The subject of this research was a pre-service mathematics teacher who had taken a geometry course. The data analysis techniques used in this study were data condensation, data display, drawing and verifying conclusions. The research results showed that the participant used epistemic actions in an abstraction, such as recognising each quadrilateral type, building-with their properties, constructing relationships among them, and consolidating the abstract results made. Thus, the abstraction in constructing relationships among quadrilaterals can be observed from the epistemic actions: recognising, building-with, constructing, and consolidation, known as RBC+C.

Mathematics module based on STEAM and Quranic approach: A study for student’s perception

2023-11-01T14:19:06+00:00

Monotonous mathematics learning focusing on textbooks only will make students bored and feel that studying mathematics is useless. Using attractive and meaningful approaches, like STEAM and Quranic approaches, is strongly motivated by the need to avoid tedious drilling for students in learning mathematics. This study aims to assess students' perceptions of the development of mathematics modules using science, technology, engineering, and art (STEAM) and AL-Quran approaches. The research approach employed in this research is embedded in mixed methods. Quantitative data was examined using percentages, while qualitative data were transcribed and then developed into codes, categories, and themes. The study recruited 146 Pidie senior high school students in the natural science stream, and five individuals were selected for one-to-one semi-structured interviews. The results of this study show that students have a negative experience in learning mathematics. However, they have a significant interest in integrated math learning with Quranic and STEAM approaches. Furthermore, they believe the modules are one learning medium ideal for mathematics. Finally, based on this study, mathematics teachers should be able to develop learning modules that can integrate STEAM approaches and the understanding of the Quran for senior high school students.

Recontextualizing Kalinga’s batek and laga into an ethnomathematical teaching resource: An application of the second generation of didactical engineering

2024-01-23T22:37:21+00:00

Instructional materials that integrate students' cultures make teaching and learning relevant to students. However, there is a lack of culture-based and research-based teaching resources in mathematics that are deemed pertinent to Kalinga’s full-modular learning and cognizant of the framework for Philippine mathematics teacher education’s principle on realistic mathematics. As such, this study aims to recontextualize the Kalinga tribe’s batek and laga into an Ethnomathematical Teaching Resource (ETR) through the Second Generation of Didactical Engineering (SGDE). Nine elementary teachers and two teacher-trainers participated in the preliminary phase, which was arranged into an ethnomathematical study, first teacher interview, and pretest. These were the basis of the design and a priori assumptions organized into Teaching Strategies (TS), Mathematical Content Knowledge (MCK), and appropriateness test. Subsequently, the realization phase tested the assumptions by administering the ETR, second interview, Communication Index (CI), and post-test. As a result, the a posteriori analysis and validation showed that teacher participants’ exposure to the ETR provided potential TS, improved their MCK, and made appropriate to their level. Consequently, the recontextualization process of the cultures described in the study strengthens the awareness and responsibility of the Kalinga teachers to their cultural community. This also contributes to the preservation of the practices.

How do you solve number pattern problems through mathematical semiotics analysis and computational thinking?

2024-02-01T07:17:27+00:00

Some countries, including Indonesia, have a framework for understanding how students receive and process math concepts as new knowledge through learning styles. Learning style, particularly Kolb's model, is one of the learning styles that contribute to students' success in learning. Experts have explored the characteristics of Kolb's learning style and found many effects on student learning outcomes as a starting point in learning mathematical concepts. However, the research still focuses on exploring integer operation materials in specific math abilities. The researchers hardly found any discourse to study, such as exploring number patterns in computational thinking and semiotic mathematics. Therefore, this study aims to explore mathematical semiotics and computational thinking on number patterns in terms of Kolb's learning style model. This research uses hermeneutic phenomenology to explore through written tests and interviews. An explanation of the components, characteristics, and semiotic characteristics of mathematical and computational thinking seen in students who have the Kolb model of learning in solving problems of number patterns is part of the interpretation. These findings can be used as benchmarks in developing mathematics materials. Thus, this knowledge is a concrete foundation to guide future advances in curriculum, assessment methods, and learning approaches in mathematics education, particularly in algebra.

Analyzing multilevel model of educational data: Teachers’ ability effect on students’ mathematical learning motivation

2023-12-28T06:44:06+00:00

Motivation to learn mathematics decreased due to the inability of teachers to implement innovative learning models and techniques. Therefore, this study aimed to investigate the effects of teachers' ability on students' motivation to learn mathematics by using quantitative methods and survey approaches. There were 32 mathematics teachers and 542 students in the 24 schools within the Depok region, selected as respondents through a stratified random sampling method. The research instruments of two questionnaires of teachers’ competence and students’ learning motivation were distributed to the respondents. Data analysis was conducted to test the random effect of teachers’ ability on students’ motivation to learn mathematics by using the effect of teachers’ random intercepts and competence as models 1 and 2, respectively. These two models were analyzed using the n-level Structural Equation Model (nSEM), and the result showed that model 2 was the best one to investigate the random effect of teachers’ ability and students’ learning motivation. The data analysis showed that the variance among teachers’ ability (0,0027) was less than learning motivation among students (0.0597). These findings indicated that the motivation levels of students taught by the same teacher varied significantly, whereas the effects of the teachers were relatively homogeneous. In other words, teachers’ ability was somewhat the same in increasing students’ learning motivation. Based on these findings, this research work suggests teachers keep improving their teaching techniques. Hence, students will be well motivated to learn so that the learning objectives will be well achieved.

How do Indonesian students learn function concepts? A praxeological analysis of textbook

2024-02-14T22:31:14+00:00

The conception of functions, defined as the relationship between magnitudes or sets of ordered pairs, varies among students depending on the contextualization of the concept within the curriculum, notably in school textbooks. This investigation endeavors to scrutinize the approach taken by Indonesian textbooks in introducing the function concept at the lower secondary school level. An eighth-grade mathematics textbook was scrutinized utilizing praxeology, the fundamental construct of the Anthropological Theory of the Didactic. The analytical process unfolded in three main phases: examination of the praxis block, analysis of the logos block, and evaluation of the textbook's praxeological structure in collaboration with experts and educators. The examination revealed that the Indonesian textbook organizes functions into three distinct local praxeological frameworks: functions as sets, bijective functions, and functions as relationships between magnitudes. The praxis primarily emphasizes tasks and techniques for functions formulated by sets, shaping the landscape of function learning in Indonesia. Consequently, a notable epistemological gap within logos stems from the disparity between two conceptions of functions: functions as sets and analytical expressions. These findings underscore the necessity for an alternative praxeological arrangement of functions, mainly to bridge the divide between the set-theoretical definition and the analytical expression of a function.

Promoting conceptual change regarding infinity in high school mathematics teachers through a workshop

2024-02-12T07:46:03+00:00

This report delineates the outcomes of an intervention conducted with in-service high school educators, focusing on elucidating three distinct scenarios within geometric and arithmetic domains: the infinitely large, infinitely numerous, and infinitesimally close. Grounded in the theoretical framework of conceptual change, it is posited that when an individual exhibits entrenched conceptions, it signifies a misclassification of the pertinent concept, necessitating a categorical shift to effectuate a transformation in their cognitive schema, particularly concerning the notion of infinity. Thus, the principal objective of this investigation was to ameliorate the entrenched conceptions held by educators pertaining to infinity through a workshop-based intervention. Preceding the workshop, educators predominantly exhibited conceptions aligned with natural and potential infinities. However, after the workshop, a discernible transition was observed, with educators engendering an actual conception of infinity or an omega-epsilon position, exemplified by their acceptance of equivalences such as 0.999…=1 and the parity in the cardinality of sets comprising natural numbers, even numbers, and perfect squares. Nonetheless, notwithstanding this progress, confident educators evinced resistance to embracing the concept of actual infinity, particularly in instances such as the hypothetical scenario depicted in Hilbert's Grand Hotel. Consequently, drawing upon the framework of conceptual change theory, it can be postulated that a complete categorical shift was not universally realized among educators due to their reluctance to revise entrenched beliefs concerning natural or potential infinity.

Elevating student engagement and academic performance: A quantitative analysis of Python programming integration in the Merdeka Belajar curriculum

2024-02-05T01:58:40+00:00

Python programming is widely employed in educational institutions worldwide. Within the Merdeka Belajar curriculum context, this programming is recognized as a suitable vehicle for mathematics instruction, significantly influencing students’ motivation and learning outcomes, particularly following periods of educational hiatus. This study examines the effectiveness of Python programming in promoting heightened learning outcomes by examining the intricate relationship between student motivation and learning. The study uses quantitative research methodologies to evaluate student learning facilitated through Python programming, encompassing problem-solving assessments and the administration of motivation questionnaires. By engaging in coding practices, students understand the symbols they manipulate, facilitating their ability to juxtapose data derived from mathematical modeling with the resultant programming output. When disparities arise, students are empowered to reassess their work, fostering a more profound comprehension of the subject matter. These exercises serve to augment students' capacity to retain and process information within memory. Furthermore, students demonstrate a favorable disposition, exhibiting persistence in resolving programming challenges by meticulously analyzing error outputs, particularly those pertaining to TypeErrors. Encouraging students to confront errors through thoroughly examining error output manifestations engenders an efficacious learning paradigm. This research proffers invaluable insights for educational institutions contemplating the integration of Python programming as an instructional adjunct.

The didactic phenomenon: Deciphering students’ learning obstacles in set theory

2024-02-16T10:23:23+00:00

Teachers play a crucial role in disseminating knowledge in educational settings, typically adhering to a credulist-testimonial approach outlined in pedagogical literature. Consequently, students often acquire knowledge through this method, potentially leading to discrepancies between their conceptual understanding and the intended educational objectives. This study investigates the phenomenon of learning obstacles encountered by junior high school students, with a particular emphasis on mathematics education. It is part of a series of Didactical Design Research (DDR) projects aimed at developing effective instructional materials. Employing an interpretive paradigm within the DDR framework, the study adopts a qualitative approach utilizing hermeneutic phenomenology design. Various research tools such as diagnostic assessments, interview guidelines, observation sheets, and audio recordings are employed. Data analysis is conducted using the Constant Comparative Method (CCM). The findings highlight ontogenic, didactic, and epistemological obstacles students face, stemming from factors such as a lack of interest in mathematics, ineffective material presentation, and misconceptions regarding set concepts. These results underscore the importance of educators employing effective teaching strategies to help students overcome these obstacles and succeed in their mathematics education.

How mathematics teachers' special knowledge changing: A case study in the Professional Teacher Education program

2024-01-17T21:42:28+00:00

The COVID-19 pandemic has catalyzed the widespread adoption of distance learning, necessitating a comprehensive understanding of how teacher knowledge evolves within the context of Teacher Professional Education (TPE) programs. Some research endeavors may employ evaluation methodologies that inadequately capture the nuanced dimensions of knowledge, highlighting the necessity for greater incorporation of evidence-based approaches in the formulation and assessment of teacher development initiatives. This study employs a qualitative methodology to explore the evolution of Mathematics Teachers' Specialized Knowledge (MTSK) within the framework of a TPE program. Data were gathered through the engagement of three educators in the preparation and execution of lessons on permutation and combination via a Learning Management System (LMS), coupled with in-depth interviews. The findings underscore the TPE program's role in fostering collaborative learning environments through participation in online educational communities. Teachers are shown to be increasingly integrating technology into their pedagogical practices, albeit with varying degrees of proficiency. The presence of Professional Learning Communities (PLCs) is identified as instrumental in supporting educators in refining instructional strategies to enhance teaching effectiveness. Nevertheless, there remains a subset of teachers necessitating more profound and more comprehensive content knowledge about their subject matter. These insights emphasize the importance of designing TPE programs that offer sustained and adaptable professional development opportunities to facilitate continuous growth among educators. Consequently, it is recommended that online learning communities geared toward addressing the diverse learning requirements of students be established, thereby aiding in the identification and resolution of pedagogical challenges.

Error analysis in algebra learning: Exploring misconceptions and cognitive levels

2023-12-28T06:48:12+00:00

This research investigates errors and misconceptions among learners in algebraic education by utilizing Koch's error analysis method alongside the Structure of the Observed Learning Outcome (SOLO) taxonomy. The primary aim of the investigation is to discern the kinds of errors and cognitive stages demonstrated by Grade 9 students when engaged in algebraic problem-solving tasks. The studies' outcomes uncover several prevalent error categories, including conjoining, cancellation, and problem-solving errors, indicating deficiencies in conceptual comprehension and procedural execution. Moreover, applying the SOLO taxonomy elucidates learners' diverse levels of understanding, with a majority position within the uni-structural or multi-structural stages. Theoretical implications underscore the necessity for tailored instructional approaches to mitigate learners' obstacles and foster a deeper grasp of algebraic principles. Consequently, this research contributes significantly to the advancement of algebraic pedagogy and provides valuable insights for curriculum enhancement, thereby facilitating improved mathematics learning outcomes.

Math lessons go online: Insights and challenges of blended learning during the pandemic

2024-01-28T13:20:25+00:00

Online learning became a necessity in many places during the COVID-19 pandemic. In the case of Hong Kong SAR, the pandemic provided a unique opportunity to establish blended learning as a norm. The authors discuss the insights and challenges related to delivering mathematics lessons online in a secondary school during and after the pandemic. A three-year-long case study was conducted to examine the differences in perceptions between a teacher and his five students regarding online mathematics instruction during the suspension of traditional in-class lessons in 2020 and after the resumption of traditional instruction in 2023. The Social-Ecological Approach with domains of structure, agency, and cultural practice was applied in the study, which investigated the perceived benefits of blended learning for both the students and the teachers. Data was collected via interviews. The study explored technological challenges, curriculum adaptations, and the impact of parental support on blended learning. Looking ahead, leveraging motivators like easy access while mitigating distractors through disciplined strategies can optimize blended learning environments. The insights gained from this study provide valuable guidance on the effectiveness of instructional strategies and technological tools, highlighting the features of best practices for future blended learning approaches. Furthermore, the paper provides valuable information for policymakers, educators, and educational technology developers.

Cross-cultural insights on computational thinking in geometry: Indonesian and Japanese students’ perspectives

2024-02-25T22:47:35+00:00

Current research indicates the presence of highly skilled and motivated students with robust computational thinking backgrounds seeking opportunities to leverage their expertise in driving innovation and success in this era. These studies also reveal that students' computational thinking skills vary widely depending on educational resources, curriculum emphasis, and individual aptitude. Nonetheless, there is a growing recognition of the importance of fostering these skills, with efforts underway to integrate them more comprehensively into education systems worldwide, including in Indonesia and Japan, as representatives of developing and developed countries. Therefore, assessing the competency of computational thinking in these two countries would be intriguing. The descriptive qualitative research method was employed to delineate the computational thinking competencies of students in Indonesia and Japan. Student worksheets, specifically designed for this purpose, were utilized to gauge the development of these competencies during the learning process using the Scratch application. The results revealed that students employed various strategies in solving the given geometry problems. On the other hand, geometry is one of the mathematics topics that can identify students' computational thinking using this application. These findings were utilized to categorize students' computational thinking skills in the two countries and to identify potential obstacles students experienced in their efforts to enhance these skills. Nevertheless, these constraints offer significant insights into potential areas for future investigation and enhancement. Subsequent endeavors could prioritize conducting experiments by implementing specific learning approaches or methods that have demonstrated effectiveness in improving students' computational thinking skills. This study not only underscores the potential for expanding research on students' computational thinking skills but also provides an overview of the learning process, learning culture, and students' competence in solving geometry problems with tiered difficulty levels using their computational thinking skills.

Assessing knowledge to teach early algebra from the Mathematical Knowledge for Teaching (MKT) perspective: A support tool for primary school teachers

2024-03-04T02:14:12+00:00

Research about the optimal methodologies for guiding the training of primary school instructors in the instruction of early algebra remains in the process of determination. This manuscript delineates the methodology involved in developing and validating an assessment tool to evaluate the mathematical acumen of prospective primary educators in the domain of early algebra during their initial pedagogical training, drawing upon the constructs delineated in the Mathematical Knowledge for Teaching (MKT) model. To this end, an instrumental inquiry comprising four distinct phases has been executed: an exhaustive review of extant literature concerning the mathematical proficiency of primary school instructors and the pedagogy of early algebra; formulation of the preliminary version of the assessment instrument; validation of said instrument via expert appraisal and a preliminary application involving ten pre-service primary educators enrolled in a Spanish academic institution; and subsequent refinement and finalization of the assessment tool. This endeavor's outcome culminated in the MKT-Early Algebra Questionnaire (6-12-year-olds), comprising six open-ended inquiries meticulously designed to explore diverse facets of early algebra while aligning with the various sub-domains delineated in the MKT model. It is deduced that the resultant instrument holds promise as an effective diagnostic apparatus, serving dual purposes: elucidating the mathematical proficiency of primary school educators in the context of early algebra and fostering introspection regarding pedagogical strategies conducive to the cultivation of algebraic cognition at this developmental juncture. By furnishing a comprehensive questionnaire that systematically addresses all facets of pedagogical knowledge requisite for the effective instruction of early algebra, this study furnishes invaluable insights into the specific components that should be integrated into teacher education curricula in the domain of algebraic didactics.

LEPscO: Mathematical literacy learning environment for the Guru Penggerak program

2024-02-14T22:19:20+00:00

Mathematical literacy stands as a critical skill imperative for navigating the complexities of the 21st century. Enhancing students' mathematical literacy necessitates comprehensive engagement across the educational landscape. This aligns with the Guru Penggerak (GP) initiative, established by the government to serve as educational leaders, propelling the entire educational system forward. Nonetheless, the current GP program needs more specific provisions addressing mathematical literacy, and the existing learning environments for mathematical literacy remain constrained. Consequently, there is a pressing need to develop a dedicated mathematical literacy learning environment within the GP framework. This study endeavors to create a mathematically literate learning environment that is both valid and practical, potentially impacting the GP program significantly. Employing a design research approach, the study progresses through three key stages: preliminary, prototyping, and assessment. Seven teachers participated as subjects, using data collection methodologies including walkthroughs, observations, questionnaires, and interviews, which were analyzed descriptively. Findings indicate the development of a model for a mathematical literacy learning environment termed D-C-C with the LEPscO framework, which is deemed valid due to its alignment with the PISA framework, Indonesian educational curriculum, and unambiguous language. Moreover, the model proves practical for implementation within the GP program, exhibiting potential effects such as enhanced teacher satisfaction, learning, organizational support, and utilization of new knowledge, alongside improved student outcomes reflecting heightened mathematical literacy proficiency. This research contributes to educational discourse by introducing the LEPscO Framework, encompassing a Digital-Class-Community learning environment, structured learning processes encompassing training, classroom implementation, knowledge sharing, and community development, and targeted learning outcomes focusing on teachers' comprehension and reinforcement of mathematical literacy in education.

Athletes as guest speakers in mathematics education: A descriptive study of a pala player in dialogue with pre-service teachers

2024-02-16T10:31:52+00:00

The integration of sports-related contexts into mathematics education, along with the inclusion of guest speakers in classroom settings, is a widely acknowledged pedagogical strategy. This study employs a descriptive research approach to analyze a didactic activity conducted with 86 third-year students pursuing a Degree in Primary Education at the University of the Basque Country. The chosen sport for this activity was Basque pala, featuring a guest speaker renowned as one of the sport's all-time greats. This activity aimed to enhance the future primary school teachers' capacity to develop and select appropriate mathematical educational materials. Data for this research comprise the mathematical inquiries generated by students' post-guest lectures and responses gathered from a post-session survey. Findings reveal that student participants held a notably favorable perception regarding using Basque pala as a mathematical context within primary school education and as a component of their pedagogical training. The involvement of the guest speaker received exceptionally high acclaim. These outcomes remained consistent across two academic years and regardless of respondents' gender. In summary, when introduced by a distinguished practitioner, Basque pala proved to be a fertile ground for generating mathematical tasks and was a highly motivating factor for pre-service teachers.