This paper reports an exploratory study on the pre-service teachers’ content knowledge on school calculus. A calculus instrument assessing the pre-service teachers’ iconic thinking, algorithmic thinking and formal thinking related to various concepts in school calculus was administered to a group of pre-service mathematics teachers. Their performance on five of the items is reported in this paper. Other than their good performance in the iconic recognition of stationary points, their recognition on points of inflexion, differentiability and notion of minimum points was relatively poor. In addition, they appeared to lack the algorithmic flexibility in testing the nature of stationary points and the formal thinking about definition of an extremum point. The implications of the findings are discussed.  

Mathematical connection ability is very important to be mastered by prospective mathematics teacher students as competency to teach in secondary schools. However, the facts show that there are still many students who have weak mathematical connection abilities. This qualitative descriptive study aimed to explore how the process, and product of the mathematical connection made by prospective mathematics teacher students when solving the integral calculus problems based on their prior knowledge. The research subjects were 58 students who were prospective high school mathematics teachers at the University of Jember, Indonesia. Data were collected using documentation, questionnaire, test, and interview methods. After the test results of all subjects were analyzed, six students were interviewed. To find the match between the results of the written test and the results of the interview, a triangulation method was carried out. Data analysis used descriptive qualitative analysis with steps of data categorization, data presentation, interpretation, and making conclusions. The results show that the research subjects have connected and used mathematical ideas in the form of procedures, facts, concepts/principles, and representations in solving integral calculus problems. Students with high prior knowledge abilities can make better mathematical connections than students with moderate and low prior abilities. From these results, it is recommended that lecturers need to improve students' prior knowledge and train the students more intensely to solve integral calculus problems so all students can develop their mathematical connection abilities into very strong categories.

The ability of students to build problem-solving models using procedural knowledge can be viewed from several aspects, including Mastery of Mathematical Problem Solving (MPS), understanding concepts and application of concepts, the relationship between learning outcomes of mathematics and interest in learning, and examine the contribution of the ability to understand concept problems, the application of concepts to the ability of MPS, as well as student difficulties and some of the advantages of students in solving problems. This experimental study aims to explain the effect of the MPS model using procedural knowledge on solving mathematical problems for Junior High School Students (JHSS). The findings showed that 1) The MPS method using procedural knowledge significantly improved learning outcomes, but the mastery of MPS for JHSS was still unsatisfactory. 2) MPS teaching could still not improve meaningful learning outcomes. However, when JHSS applied the concepts, calculations, and problem-solving aspects, MPS teaching improved meaningful learning outcomes. 3) Students' interest in learning mathematics in the two sample classes was classified as positive. Shortly, MPS teaching accustoms students to think systematically and creatively and not just give up on the problems they face.

This study tested hypotheses of a hypothetical model determining the influence of teacher clarity and real-world applications while teaching group theory concepts on students’ achievement in modern algebra. The data collected from 139 undergraduate students were analyzed by regression analysis using Stata14’s structural equation model building and estimation. The path regression analysis of the model using SEM model building and estimation confirmed the research hypotheses. First, the utilization of real-world application problems while teaching group theory concepts has a significant influence on students’ achievement in modern algebra. Second, the clear presentation of group theory concepts by the teacher has a significant influence on students’ achievement in modern algebra. Finally, both teachers’ clear presentation of group theory concepts and utilization of its real-world applications have a significant influence on students’ achievement in modern algebra.

Much research in Mathematics instruction has focused on collaborative learning and differentiated instruction. However, very little research in the Philippines focused on utilizing writing activities as an instructional intervention. Even in Mathematics, a subject grounded in computations, this can be beneficial. By explaining how a problem is solved, or why a solution is erroneous, students will learn how the concepts may be applied in a deeper sense. Given the pandemic's limits and the Philippines' low-performance ratings in international assessments, there is a pressing need to develop innovations to continue learning. Hence, this study investigated whether writing activities are effective in improving academic achievement in mathematics classrooms. Using an explanatory sequential mixed methods design, the study involved selected Grade 8 students in a public school in Pasig City. The results of the quantitative data showed a significant difference in the pre-test and post-test scores of the experimental group as compared to the control. This was supported by the qualitative data which revealed that writing activities help understand the topics, remember concepts, and serve as a reviewer before an assessment. Overall, the study suggests that writing activities as an intervention in mathematics are effective in improving the student’s academic achievement.

This study aims to describe the implication of the Aptitude Treatment Interaction (ATI) model integrated with character values to increase the students’ skill in solving mathematics story problems. This study applied a quasi-experimental research type using a non-equivalent control group design involving two classes with 30 students each. Data was collected using a test instrument for solving mathematics story problem. Data were analyzed using n-gain descriptive statistical analysis to see the increase in students' skill in solving mathematics story world problems. The results showed that the average score of student's aptitude in solving mathematics story problems is 91.26 which is in the category of very high. There is an increase in the students’ ability with score of an n-gain of 0.77 which is in the category of high. In addition, the results of observations related to the implementation of learning model of the ATI with a percentage of 87.5% in the category of very good. Thus, the character-based ATI learning model can be used to increase the students’ skill in solving mathematics story problem. In addition, it accommodates the character of students who are concerned with learning mathematics so that learning goals can be achieved both from cognitive and attitudinal aspects.

Online learning platforms and resources created by the Indonesian Ministry of Education, Culture, Research, and Technology were a blessing in disguise out of the unprecedented school closure caused by the Covid-19 pandemic. These learning resources are yet to be examined to ensure their usability and their role in improving the quality of learning in science classes. This study analyzed the learning modules and a sample lesson plan from the Teachers Learn Teachers Share platforms based on the three-dimensional learning framework. It examined to what extent is the 3-dimensional learning framework incorporated into the grade 4 learning modules and lesson plan on Energy. The methodology for analyzing the sufficiency of disciplinary crosscutting concepts, scientific practices, and core ideas applied here will enrich the Science, Technology, Engineering, and Mathematics (STEM) based education corpus of knowledge. Findings show that the disciplinary core ideas dimension is the most sufficiently covered of all three dimensions while the practices dimension is only partially covered as some of the points are mostly inferred, and the crosscutting concepts dimension still shows much room for improvement. Primary school teachers and schools’ curriculum development units should enrich the learning modules by expanding the discussions on the module coverage with crosscutting concepts.

Understanding and handling diversity, as well as inclusion, are critical in ensuring effective teaching and learning, especially in the mathematics classroom, where students have varied abilities. Despite the growing research in inclusive education, little is known about how mathematics teachers in the Ghanaian context understand the theory of multiple intelligences (MIs), leaving a gap in how this theory can be applied in the classroom to improve practice and inclusion. In this study, the authors explored Ghanaian mathematics teachers’ conceptions of the theory of MIs using a basic qualitative method design. 12 senior high school mathematics teachers in one municipality of Ghana were engaged through questionnaires and semi-structured interviews, including field notes, to provide information on their conceptions of the theory of MIs. Thematic analysis revealed that mathematics teachers conceived the theory of MIs as a theory of different styles for learning, multiple teaching strategies, and a theory for catering to diverse student needs. The findings highlight the need for professional development and teacher training curriculum development to enhance teachers' understanding of the theory of MIs to improve their practice and handling of inclusiveness and diversity in the classroom.

Comparison of mathematics textbooks between Indonesia and Singapore is one way to assess the educational process. This article provides insight into how mathematical concepts are taught and applied in problem-solving in each country. The study provides knowledge about how mathematical concepts are constructed by teachers and students and implemented in problem-solving between countries. This study aims to compare task designs in high school mathematics textbooks between Indonesia and Singapore based on the type of task, technique, technology, and theory used, with a focus on cubes and cuboids. The comparative analysis of the two books uses praxeological theory, the main construction of Didactic Anthropology Theory, with reference to epistemological model (REM) model analysis. The research results show that there are differences in the approaches, methods, and habits used in task design in the two countries. The techniques, technology and theories found in the two task designs show that Indonesian mathematics textbooks use more verification and drawing up conclusions which are influenced by perceptual techniques. Meanwhile, the task of designing Singapore's mathematics textbooks involves more direct investigations into forming students' knowledge through physical and operational techniques. The techniques, technology, and theories used in both designs influence the number of learning obstacles. Epistemological constraints occur in Indonesian textbooks and only a few in Singapore textbooks. These findings provide insight into how to build mathematical knowledge for students through good assignment design based on a country's educational character.

In this study, a topic-based analysis of students’ academic performance in mathematics across specific topic areas in selected lower secondary schools in Rwanda was conducted. The research examined third-term exam scripts (2022-2023 and 2023-2024) of 267 Senior One (S1) and Senior Two (S2) students at Groupe Scolaire Rushara, Groupe Scolaire Sheli, and Groupe Scolaire Nyarugugu, along with data from their eight mathematics teachers. A quantitative approach was employed using ANOVA to compare students’ performance across five key mathematics topics: algebra, metric measurement, proportional reasoning, geometry, and statistics and probability. The findings revealed significant improvement in statistics and probability (p =.000, η² = 0.293) and geometry (p =.000, η² = 0.178) between S1 and S2 students. In contrast, metric measurement showed no significant difference (p =.234, η² = 0.003), while algebra demonstrated minimal improvement (p =.050, η² = 0.007). Proportional reasoning showed moderate progress (p =.000, η² = 0.057), although students continued to struggle with applying proportional relationships. These results indicate that while notable gains were made in some areas, others require targeted pedagogical interventions to improve students’ conceptual understanding and performance in mathematics. The study underscores the importance of adaptive teaching strategies, enhanced instructional materials, and a more student-centered approach to mathematics education in lower secondary schools in Rwanda.