This article presents an international study that documented the conceptions of atomic models held by 1062 in-service high school science teachers from 58 countries. First, a previous study on pre-service science teachers’ conceptions of atomic models was successfully replicated as a pilot study with an international sample of in-service science teachers. Teachers’ conceptions were investigated by analysing their drawings of atomic models. Based on these results, a multiple-choice questionnaire was developed for the main study. This questionnaire collected data on teachers’ conceptions of atomic models, teachers’ knowledge about their students’ conceptions of atomic models, and teachers’ use of atomic models in the classroom. The results show that the teachers’ conceptions of atomic models are almost evenly distributed over six different atomic models. These models are the Bohr model, the Rutherford model, the probability model, the orbital model, the probability orbit model, and the wave model. The vast majority of teachers assume that their students’ conceptions are centred on two historical atomic models, namely the Bohr model and the Rutherford model. Furthermore, the majority of teachers prefer to use historical atomic models over modern atomic models in the classroom. However, the findings also highlight that the use of modern atomic models in the classroom is positively correlated with growing teaching experience, and that teachers’ conceptions of atomic models and their knowledge of students’ conceptions of atomic models significantly influence teachers’ classroom practice.

This study aims to acquaint high school students with the process of modelling in mathematics teaching. The research lasted 5 weeks with a group of (N=36) high school students of Zenica-Doboj Canton (Bosnia and Herzegovina). Students had an opportunity to learn about functions and their properties, and subsequently about mathematical modelling with linear, quadratic, and logarithmic functions. Examples in the research were related to real-world phenomena and processes. The problems were composed of the following subtasks: creating or testing a model, explaining the results, finding the domain and range, and critical thinking about the model. The research identifies the importance of mathematical modelling in teaching. The results display a positive impact of such an approach on students, their thinking, attitude towards teaching, understanding of the materials, motivation and examination scores. The experiences that both students and teachers may have in a mathematical modelling framework could be extremely important for the academic success. A control group of 36 students took the final exam as well. The students of the experimental group got much better results than the students of the control group. Indeed, learning through mathematical modelling has been shown to contribute to all the aspects of students' expected development.

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.  

A mathematics instructor with limited knowledge of content and pedagogy has little room for improvement or novelty in the classroom or the ability to arouse students' interest in learning mathematics. This case study was conducted in a foundation center of one of the public universities in Malaysia. The target of current research was to investigate the influence of lesson study (LS) on lecturers’ pedagogical content and content knowledge. The LS group comprises of seven lecturers of the mathematics group and the researcher. The group collaboratively prepared a research lesson on the subject of even and odd functions. Data gathered through interviews and observations on the lecturers’ activities in discussion meetings. Data from observations and interviews were analyzed descriptively and through thematic analysis method respectively. The results of this study show lecturers improved their knowledge in content and pedagogy considerably about even and odd functions. They enhanced their teaching knowledge through collaborative work and sharing of experiences. It seems the findings of this research not only help lecturers to have better performance in teaching the even and odd functions but also encourage them to experience the LS approach in teaching other mathematical concepts.

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.

In the domain of engineering education, the crucial role of mathematics, especially Calculus, cannot be overstated, as it lays the foundational groundwork for numerous sciences, technology, engineering and mathematics (STEM) courses. The integration of mathematics into STEM disciplines is achieved through the practical application of mathematical concepts in real-world scenarios or in conjunction with other STEM subjects, thereby enhancing the coherence of engineering studies and acting as a significant motivational catalyst for students. This paper presents an analytical narrative of a practical mathematics assignment, woven into the Calculus curriculum and other STEM courses from 2013 to 2018. It delves into the potential impacts of these practical assignments on student performance and attitudes by evaluating data sourced from final exam scores and anonymous course surveys, both before and after the intervention period. Through the analysis of an extensive dataset comprising 1526 final exam scores, this study endeavors to make a substantive contribution to Future Technology Studies (FTS), focusing on the strategic harmonization of mathematics and STEM courses to enrich the educational experience and foster a more cohesive and applied learning framework in these disciplines.

Global concern surrounds students' mathematics learning, development, and achievement. Scholarly discussions have explored various factors influencing students' mathematics performance. However, more information is needed to understand the impact of mathematics teaching styles on student outcomes in developing contexts like Nepal. This study examines the moderators of mathematics teaching styles and their influence on students' performance. To achieve this, the Teachers' Teaching Style Questionnaire (TTSQ) collected quantitative data from 469 grade nine students across 14 high schools in Kathmandu, Lalitpur, and Bhaktapur districts of Nepal. Confirmatory factor analysis, path analysis, and moderation analysis were performed to examine the effects of teaching styles on student achievement in mathematics. Key findings indicate that teaching styles, such as consideration and openness, are not significant predictors of student achievement, but rigid teaching styles can predict student achievement in mathematics. However, impact of the rigid teaching style was negative on student achievement. School type influenced the relationship between performance and considerate teaching, favoring private schools. School location influenced the relationship between considerate teaching and student performance in mathematics, favoring rural schools. Likewise, urban schools had a negative effect on the relationship between teacher openness and student performance, but rural schools had a positive effect on their relationship. Furthermore, low and high-ability students moderated the relationship between considerate teaching and student achievement, with the negative effect of low ability on considerate teaching and student performance and the positive influence of high ability on considerate teaching and student achievement. Student ability influenced the relationship between teacher openness and student performance, with a negative moderations of low and moderate ability students. The study concludes by emphasizing the importance of teacher training in teaching styles for high schools in Nepal and similar contexts.

For decades, a global trend in mathematics curriculum development has placed greater emphasis on learning goals that seek to capture different kinds of processes that students should master. For Danish primary and secondary mathematics education, these ambitions are expressed in terms of a set of mathematical competencies, in line with the so-called KOM framework. However, it has proved challenging to implement the competencies in mathematics classrooms and actual teaching practice. Matematrix is a series of Danish mathematics textbooks for grades K-9 designed to support mathematics teachers in facing this challenge. Following a short introduction to the KOM framework, I – as one of the designers and authors of the textbooks – present a key element in this endeavour: A three-dimensional model of content and objectives combining mathematical competencies, mathematical core concepts and grade levels. I then describe the use of this model in the specific case of Matematrix at three different levels of textbook design: The structure of the general content of the books, the focal points for each chapter, and the development of different kinds of tasks for the students to work with.