This research is included into development research type. This research uses a 4-D model (define, design, develop, and disseminate) Thiagarajan, Semmel, and Semmel. This research is organized by learning media and instruments, namely: the student's handbook, the teacher's handbook, lesson plan, the student's exercise sheet, the student's…

Mathematical reasoning with algebraic and geometric representations is essential for success in upperdivision and graduate-level physics courses. Complex algebra requires student to fluently move between algebraic and geometric representations. By designing a task for middle-division physics students to translate a geometric representation to…

In 1936, Albert Einstein wrote a brief article where he suggested the possibility that a massive object acted as a lens, amplifying the brightness of a star. As time went by, this phenomenon--known as gravitational lensing--has become a powerful research tool in astrophysics. The simplest and symmetrical expression of a gravitational lens is known…

Errors are a major component of the pedagogical content knowledge (PCK) needed for teaching mathematics. In this study, 25 prospective teachers (PTs) in high schools were invited to solve a trigonometric task that had been assigned to high-school students and, subsequently, to relate to an authentic solution containing mathematical errors, which…

Generalization is a critical component of mathematical reasoning, with researchers recommending that it be central to education at all grade levels. However, research on students' generalizing reveals pervasive difficulties in creating and expressing general statements, which underscores the need to better understand the processes that can support…

Educational technologies develop quickly. Which functions of face-to-face education can be substituted by technology for distance learning? One of the risks of online education is the lack of embodied interactions. We investigate what embodied interactive technologies might offer for teaching trigonometry when learning at a distance. In a multiple…

This study aims to discover the effectiveness of the blended learning model in mathematics learning to improve the achievement of mathematical concepts. This study employed a quasi-experimental design with a non-equivalent control group. The experimental class was taught through blended learning, while the control class was taught through the…

In this paper, research on some problematic aspects high school students have in learning trigonometry is presented. It is based on making sense of mathematics through perception, operation and reason in the case of trigonometry. We analyzed students' understanding of trigonometric concepts in the frame of triangle and circle trigonometry…

A Trigonometric function is one of the challenging materials for not only high school students but also pre-service teachers and teachers. On the other hand, An understanding of trigonometric function is an initial stage in understanding calculus derived from it such as limit, derivative, and integral. Thus, the competency in trigonometric…

High school students often ask questions about the nature of infinity. When contemplating what the "largest number" is, or discussing the speed of light, students bring their own ideas about infinity and asymptotes into the conversation. These are popular ideas, but formal ideas about the nature of mathematical sets, or "set…

Review of the history of trigonometry content and pedagogy indicates the necessity and importance of trigonometry in the school curriculum (e.g., van Brummelen, 2009; van Sickel, 2011). For example, understanding trigonometric functions is a requirement for understanding some other areas of science, such as Newtonian physics, architecture,…

How do diagrams and illustrations affect mathematical problem solving? Past research suggests that diagrams should promote correct performance. However, illustrations may provide a supportive context for problem solving, or they may distract students with seductive details. Moreover, effects may not be uniform across student subgroups. This study…

Two important pedagogical techniques for developing deeper mathematical understanding are to prove a given theorem in different ways and to unify the proofs of different theorems. Trigonometric angle sum and difference identities are introduced in Unit 2 of Specialist Mathematics in the Australian Curriculum (Australian Curriculum, Assessment and…

This paper explored pre-service teachers' perceptions and knowledge of trigonometric concepts. Convenience sampling technique was used to select a sample of 119 (25 females, 94 males) second year science/mathematics pre-service teachers from two Colleges of Education in the Northern Region of Ghana. Trigonometry Perception Questionnaire (TPQ) and…

When mathematics teachers plan lessons, they interact with curriculum materials in various ways. In this paper, we draw on Brown's (2009) "Design Capacity for Enactment" framework to explore the practice of "adapting" curriculum materials in the case of a Singapore secondary mathematics teacher. Problems from the textbook used…