In this article, we state an interesting geometric conservation property between the three angle bisectors of three similar right triangles and provide a proof without words for its justification. A GeoGebra applet is also presented to help with the understanding of the progression of the proof from inductive to deductive stage.

This literature review covers 42 years and has two main objectives: to identify the obstacles to learning the polar coordinate system and to explore the teaching proposals suggested to overcome them. These questions are answered by locating and analysing articles related to the topic published in research and practitioner journals specialising in…

As new technological developments continue to change the educational landscape, it is not an exception in the area of proof and proving. This classroom note introduces the use of one of the trending proofs assistants -- the Lean theorem prover. We first provide a technical account of Lean, then exemplify Lean proofs in propositional logic, number…

The notion of function is central in all of the secondary curriculum, and indeed functional models appear in almost all higher education that is based on mathematics. However, in secondary education, functions usually appear in restricted and somewhat sterile forms. In this (mostly theoretical) paper, we present a proposal -- exemplified by a…

In the wake of the present inclusion of programming in mathematics education, which is a feature of curricular revisions in many countries, we have analysed newly inserted programming activities in mathematics textbooks. The aim was to investigate how such activities relate to and potentially affect students' opportunities to learn mathematics.…

The issue of mathematical knowledge in teaching has been widely discussed over the years. In this study, we carried out a systematic review of the literature with the aim of understanding, quantitatively and qualitatively, the studies developed related to the mathematical knowledge necessary for the teaching of Mathematics, with a focus on Numbers…

In this case study, we investigate how an inquiry-oriented interactive calculus textbook supported one U.S. college instructor's classroom teaching. We utilized analytical inquiry-oriented frameworks on observation data from a small classroom to capture textbooks' influence on the instruction conceptualized by the Teacher-Mathematics-Student face…

The expectations gap -- the difference between the level at which high schools prepare students and the preparation colleges expect -- is believed to be accountable for hindering access to, and success in, higher education. It has been largely attributed to misalignment of priorities and lack of communication among policy makers and educators and…

Storytelling is a valuable form of human expression that allows audience members to connect their own experiences with the narrative. As a pedagogical tool, storytelling has been explored mainly in primary school education but rarely in higher education. However, its potential for assisting students in learning mathematics and the societal…

'Group work' is a vague description of an instructional activity, because many factors shape its character and effect on students. One important factor is group formation, that is, how groups are formed by the instructor. In this paper, we sought to better understand the variation of group work with respect to group formation by addressing: How do…

Since COVID-19, Dynamic Mathematics Software (DMS) has been more widely used in mathematics classes, and many studies have been published. These data, generated because of technological updates and the popularity of COVID-19, should be addressed. To examine comprehensively the effectiveness of DMS on K-12 students' mathematics learning, this…

The aim of this study is to develop a descriptive framework for teacher educators to assist teachers to plan and realize modelling implementations in their classrooms and for researchers to describe and analyse how modelling is implemented. The planning process and implementations of 12 middle and high school mathematics teachers who conducted…

College calculus plays an important role in STEM students' degree and career aspirations. One of the key factors considered in assessing a student's ability to be successful in calculus is their proficiency in topics from prior mathematics courses such as algebra and precalculus. This study set out to examine the impact of students' precalculus…

The use of technologies in mathematics education at all levels has been discussed extensively for a number of years. It is one of the few themes that was the object of two ICMI studies, the most recent being published in 2010. Two new approaches, emerging lately in the teaching and learning of Mathematics at all levels, will be discussed:…

Both digital and non-digital games have been shown to be effective for supporting student engagement in mathematics. However, little is known about educator preferences for a particular game mode (i.e. digital versus non-digital), and what factors influence these preferences. To address this gap, 111 Australian primary school educators completed a…