In this paper, a simple proof of the Morley's Trisector Theorem is presented which involves basic plane geometry only. The use of backward geometric approach, trigonometry or advanced mathematical techniques is not required. It is suitable for introducing to secondary or undergraduate students, as well as teachers or instructors for learning or…

Students' difficulties with proofs are well documented. To remedy this, it is often recommended that reasoning and proving be focused on in all grades and content areas of school mathematics. However, proofs continue to have a marginal place in many classrooms, or are only given explicit attention in courses in Euclidean geometry. Geometry is also…

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…

Scholarly interest about how students learn and retain learned skills is vast. Cognitive psychologists have recommended various techniques used to increase retention. One technique, spaced retrieval practice, involves extending opportunities to retrieve course content beyond a customarily short window following the initial learning process. Our…

We propose an alternative formula for solving the biquadratic equation x[superscript 4] + bx[superscript 2] + c = 0, which is more convenient than the classical one whenever c is a perfect square. The method is suitable to be introduced to high school students together with the standard approach of the substitution y = x[superscript 2]. A…

This study investigates the analogies used by a sample of secondary mathematics teachers when they described the concept of function. The study is concerned with understanding what analogies were used by the participant teachers and conceptions of functions positioned in those analogies. Using examples from a set of responses to five open-ended…

Generalization is one of the core aspects of algebraic thinking, and research literature points to the importance of objectification when generalizing mathematical discourses. To increase the field's understanding of the objectification process in various algebra discourses, our study analyses Grade 6 teachers' use of words, symbols, routines and…

In high school, unit discs were all circular. Squares and diamonds were added to the list of shapes in a Real Analysis course and although more bizarre shapes appeared in graduate school, the list of possible shapes didn't appear endless. In this note, we'll show that unit discs can have almost any shape imaginable.

This paper explores the specialized knowledge mobilized by a mathematics teacher in the selection and use of examples for teaching sequences. Taking an experimental case study approach, we analyse the examples deployed in a series of third-year secondary level lessons on sequences and identify the different knowledge subdomains activated according…

The goal of this note is to obtain the area enclosed between a parabola and two tangent lines using visual arguments. The first step that we have to follow, in order to do that, is noticing that the area between a parabola and a tangent line only depends on the leading coefficient of the quadratic function of the parabola. Finally, the…

We consider the following hypothesis: whereas, the institutions in charge of the teaching of mathematics for future professional mathematicians (IPM, in short) share a "didactic paradigm" (strongly based on logical arguments), there does not seem to be such a thing in secondary mathematics education. In this work, we analyse the notion…

The Tchokwe people lived on the African continent, in Mozambique and Angola. The sona belong to their cultural tradition. The sona are drawings made in the sand by older members of the tribe to tell stories, essential in the youngests' formation. In this article, we show a relationship between the sona and the greatest common divisor (GCD) of two…

The transition from school to university is a challenging process for many students which is reflected in high dropout and low examination success rates during the first year at university. Qualitative studies have found hints that students' beliefs play an important role during the transition. Due to their dialectic nature with cognitive as well…

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…

This study through a quantitative research methodology investigated mathematics productive disposition as a correlate of senior secondary school students' achievement in mathematics in Nigeria. A correlational research design was implemented for the study in which three research questions were answered. The sample consisted of 1600 senior…