This paper shares a flexible activity for engaging people in mathematical inquiry that does not depend on fixed prior knowledge built on a famous property of Möbius strips. The discussion includes the implementation of the activity and its extensions, facilitator moves and common participant thinking, suggestions for adaptation and integration…

The use of tasks to promote mathematical reasoning (MR) in teaching practice is essential to meet curricular goals. However, that practice is often a huge challenge for teachers, and particularly for prospective teachers and thus it is essential to highlight it as a goal for initial teacher education. This study focuses on preservice mathematics…

In this article, we use a case study to explore the views of first-year university students on the differences between mathematics at school and at university, and on the changes to their study methods as they make the transition to university mathematics. We also consider their views on the differences and affordances of tasks that they encounter…

We propose a divisibility criterion for elements of a generic Unique Factorization Domain. As a consequence, we obtain a general divisibility criterion for polynomials over Unique Factorization Domains. The arguments can be used in basic algebra courses and are suitable for building classroom/homework activities for college and high school…

Inherent in the Common Core's Standard for Mathematical Practice to "look for and express regularity in repeated reasoning" (SMP 8) is the idea that students engage in this practice by generalizing (NGA Center and CCSSO 2010). In mathematics, generalizing involves "lifting" and communicating about ideas at a level where the…

We propose a generalization of the classical Remainder Theorem for polynomials over commutative coefficient rings that allows calculating the remainder without using the long division method. As a consequence we obtain an extension of the classical Factor Theorem that provides a general divisibility criterion for polynomials. The arguments can be…

We study here an aspect of an infinite set "P" of multivariate polynomials, the elements of which are associated with the arithmetic-geometric-mean inequality. In particular, we show in this article that there exist infinite subsets of probability "P" for which every element may be expressed as a finite sum of squares of real…

In this article, the authors present a writing activity that allowed pre-service teachers to be creative in the mathematics classroom. Inspired by "The Important Book" by Margaret Wise Brown, students explored secondary-level mathematics concepts, discussing various attributes/characteristics of each concept through their written…

Many mathematics teacher educators encounter the challenge of creating or choosing mathematical tasks that evoke important mathematical insights and connections yet remain firmly grounded in school mathematics. This challenge increases substantially when trying to meet the needs of practicing secondary mathematics teachers pursuing graduate work…

The purpose of the study is to identify the classroom mathematical practices developed within a learning environment designed by Realistic Mathematics Education for teaching cone and pyramid to preservice teachers. A teaching experiment including five-week instructional sequence by a hypothetical learning trajectory about the solids of cone and…

Applying the Mathematical Knowledge for Teaching framework, we discuss the components of teacher knowledge that might be useful in supporting mathematical inquiry, and examine ways in which we strive to develop this knowledge within a middle grades mathematics program for undergraduate students who are prospective teachers. Using sample activities…

There are many geometrical approaches to the solution of the quadratic equation with real coefficients. In this article it is shown that the monic quadratic equation with complex coefficients can also be solved graphically, by the intersection of two hyperbolas; one hyperbola being derived from the real part of the quadratic equation and one from…

The purpose of this research is to determine pre-service mathematics teachers' skills in the development of activities. The research was carried out using the case study which is descriptive method. For the collection of data, 57 pre-service mathematics teachers' in their final year secondary math teachers' education department…

The simple question of how much paper is left on my toilet roll is studied from a mathematical modelling perspective. As is typical with applied mathematics, models of increasing complexity are introduced and solved. Solutions produced at each step are compared with the solution from the previous step. This process exposes students to the typical…

Although creativity plays a critical role in mathematics, it remains underestimated in the context of a mathematics classroom. This study aims to explore the views and differences creativity displays in prospective teachers and one of their lecturers with respect to the characteristics and practices of creative teachers and the characteristics of…