One of the main objectives in mathematics education is to motivate students due to the fact that their interest in this area is often very low. The use of different technologies, as well as gamification in the classroom, can help us to meet this goal. In this case, it is presented the use of two techniques, which are a digital escape room, using…

Visual thinking plays an essential role in solving problems and in learning mathematics. Many students do not understand how to graphically or geometrically represent problems and solve algebra problems. Visual thinking is the ability, process, and results of creating, interpreting, using, and imagining images and diagrams on paper or with…

We propose some generalizations of the classical Division Algorithm for polynomials over coefficient rings (possibly non-commutative). These results provide a generalization of the Remainder Theorem that allows calculating the remainder without using the long division method, even if the divisor has degree greater than one. As a consequence we…

In the spirit of the networking of didactical theories, it is advocated in this presentation in favor of a mixed networking of philosophical theories, namely Husserlian phenomenology and hermeneutics, and didactical theories to produce a fertile interplay between philosophy and mathematics education. The cross-analysis of students' work on a…

Introductory and remedial courses in college mathematics often serve as a gateway to student success. However, these university courses have seen little innovation despite historically low success rates. We sought to address deficits of the traditional lecture model and enhance student learning in an introductory college algebra course through the…

College algebra has been noted as a critical course in post-secondary institutions because it serves as a gateway for major selection and college completion. Combinatorial topics like repeatable permutations are often overlooked in K-12 and undergraduate curricula. Likewise, students' achievement and motivation are affected by the type of…

This study aims to understand the instructional interactions that foster students' generalizing. By analysing video-recorded lessons from 13 different Grade 3 classrooms in which an early algebra intervention was implemented, activities related to generalizing and students' generalizing activities were identified, and the nature of the…

There is an ongoing need to support students' learning of linear functions, and the study of slope makes up a foundational component of this learning. We applied techniques from systemic functional linguistics to document the meanings that were established through spoken interaction between a student and her tutors during discussions of slope. We…

Students in upper secondary education encounter difficulties in applying mathematics in physics. To improve our understanding of these difficulties, we examined symbol sense behavior of six grade 10 physics students solving algebraic physic problems. Our data confirmed that students did indeed struggle to apply algebra to physics, mainly because…

We present an algorithm for a matrix-based Enigma-type encoder based on a variation of the Hill Cipher as an application of 2 × 2 matrices. In particular, students will use vector addition and 2 × 2 matrix multiplication by column vectors to simulate a matrix version of the German Enigma Encoding Machine as a basic example of cryptography. The…

We hypothesize that one thing that has been holding the field back from recognizing the algebraic potential of young children's early experiences is an emphasis on specific definitions of what counts as algebra-relevant knowledge. In this article, we seek to develop a perspective on algebraic thinking that foregrounds the algebraic potential of…

The learning of algebra represents a difficulty within the mathematics learning process. Precisely because of their epistemological and ontological nature, semiotics provides a good key to understanding the main difficulties that hinder the learning of algebraic objects. The answers to a large scale assessments task that requires a treatment in…

Like terms are usually defined for variables with numerical coefficients. While the definition is sufficient to combine polynomial terms, it does not help the students to combine radical, logarithmic, or trigonometric terms. The purpose of this paper is to propose a lesson that introduces a broader definition of like terms and trialed with a group…

The purpose of the present article is to investigate the definition of matrix multiplication as a central issue in linear algebra courses. Applying both historical and pedagogical approaches, it focuses on the philosophy of generating the usual matrix multiplication, as a special binary operation, with its partly unexpected form compared with the…

The process of pairing a name with representations or peculiar properties permeates many mathematics classroom situations. In school, many practices go under the label 'definition', even though they can be very different from what mathematicians conceive as a formal definition, and in fact there are substantial differences between these different…