This work is a segment of an ongoing doctoral research in Brazil. The Leonardo numbers and the Leonardo sequence have gained attention from mathematicians and the academic community. Despite being a relatively new sequence within mathematical literature, its discussion has intensified over the past five years, giving rise to other branches, with…

Mathematical "magic," or experiences of beauty and creativity for K-12 mathematics students, can contribute to deepened content understanding. However, creating opportunities for mathematical "magic" in mathematics classrooms has been a challenge for classroom practitioners. To support development of these experiences in…

Mathematical modelling has been included in many mathematics curricula worldwide, and China's curricula are no exception. The development of modelling competencies has recently been listed among the Chinese mathematics curriculum's six key objectives. However, the manner in which nationwide learning and teaching of modelling should be conducted…

Learning to create, use, and evaluate models is a central element of becoming a scientist. In physics, we often begin an analysis of a complicated system with highly simplified or toy models. In introductory physics classes, we tend to use them without comment or motivation. Some students infer that physics is irrelevant to their understanding of…

In the paper we deploy two related theoretical and methodological approaches to see how they complement each other in the analysis of oral communication in mathematics group work. The first approach is an authority framework that builds on positioning theory and the second is politeness theory, with a focus on the sociological notion of face.…

The study aimed to analyze the interaction effect teaching models and cognitive style field dependent (FD)-field independent (FI) to students' mathematical problem-solving ability (MPSA), as well as students' MPSA differences based on teaching models and cognitive styles. Participants in this study were 145 junior high school students, with…

In this paper, we propose an analytic tool for describing the mathematics made available to learn in a "textbook lesson". The tool is an adaptation of the Mathematics Discourse in Instruction (MDI) analytic tool that we developed to analyze what is made available to learn in teachers' lessons. Our motivation to adapt the use of the MDI…

Educational data mining constitutes a recent research field which gained popularity over the last decade because of its ability to monitor students' academic performance and predict future progression. Numerous machine learning techniques and especially supervised learning algorithms have been applied to develop accurate models to predict…

To be literate in a society where the information shared online is often exploited, learners should be exposed to multiple aspects of contemporary predictive modeling. This article explores an activity in which grade 10 students learned how a famous AI algorithm (the Apriori algorithm) uses conditional probability to automate the process of…

This paper provides an analysis of a teaching episode of the multidigit algorithm for multiplication, with a focus on the influence of the teacher's mathematical knowledge on their teaching. The theoretical framework uses Mathematical Knowledge for Teaching, mathematical pertinence of the teacher and structuration of the milieu in a descending and…

In this paper we address the question, how do quantitative reasoning and covariational reasoning present as students build structural conceptions of real-world situations. We use data from an exploratory teaching experiment with an undergraduate STEM major to illustrate the explanatory roles quantitative reasoning and covariational reasoning play…

The African Data Initiative started as a crowd-sourced campaign to improve the teaching of statistics in African universities. The analysis of climate data provides one suitable context to illustrate ideas that lead to a radical new form of teaching. The problem within the context comes first, the technicalities are largely reduced -- mathematics…

Two sections of a college discrete mathematics class were taught using cooperative learning techniques throughout the semester. The 33 students attending these sections were randomly assigned into groups of three. Their final examination consisted of an individual and group blended examination where students worked in their groups and discussed…

Recursion is one of the most difficult programming topics for students. In this paper, an instructional method is proposed to enhance students' understanding of recursion tracing. The proposal is based on the use of rules to translate linear recursion algorithms into equivalent, iterative ones. The paper has two main contributions: the…

In this paper we propose a refinement of Michener's (1978) well-known example classification based on data from university mathematicians. The refinement takes into account the mathematician's perspective on the role of examples in doing mathematics. More specifically, our work provides insight into the ways in which mathematicians talk about…