This lecture reports on aspects of a larger research programme focused on studying mental mathematics in elementary and secondary mathematics classrooms. It specifically addresses an unplanned aspect that became salient through the work conducted in these classrooms. In this research programme, mental mathematics sessions are designed on a variety…

Verification and validation are essential aspects of mathematics and beyond in STEM, but these constructs are not consistently defined in research nor in curricula documents. In this theoretical paper, we argue that verification and validation are largely characterized as binary judgments by teachers and researchers about what students do. We then…

In this article, the authors explore a number of interesting games as contexts for students learning geometry and enhancing their development of problem solving and reasoning. The games selected were appealing, content-aligned games for approximately four players with simple rules and 10-30 minutes of play time. The games were integrated by…

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…

Technology integration in K-12 mathematics has received increased attention in the last decade as new mathematical technologies have been developed and implemented more often. There is a need for further research on these technologies and for effective implementation practices of technology in mathematics education in general. in practice,…

Originally written 30 years ago, this paper is an analysis of the central challenge of schooling--that of engaging fully the powers of students' minds in classroom learning. This challenge maintains its relevance today. The work of engaging what John Dewey referred to as students' "inner attention" becomes the focus of an investigation…

This paper aims to revisit and clarify the term problem context and to develop a theoretical classification of the construct of levels of context use (LCU) to analyse how the context of a problem is used to formulate a problem in mathematical terms and to interpret the answer in relation to the context of a given problem. Two criteria and six…

The use of the dynamic mathematics software GeoGebra to solve geometric problems on conics and loci from an 18th century textbook will be presented. In particular, examples will be shown of how the use of this program helped the authors to understand the method that our predecessors used to deal with conic sections together with solving loci…

This paper attempts to engage the field in a discussion about what mathematics is needed for students to engage in society, especially with an increase in technology and digitalization. In this respect, mathematics holds a special place in STEM as machines do most of the calculations that students are taught in K-12. We raise questions about what…

Learning about statistics is a lot like learning about science: the learning is more meaningful if you can actively explore. This tenth installment of "Explorations in Statistics" explores the analysis of a potential change in some physiological response. As researchers, we often express absolute change as percent change so we can…

This paper focuses on children's number fact knowledge from a study that explored the impact of using multiplication and division contexts for developing number understanding with 34 five- and six-year-old children from diverse cultural and linguistic backgrounds. After a series of focused lessons, children's knowledge of number facts, including…

Designing an optimal Norman window is a standard calculus exercise. How much more difficult (or interesting) is its generalization to deploying multiple semicircles along the head (or along head and sill, or head and jambs)? What if we use shapes beside semi-circles? As the number of copies of the shape increases and the optimal Norman windows…

Analogical reasoning is believed to be an efficient means of problem solving and construction of knowledge during the search for and the analysis of new mathematical objects. However, there is growing concern that despite everyday usage, learners are unable to transfer analogical reasoning to learning situations. This study aims at facilitating…

This paper refers to the concept of semiotic and theoretic control describing resources to conduct decisions in epistemic processes. We consider an argumentation process from a complex problem-solving activity involving different conceptual frames related to parabolas. Using a micro-analytical interpretative lens, we will show that, in order to…

This is a narrative article, highlighting effective teaching strategies for teacher candidates at a four-year university in the South. The author examined preconceived negative notions teacher candidates expressed about being enrolled in a Math Block class and having to teach children about mathematics. After involving the teacher candidates in a…