While there is widespread agreement that "all" learners of the 21st century need to be numerate and literate, reforming pedagogical practices to achieve such an outcome is challenging for many teachers. This is a report of one aspect of a project which aims to integrate a culturally responsive pedagogical mathematics practice within…

The nature of mathematical objects, their various types, the way in which they are formed, and how they participate in mathematical activity are all questions of interest for philosophy and mathematics education. Teaching in schools is usually based, implicitly or explicitly, on a descriptive/realist view of mathematics, an approach which is not…

In this article, we present investigative tasks that concern loci, which integrate the use of dynamic geometry software (DGS) with mathematics for proving the obtained figures. Additional conditions were added to the loci: ellipse, parabola and circle, which result in the emergence of new loci, similar in form to the original loci. The…

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…

The article first investigates the basis for designing teaching activities dealing with aspects of history, applications, and philosophy of mathematics in unison by discussing and analyzing the different "whys" and "hows" of including these three dimensions in mathematics education. Based on the observation that a use of history, applications, and…

The aim of this paper is to build up an argument about the importance of a mathematical analysis of young children's activity in relevant for the age educational tasks. Most of current approaches (psychological, social, and pedagogical) are limited to the study of the development of children's thinking, paying less attention to the involved…

The brief explains how exposing young children to early math concepts supports their development of reasoning and problem solving skills and later success in and out of school. It describes the unique ways each of five family engagement programs funded by the Heising-Simons Foundation developed, tested, and integrated early math learning into…

Developmental mathematics has been under the radar within higher education for some time. The reality is that there are many proven best practices in developmental math. Unfortunately, there are many obstacles that prevent student success. Moreover, the high rates of attrition and failure have led state legislators and college administrators to…

Although low performers should invest more time and effort in their studies, they seldom do. One reason is because they often feel that they get no return on their investment: more studying does not automatically lead to better marks in school. But with the right kind of in-school support, including creative and engaging mathematics-related…

This paper presents discussions on stochastic education in early childhood, based on two doctoral research projects carried out with groups of preschool teachers from public schools in the Brazilian cities of Suzano and São Paulo who were participating in a continuing education program. The objective is to reflect on the analysis of two didactic…

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…

This article presents a set of spatial tools for classroom learning about spatial justice. As part of a larger team, we designed a curriculum that engaged 10 learners with 3 spatial tools: (a) an oversized floor map, (b) interactive geographic information systems (GIS) maps, and (c) participatory mapping. We analyze how these tools supported…

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…