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,…

This paper suggests a set of key features that might be appropriate when talking about digital textbooks or e-textbooks for mathematics education. The set of features are presented in a coherent framework and the paper will discuss each of the six features: widgets, interactivity, feedback, storing results, instructional design, authorability,…

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…

In this article I present examples of young children's interaction in collaborative group work in mathematics and consider how the children shared intentions, that is, how they influenced the thinking of another. By analysing the children's use of deixis as an aspect of indexicality, I examined how the students pointed out mathematical…

In this paper, we emphasize the methodological challenges of analyzing data with/in an enactivist framework in which (1) all knowing is doing is being, while focusing on, (2) how an entry by the observer transforms usual ways of analyzing data. In this sense, the association of knowing with doing suggests a shift in attention away from what…

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…

From a discursive perspective, differences in the language in which mathematics questions are posed change the nature of the mathematics with which students are expected to engage. The project The Evolution of the Discourse of School Mathematics (EDSM) analysed the discourse of mathematics examination papers set in the UK between 1980 and 2011. In…

The analytical scheme used in the project The Evolution of the Discourse of School Mathematics (EDSM) was developed to analyse the change over time in examination texts. An adapted version of the EDSM scheme has been deployed to analyse the nature of mathematics construed in Palestinian schools' textbooks and the mathematical activity expected of…

The [National Council of Teachers of Mathematics] NCTM research committee made a recent, urgent call for mathematics education researchers to "examine and deeply reflect on our research practices through an equity lens." With this in mind, we use this paper to reflect on the ways in which Steffe's work has contributed to three facets of…

Adolescents and youth represent a substantial number of individuals living with HIV/AIDS (hereinafter HIV) in the United States. Infected youth and young adults aged 13-29 (n = 100,724) made up 10% of all U.S. individuals living with HIV at the end of 2014 (Center for Disease Control [CDC], 2016). This same age group comprises 42% of all new HIV…

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…

The symposium provides an overview of the Early Years STEM Australia (ELSA) program. The conceptual underpinnings of the program are framed within STEM practices, rather than traditional thinking concerning the integration of discipline content knowledge. We will argue that our focus on practices is more aligned with the play-based and intentional…

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…

Access to science, technology, engineering, and mathematics fields serves as a key entry point to economic mobility and civic enfranchisement. Such access must take seriously the intellectual power of the knowledge and practices of non-dominant youth. In our case, this has meant to shift epistemic authority in mathematics from academic…