Taking as its point of departure, situations arising in classrooms exposed to a heavy use of CAS, exemplified by the Danish upper secondary school mathematics program, the paper discusses the use of "old" cognitive frameworks of mathematics education as an alternative to more recent theoretical developments in the field. The paper draws…

Since data collection technologies has become a part of daily life, measurement and data requirements now permeate many state mathematics standards, beginning as early as kindergarten and extending through high school. For example, the Standards for Mathematical Content, recommend that kindergarteners "describe and compare measurable…

Mathematical modelling is acknowledged to be one of the major dimensions of mathematical competence, and well-designed modelling activities can provide students with the opportunity to use mathematical concepts and procedures in a meaningful way. Additionally, modelling activities are regarded as suitable contexts for enabling students to use…

The EnCoMPASS project (Emerging Communities for Mathematical Practices and Assessment) at the Math Forum and Drexel University has produced a web-based software tool for the assessment of student work. This paper discusses research on the impact of the tool on teachers' attitudes toward work with students in the software environment. The tool…

Whereas some educational designers believe that students should learn new concepts through explorative problem solving within dedicated environments that constrain key parameters of their search and then support their progressive appropriation of empowering disciplinary forms, others are critical of the ultimate efficacy of this discovery-based…

The ubiquity of mobile devices demands the exploitation of their potentials in distance and face-to-face teaching, as well for complementing textbooks in printed or electronic format. There is a strong need to develop innovative resources that open up new dimensions of learning and teaching through interactive and platform-independent content.…

CATO is a new user interface, developed by the author as a response to the significant difficulties faced by scientists, engineers, and students in their usage of computer algebra (CA) systems. Their tendency to use CA systems only occasionally means that they are unfamiliar with requisite grammar and syntax these systems require. The author…

Automated theorem proving (ATP) for Propositional Classical Logic is an algorithm to check the validity of a formula. It is a very well-known problem which is decidable but co-NP-complete. There are many algorithms for this problem. In this paper, an educationally oriented implementation of Semantic Tableaux method is described. The program has…

This document provides Q&A with webinar presenter, Susan Riley. Riley's presentation looks at broad ideas of clarifying best practices in using arts integration (AI) and/or STEAM at any grade level. Questions cover topics such as: the creativity crisis in US schools, integrating art into math adult education (GED and ESL), theater arts in the…

This paper offers an account of what early mathematics education could look like in an age of young digital natives. Each "Tubby," as the tablets are called, presents Nicole (our generic little child) with stimulating mathematics microworlds, from which, beginning at age 3, she can learn basic math concepts, as well as methods of…

Computer-aided assessment (CAA) has been used at a university with one of the largest mathematics and engineering undergraduate cohorts in the UK for more than ten years. Lecturers teaching mathematics to first year students were asked about their current use of CAA in a questionnaire and in interviews. This article presents the issues that these…

Space-filling curves are related to fractals, in that they have self-similar patterns. Such space-filling curves were originally developed as conceptual mathematical "monsters", counter-examples to Weierstrassian and Reimannian treatments of calculus and continuity. These were curves that were everywhere-connected but…

Gabriel's Horn is a solid of revolution commonly featured in calculus textbooks as a counter-intuitive example of a solid having finite volume but infinite surface area. Other examples of solids with surprising geometrical finitude relationships have also appeared in the literature. This article cites several intriguing examples (some of fractal…

A technique for automatic error analysis using interval mathematics is introduced. A comparison to standard error propagation methods shows that in cases involving complicated formulas, the interval approach gives comparable error estimates with much less effort. Several examples are considered, and numerical errors are computed using the INTLAB…

Middle school students need to know about energy concepts and how they can reduce their energy use. New energy-monitoring tools provide powerful opportunities for students to engage in authentic investigations rich in the science practices described in "A Framework for K-12 Science Education" (NRC 2012), while at the same time advancing their…