In computing real-valued functions, it is ordinarily assumed that the input to the function is known, and it is the output that we need to approximate. In this work, we take the opposite approach: we show how to compute the values of some transcendental functions by approximating the input to these functions, and obtaining exact answers for their…

This exploratory study examined the design issues related to a virtual-reality-based, gamelike learning environment (VRGLE) developed via OpenSimulator, an open-source virtual reality server. The researchers collected qualitative data to examine the VRGLE's usability, playability, and content integration for math learning. They found it important…

In this article, the author reports on a participant-observation case study that explored how alternatively certified, middle school teachers' expectations of tracked students affect their ability to learn to teach in ways that promote students' mathematical struggle and participation in productive mathematical discussions. Two teachers--one…

The study explores the development of 11-year-old students' informal inference about random bunny hops through student talk and use of computer simulation tools. Our aim in this paper is to draw on dialogic theory to explain how students make shifts in perspective, from intuition-based reasoning to more powerful, formal ways of using probabilistic…

This study examined how small groups of second-grade children developed understandings of the concept of congruence while collaboratively exploring and solving problems with dynamic representations of triangles using Sketchpad on the iPad. One case study is presented to illustrate how young learners can infer geometrical relationships between…

This study responded to a national call to improve the outcomes in mathematics in the Grade 12 matriculation examination in South Africa by reporting learners' perceptions of the introduction of computer-assisted learning in their mathematics classrooms. Three Grade 12 mathematics classes in a peri-urban school in South Africa were visited over a…

Educators across the nation are now well under way in implementing the Common Core State Standards (CCSS; National Governors Association Center for Best Practices & Council of Chief State School Officers [NGA & CCSSO], 2010) for mathematics. The emerging literature regarding CCSS mathematics instruction for students with disabilities urges…

The solution of simple kinetic equations is analyzed without referencing any topic from differential equations or integral calculus. Guided by the physical meaning of the rate equation, a systematic procedure is used to generate an approximate solution that converges uniformly to the exact solution in the case of zero, first, and second order…

Ill-structured problems can be regarded as one of the measures that meet recent social needs emphasizing students' abilities to solve real-life problems. This study aimed to analyze the mathematical abstraction process in solving such problems, and to identify the mathematical abstraction level ([I] Recognition of mathematical structure through…

In the process of learning mathematics, students practice various forms of thinking activities aimed to substantially contribute to the development of their different cognitive structures. In this paper, the subject matter is a "cognitive obstacle", a phenomenon that occurs in the procedures of solving mathematical tasks. Each task in…

In this work, we examine students' ways of thinking when presented with a novel linear algebra problem. Our intent was to explore how students employ and coordinate three modes of thinking, which we call computational, abstract, and geometric, following similar frameworks proposed by Hillel (2000) and Sierpinska (2000). However, the undergraduate…

In this article the connection between transfer, interaction and reflective thinking is analyzed, especially within the context of learning mathematics. Attention is paid to the question of how to use or to explore the knowledge that has already been acquired. It may be relevant to make a distinction between the "classical" concept of…

A considerable number of children rely on counting to solve single-digit addition problems when they are expected to use accurate retrieval-based strategies. There are different reasons why this may be so. Children may use inefficient counting strategies, produce errors when applying backup strategies or lack sufficient confidence to just state…

We have been incrementally adding data-driven methods into the Deep Thought logic tutor for the purpose of creating a fully data-driven intelligent tutoring system. Our previous research has shown that the addition of data-driven hints, worked examples, and problem assignment can improve student performance and retention in the tutor. In this…

Designers of interactive learning environments with a focus on word problem solving usually have to compromise between the amount of resolution paths that a user is allowed to follow and the quality of the feedback provided. We have built an intelligent tutoring system (ITS) that is able to both track the user's actions and provide adequate…