Cognitive scientists investigate mental models (how humans organize and structure knowledge in their minds) so as to understand human understanding of and interactions with the world. Cognitive and mental model research is concerned with internal conceptual systems that are not easily or directly observable. The goal of this research was to…

With the world moving rapidly into digital media and information, the ways in which learning activities in mathematics can be created and delivered are changing. However, to get the best results from the integration of ICTs in education, any application's design and development needs to be based on pedagogically appropriate principles, in terms of…

The overall aim of this study is to search whether teaching geometry with Cabri Geometry Plus II software have effects on 7th grade students' learning transformation geometry in mathematics. In this context, the researcher has used a pre-test and post-test research design with a control group. The research sample consisted of 135 students in total…

In order to find its circumference, Archimedes famously boxed the circle between two polygons. Ending the first of a series of articles (MT179) with an aside, Francis Lopez-Real reverses the situation to ask: Which polygons can be boxed between two circles? (The official term for such polygons is "bicentric".) The sides of these polygons are…

Following an introduction to the diagonalization of matrices, one of the more difficult topics for students to grasp in linear algebra is the concept of Jordan normal form. In this note, we show how the important notions of diagonalization and Jordan normal form can be introduced and developed through the use of the computer algebra package…

Dynamic geometry software (DGS) aims to enhance mathematics education. This systematic review and meta-analysis evaluated the quasi-experimental studies on the effectiveness of DGS-based instruction in improving students' mathematical achievement. Research articles published between 1990 and 2013 were identified from major databases according to a…

We investigate the impact of integrating dynamic geometry environments with haptic devices, which allow users to not only see and manipulate geometric figures on a screen but also feel, through force-feedback, the result of interacting with such objects. The feedback loop can be assigned to varying attributes of objects, for example, the changing…

This article integrates research in intelligent tutors with psychology studies of memory and math fluency (the speed to retrieve or calculate answers to basic math operations). It describes the impact of computer software designed to improve either strategic behavior or math fluency. Both competencies are key to improved performance and both…

Dynamic geometry software (DGS), such as Geometer's Sketchpad[TM], Cabri Geometry[TM], and GeoGebra[TM] has become a widely used classroom technology. The broad availability of DGS has given students the opportunity to engage in many aspects of reasoning and proof, including exploration, conjecture development, and proof, in its many roles. By…

A number of underlying principles for including technology in the mathematics classroom is provided by Way and Webb (2006). They see technology, if incorporated in a rich and meaningful way, as potentially providing: (1) a shift from "instructivist" to constructivist education philosophies; (2) a move from teacher-centred to…

Designing didactic objects involves imagining how students can conceive of specific mathematical topics and then imagining what types of classroom discussions could support these mental constructions. This study investigated whether it was possible to design Java applets that might serve as didactic objects to support online learning where…

Through the Common Core State Standards (CCSS) Initiative, states and territories have collaborated in the development of a common core of standards in English Language Arts and mathematics for grades kindergarten through twelve that are now being adopted by states. Designed not only for the purpose of providing strong, shared expectations, the…

This article describes how a demonstration of statistical (or other) software can be recorded without expensive video equipment and saved as a presentation to be displayed with software such as Microsoft PowerPoint. Work carried out on a tablet PC, for example, can also be recorded in this fashion.

Most students now have access to devices such as digital cameras and mobile phones that are capable of taking short video clips outdoors. Such clips can be used with powerful ICT tools, such as Tracker, Excel and TI-Nspire, to extract time and coordinate data about a moving object, to produce scattergrams and to fit models. In this article we…

Many classes of differential equations are shown to be open to solution through a method involving a combination of a direct integration approach with suitably modified Picard iterative procedures. The classes of differential equations considered include typical initial value, boundary value and eigenvalue problems arising in physics and…