This study offers a view on students' technology-based problem solving activity through the lens of a theoretical model which accounts for the relationship between mathematical and technological knowledge in successful problem solving. This study takes a qualitative approach building on the work of a 13-year-old girl as an exemplary case of the…

This article condenses five years of professional development based on Technological Pedagogical and Content Knowledge (TPACK) integration principles, National Council of Teachers of Mathematics Principles to Actions (2014), and ISTE Student and Teacher standards to give a launch point for teachers and teacher educators to integrate 3D modeling…

This work is about analyzing games as models of systems. The goal is to understand the techniques that have been used by game designers in the past, and to compare them to the study of mathematical game theory. Through the study of a system or concept a model often emerges that can effectively educate students about making intelligent decisions…

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…

Empirical research has provided evidence supporting the validation and prediction of 4 major sources of self-efficacy: enactive performance accomplishments, vicarious experiences, verbal persuasion, and emotional states. Other research studies have also attested to the importance and potency of self-efficacy in academic learning and achievement.…

Studying geometry is an integral component of learning mathematics because it allows students to analyse and interpret the world they live in as well as equip them with tools they can apply in other areas of mathematics. Therefore, students need to develop an understanding of geometric concepts as well as gaining adequate geometry related skills.…

The ability of interlocking polygonal tiles, like those in the "Polydron Frameworks kit," to flex can give rise to polyhedra whose faces don't quite fit. In this article, the author discusses what happens with polyhedra whose faces don't quite fit. (Contains 2 notes.)

Display took a wide variety of forms ranging from students presenting their initial planning and thought processes, to displays of their finished work, and their suggestions for extending the task should they, or others, have time to return to it in the future. A variety of different media were used from traditional posters in many shapes and…

Mathematics education researchers conducting instruction experiments using a design research methodology are challenged with the analysis of often complex and large amounts of qualitative data. In this paper, we present two case studies that show how multimedia analysis software can greatly support video data analysis and theory development in…

This paper shows the basic concept of Functional Modelling in mathematics education which has become more and more important in recent years. Hence it is necessary to think about suitable graphical methods to explain the fundamental idea of a function and its influence on values and other functions. PROGRAPH diagrams are a potentially good way to…

The ever increasing availability of mathematics education software and internet-based multimedia learning activities presents teachers with the difficult task of deciding which programs are best suited for their students' learning needs. The challenge is for teachers to select pedagogical products that not only promote significant mathematical…

In this paper, a didactical proposal is presented to introduce the variational methods for solving boundary value problems to engineering students. Starting from a couple of simple models arising in linear elasticity and heat diffusion, the concept of weak solution for these models is motivated and the existence, uniqueness and continuous…

The use of a computer software package called "Exploring Measurement, Time and Money--Level 1" to help children explore many different arrangements of data and the effects of changing that data is presented. Activities which may be used to prepare students for this instruction are described. (CW)

This Note describes several versions of an intelligent tutor for basic algebra that have been developed at the RAND Corporation. The versions of the tutor were built around several core components, including an algebra expert system and a student modeling component that can make inferences about misconceptions underlying students' errors. The…

Presents an analysis of the question in the title which involves a discussion of fractions, number theory, and probability through modeling, exploring, and other mathematical connections. (MKR)