This paper discusses two "GeoGebra" applets, "Radical" and "Parabola," that are designed to strengthen the conceptual understanding of specific topics in algebra. The design and pedagogical basis of the applets are presented. The integration of the applets in teaching Grade 9 mathematics in a partner high school in…

Embodied mathematics activities involve students engaging in physical actions to help them better understand mathematics concepts. Current research shows these types of activities have great potential to help students develop conceptual understanding. The authors present four principles for designing embodied mathematics activities and give…

The author shares the lesson that he used to introduce the quadratic unit to students in an extended second-year algebra class, demonstrate why it was appropriate for his struggling learners, and discuss possible future modifications to this lesson.

One of the definitions of mathematics is that it is "a science of patterns and themes". Within the scope of this definition, the current software technology facilitates the creation of visuals and patterns. Thus, GeoGebra software was used. The study was carried out in two stages. In the first stage, the Dynamic Geometry Software and the…

In a series of two "in vivo" experiments, we examine whether correct and incorrect examples with prompts for self-explanation can be effective for improving students' conceptual understanding and procedural skill in Algebra when combined with guided practice. In Experiment 1, students working with the Algebra I Cognitive Tutor were randomly…

Three-dimensional dynamic geometry software has the power to enhance students' learning of spatial geometry. The purpose of this research is to clarify what potential using three-dimensional dynamic geometry software can offer us in terms of how to develop the spatial geometry curriculum in lower secondary schools. By focusing on the impacts the…

Motion planning is a core problem in robotics concerned with finding feasible paths for a given robot. Motion planning algorithms perform a search in the high-dimensional continuous space of robot configurations and exemplify many of the core algorithmic concepts of search algorithms and associated data structures. Motion planning algorithms can…

Many students find it difficult to engage with mathematical concepts. As a relatively new class of learning tools, visualization tools may be able to promote higher levels of engagement with mathematical concepts. Often, development of new tools may outpace empirical evaluations of the effectiveness of these tools, especially in educational…

This paper is a mathematical (Boolean) analysis a set of cognitive maps called Thinking Maps[R], based on Albert Upton's semantic principles developed in his seminal works, Design for Thinking (1961) and Creative Analysis (1961). Albert Upton can be seen as a brilliant thinker who was before his time or after his time depending on the future of…

This research aims to explore the role of physical representations in young children's numerical learning then identify the benefits of using a graphical interface in order to understand the potential for developing interactive technologies in this domain. Three studies are reported that examined the effect of using physical representations…

In this paper we report on the sustained research and development work at the AMSTEL Institute of the University of Amsterdam to improve mathematics and science education at primary and secondary school level, which has lead amongst other things to the development of the integrated computer working environment Coach 6. This environment consists of…

Many epistemic activities, such as spatial reasoning, sense-making, problem solving, and learning, are information-based. In the context of epistemic activities involving mathematical information, learners often use interactive 3D mathematical visualizations (MVs). However, performing such activities is not always easy. Although it is generally…

New methodologies in science (or mathematics) learning process and scientific thinking in the classroom activity of engineer students with ICT (information and communication technology), including graphic calculator are presented: visual modelling with ICT, action research with graphic calculator, insight in classroom and communications and…

This paper examines the extent to which mathematical knowledge, and its related pedagogy, is inextricably linked to the tools--physical, virtual, cultural--in which it is expressed. Our goal is to focus on a few exemplars of computational tools, and to describe with some illustrative examples, how mathematical meanings are shaped by their use. We…

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…