In this study we analyze and contrast approaches that future high school math teachers show when solving word problems with the use of pencil and paper and later, with the use of a Dynamic Geometry System (DGS). The resources, representations, strategies and forms of mathematical reasoning that the participants exhibit when they use GeoGebra in…

Advancement of self-regulation during complex problem solving and the development of strategical reasoning are among the central educational goals linked to 21st century skills. In this paper we introduce the notion of "Stepped Tasks", which are specially designed in Top-Down structure to achieve these goals in mathematics instruction.…

Computational thinking--a set of mental and cognitive tools applied to problem solving--is a fundamental skill that all of us (and not just computer scientists) draw on. Educators have found that computational thinking enhances learning across a range of subjects and reinforces students' abilities in reading, writing, and arithmetic. This book…

Around 430 BCE it is reported that a typhoid epidemic carried off about a quarter of the population of Athens in ancient Greece. When the gods were asked what could be done to halt this raging epidemic, they apparently replied that the altar in the Temple of Apollo in Delios would have to be doubled in size. After several attempts to double the…

This paper analyzes the thought process involved in problem solving and its categorization as creative thinking as defined by psychologist R. Weisberg (2006). Additionally, the notion of insight, sometimes present in unconscious creative thinking and often leading to creative ideas, is discussed in the context of geometry problem solving. In…

Mathematical problem solving ability is one of the most important abilities students must have to process the information provided in solving problems. Before using mathematical problem solving skills, prior knowledge becomes the most crucial thing that makes students able to connect all available information so that they can construct new…

Building from the evidence-based learning progression in geometric reasoning from the RMFII project, this paper presents data from students' solutions to three problems in geometry and measurement situations to identify key components needed to nurture reasoning. To show emerging analytical reasoning students must coordinate multiple pieces of…

The literature on the association between reading comprehension and mathematics skills is complicated and conflicting. This study seeks to illuminate the nature of the association between mathematics skills and reading comprehension by incorporating potential moderators, namely components of mathematics skills, domains of content standards in…

Justification skills should be fostered in teaching mathematics as they are highly related to effectiveness in problem solving. However, pre-service mathematics teachers do not always have the necessary skills in using mathematically convincing language and justifying their solutions. Thus, they should be introduced to a variety of instructional…

In this paper, the development of the MAR (mobile augmented reality) remedial teaching program is described. It allowed students to manipulate augmented objects through AURASMA app via internet and find leads to solve geometry problems regarding compound-cube-surface area. In order to foster students' spatial abilities, the program provided…

This paper focuses on pre-service mathematics teachers' geometrical construction processes while using a duo of artefacts, namely the paper-and-pencil environment (PPE) and a dynamic geometry system (DGS). The participants of this case study were two pre-service mathematics teachers, who had limited DGS experiences in solving geometry tasks. The…

It has been more than two decades since researchers advocated the inquiry-based instruction in their classes. The idea, as appealing as it is in the theory, appeared not to be as fruitful in implementation. There are reports of students' resentments, frustrations, withdrawals, as well as challenges that instructors faced in their choice of…

In this paper we present the results of a study which was carried out in an inquiry-based teaching and learning environment with the use of 'what if not' methodology coupled with the integration of dynamic geometry software. The vast majority of the students reported that they perceived themselves as participants rather than spectators. Most of…

Searching for loci belongs to classical topics of school curricula at schools of different levels all over the world. In the text investigation of loci by GeoGebra using the command "LocusEquation," the tool which has recently been implemented into GeoGebra and which brings a new approach in searching for loci of points, is given. This…

"Principles to Actions: Ensuring Mathematical Success for All" (NCTM 2014) gives teachers access to an insightful, research-informed framework that outlines ways to promote reasoning and sense making. Specifically, as students transition on their mathematical journey through middle school and beyond, their knowledge and use of…