This article examines the development of professional knowledge in pre-service mathematics teachers. From the discussion of a task associated with the multiplication of consecutive integer numbers, generalization is recognized as a process that allows to explore, to explain, and to validate mathematical results, and as an essential ability to…

Gifted students have potential to improve countries and this potential can be revealed and developed in schools where they spend most of their times with other regular students. However, these classrooms have some limitations for them; hence, they need some differentiated activities. Usage of dynamic geometry in mathematics lessons could be an…

Functions is considered an important mathematical literacy concept within the Organization for Economic Cooperation and Development's (OECD's) Programme for International Student Assessment (PISA), and it has been shown that Japanese junior high school students are experiencing problems understanding functions. This paper examines the difficulty…

Although Ball and her colleagues provided empirical evidence to support the existence of the six subdomains in mathematical knowledge for teaching (MKT) and further explained or defined the majority of these sub-domains, there were few explanations of what horizon content knowledge (HCK) embedded in MKT meant and they merely provided ideas about…

This paper describes how a dynamic figure was used as the basis for a task designed to support students in developing the hierarchical classification of the kites and their subsets. Following on from a previous study using the task with pairs of students, I describe how I embedded the task into a pedagogical sequence of activities, which included…

The paper deals with searching for synthetic solution supported by the means of dynamic geometry. It consists of two parts. The first one describes how software influences searching for synthetic solutions of geometric problems. The second one describes a small pilot experiment in which students of Faculty of Education solved two more difficult…

Geometry is essential for mathematics learning given that it is strongly related to our surroundings; however, few studies concentrated on using geometry in our daily life, especially using mobile devices with their sensors. Thus, this study proposed one app, Ubiquitous Geometry (UG), and explored its effects on learning angles and polygons in…

In this article, we examine the ways in which the creation of a third space can bridge the divide between coursework and practice for preservice secondary mathematics teachers (PSTs) taking a technology, pedagogy, and content course. A university-based instructor partnered with two high school teachers to create a space in which PSTs draw upon and…

Usually, all the applications of dynamic geometry systems (DGS) presented to our students are strictly mathematical, meanwhile their interests are normally far away from mathematics. We would like to introduce here a motivating example outside the "standard applications" of DGS, presenting a completely different application of this kind…

In mathematics education research paradoxes of infinity have been used in the investigation of students' conceptions of infinity. We analyze one such paradox--the Painter's Paradox--and examine the struggles of a group of Calculus students in an attempt to resolve it. The Painter's Paradox is based on the fact that Gabriel's horn has infinite…

Understanding spatial reasoning is important to success in mathematics. This article shows how the proficiency strands in the "Australian Curriculum: Mathematics" provide the tools needed for effective teaching and learning of spatial thinking.

Several studies related to mathematical proof have been done by many researchers on high-level materials, but not yet examined on the material of transformation geometry. The aim of this research is identification learning obstacles pre-service teachers on transformation geometry. This study is qualitative research; data were collected from…

This study aims to develop geometry learning media on curved-solid objects using Ispring Suite 8 with 3D effects supported by Google SketchUp. It also aims to find the effectiveness of the media towards the basic geometry skills and the learning result of 9th -grade students of junior high school. This study is a development study which refers to…

In a study about pre-service secondary mathematics teachers' (PSMTs) understanding about the nature of theorems in geometry, the researcher noticed that it was challenging for the PSMTs to visualize and draw counterexamples to disprove the given mathematical statements. Meanwhile, the use of the dragging feature of dynamic geometry environments…

Much remains under-researched in how learners make use of domain-specific feedback. In this paper, we report on how learners' can be supported to overcome logical circularity during their proof construction processes, and how feedback supports the processes. We present an analysis of three selected episodes from five learners who were using a…