Conjectures are a key component of mathematical inquiry, a process in which the students raise conjectures, refute or dismiss some of them, and formulate additional ones. Taking a design-based research approach, we formulated a design principle for personal feedback in supporting the iterative process of conjecturing. We empirically explored the…

It is generally agreed that making real-world connections in mathematics teaching increases students' motivation and interest and contributes to meaningful and permanent learning. In this paper we propose a simple and fast activity to find a rectangular hyperbola in real life and we show how to operate the data to retrieve a straight line. Since…

In this study, we designed geometry learning activities so that students could apply newly learned knowledge to solve real-life problems, such as estimating the distance to real objects they find in their local community, measuring objects' length, width, and height, and calculating objects' surface area. Our participating students were divided…

We present the result of an eight-year didactic experiment in two primary school classes involving comparative geometry activities: a comparison between Euclidean plane geometry and spherical geometry that took place over five years. Following the didactic experiment, three years on from the end of the experiment, final questionnaires were…

This paper presents a part of a larger study, in which we asked "How are learning and teaching of mathematics at high level linked to students' general giftedness?" We consider asking questions, especially student-generated questions, as indicators of quality of instructional interactions. In the part of the study presented in this…

The teaching of primary school mathematics is greatly oriented towards the development of basic mathematical literacy and cognitive skills such as remembering, understanding and applying (according to Bloom's revised taxonomy). Nowadays, it is very important to implement teaching methods that are motivating for children and lead to more effective…

Interactive learning technology is an emerging innovation for future communication-aided teaching and learning that could positively enhance students' engagement and intrinsic motivation. Due to the virtue of interactive communication, classrooms are now anticipated to enable a variety of interaction-based learning technologies with diverse…

Mathematics is often portrayed as an "abstract" cerebral subject, beyond the reach of many. In response, research with digital technology has led to innovative design in which mathematics can be experienced much like everyday phenomena. This lecture examines how careful design can "phenomenalise" mathematics and support not only engagement but…

The information and communication technologies of Web 2.0 are arriving in our schools, allowing the design and implementation of new learning environments with great educational potential. This article proposes a pedagogical model based on a new geometry technology-integrated learning environment, called "Geometry 2.0," which was tested…

Social development, the progress of technology, and changing economic forces certainly affect the development of the current educational system. One of the main problems of today's school system is how to maintain focus, concentration, and interest among students with regards to the learning that takes place during classes. An important feature of…

This mixed-method, longitudinal study investigated the benefits of project-based learning (PBL) on secondary-mathematics students' academic skill development and motivated strategies for learning (i.e., cognitive, social, and motivational). The focus of this study was academic skill development (algebra- and geometry-assessment scores) and other…

This monograph offers an overview of the current research work carried out in Croatia and the surrounding countries, and specifically an interesting insight in teaching and learning issues in these countries. The authors discuss the need of the general population for becoming good problem-solvers in society of today, which is characterised by…

This dissertation was conducted in a gendered academy in a low-income community in northern Indiana. The study examined how involvement with inquiry-based mathematical tasks embedded in a curricular unit impacted the geometric reasoning of elementary aged African-American males. The curriculum included activities focused on angles, lines and…

The first goal of this article to show the profound difference between how equality and similarity are understood in Greek geometry and how they are presented in modern mathematics classes. It highlights that the formula "equal-and-similar" reflects the distinct character of "equal" and "similar" as signs in Greek…

It is easy to fall into the trap of thinking that teaching mathematics should greatly differ from teaching language arts. Classroom teachers at Munich International School in Starnberg, Bavaria, Germany, did not pay much attention to what language means to learning and teaching mathematics--until their geometry students offered language surprises…