Special tasks for pre-service teachers (PSTs) in university mathematics courses ("interface tasks") are a common innovation in recent years to overcome the second discontinuity. By this, we mean tasks that are situated by typical everyday challenges of mathematics teaching and in which PSTs must use their mathematical knowledge and…

This research aims to investigate the construction of the area of rectangle with GeoGebra and how students can formulate it. It focuses on describing the cognitive process involved in constructing this concept and how technology mediates such a process. The research was conducted in a classroom with 5th grade students in a secondary school and was…

This article presents activities focused on developing some essential Year 1-3 fraction understandings (i.e., joining/composing, decomposing/ partitioning) while aligning these activities to the Australian Curriculum content strands and content descriptions. Additionally, the authors describe the materials/resources needed, the key vocabulary…

This study is an attempt to design and develop as well as validate sets of Online Instructional Materials in Mathematics VI at selected elementary schools in DCS, Manila, specifically, focused on the study of Geometry and Measurement. Using both documentary analysis and descriptive method of study, two (2) major groups of respondents were chosen…

In this study, we examined and compared volume and volume-related lessons in two common core aligned U.S. textbook series and Korean elementary textbooks. Because of the importance of textbooks in the lesson enactment process, examining what textbooks offer to students and teachers is important. Since different parts of a textbook provide…

Guided Mathematical Inquiry (GMI) supports the development of deep understandings about mathematics concepts as students learn to address inquiry questions with evidence-based claims. Developing an evidence-based focus has been shown to be problematic with children. This paper presents how a framework for evidence was developed through the expert…

Thomas Kuhn (1962/2012) introduced the term "paradigm shift" to the scientific literature to describe how knowledge in science develops. The aims of this article are to identify paradigm shifts, or revolutions, that have occurred in mathematics, and to discuss their relevance to teaching mathematics in schools. The authors argue that…

This article aims to describe the mathematical identity of elementary school students during studying mathematics. When studying mathematics, the students often face difficulties in understanding the concepts which results the decrease in their learning motivation. It will lead to the lack of development of their mathematical identity. The…

In this article, the authors present two activities in which students explore angles and related geometric properties in the context of dance, namely ballet. The activities have been successfully implemented in pre-service numeracy classes at Monash University's two-year, post-degree teacher education program (MTeach). Specifically, the activities…

Equality is such an important concept for children to develop. In this article it is argued that a precise definition is needed to ensure that students are provided with a consistent "picture" of what it is that equality really means.

Trying to find quality apps for use in mathematics classes can be time consuming and bewildering. This article outlines a process for evaluating apps and provides teachers with access to comprehensive qualitative evaluations of 53 geometrical apps based on pedagogical, mathematical and cognitive fidelities.

This study addresses the embodied approach of convergence of numerical sequences using the GeoGebra software. We discuss activities that were applied in regular calculus classes, as a part of a research which used a qualitative methodology and aimed to identify contributions of the development of activities based on the embodiment of concepts,…

Measurement is an important component of K-grade 12 mathematics curricula. The concepts of area and perimeter of polygons are first introduced in third grade and serve as the basis for teaching in the upper grades. Without a strong understanding of measurement, students will struggle to meaningfully grasp three-dimensional measurement concepts…

Students in this era need to grasp the concept of geometry instead of memorizing formulae. This is important for them to further their knowledge in geometry. The purpose of the research was to determine whether GeoGebra software influences year one students' performance in geometrical reflection. The research utilized an experimental research…

Helping students develop their ability to use the mathematical practices relies on their awareness of and ability to share their thinking to be used as part of classroom instruction. This type of instruction tends to be different from most teachers mathematics learning experiences thus requiring teachers to rethink what it means to teach…