The authors use finding the area of irregular shapes as the context for developing flexible strategies for measuring area. This article builds on their paper, "Setting a Design Challenge: Promoting the Discovery of the Relationship between Area and Perimeter" (EJ1272407). As part of Lesson Study research within an initial teacher…

The purpose of this article is to report how Year 6 teachers used geometric reasoning tasks to foster students' mathematical attitudes and dispositions by encouraging communication as students constructed mathematical meaning for themselves. The Year 6 teachers implemented two tasks to provide a rich mathematical assessment opportunity…

The concept of angles is important for future geometric knowledge (Arslan et al., 2016; Moore, 2013; Yigit, 2014). However, although Piaget (1948) suggests angles lead to the discovery of lines, angles are typically taught later in schools, after points, lines, and planes (Charles, 2011). Therefore, the way in which angles are taught can affect…

In this paper, we present opportunities with the uses of origami and technology, in our case GeoGebra, in teaching formal geometric definitions for fifth-grade primary school students (11-12yrs). Applying origami in mathematical lessons is becoming to be recognized as a valuable tool for improving students' mathematical knowledge. In previous…

Guided inquiry pedagogy is gaining recognition for promoting deep learning as students connect concepts, understandings and meanings to defend and justify their mathematical ideas. Research describes how it promotes the development of deep understandings, yet the approach can seem at odds with explicit teaching pedagogies that show potential for a…

In recent years, mathematics classrooms in the U.S. and around the world have seen an increasing integration of educational robotics with interest from both students and teachers. Through their robotics coding activities, students in the present study discovered the concepts of special angle pairs in geometry--namely, complementary and…

Previous research has verified the benefits obtained when learners trace out worked examples with the index finger. Our study conducted two experiments to explore the reasons for this phenomenon and its generalizability. Experiment 1 compared the learning effects among tracing, non-tracing, and cueing methods. The cueing method was included to…

We examine the effects of 3 interventions designed to support Grades 2-5 children's growth in measuring rectangular regions in different ways. We employed the microgenetic method to observe and describe conceptual transitions and investigate how they may have been prompted by the interventions. We compared the interventions with respect to…

This study aims to explore an educational learning environment that supports students to learn conceptual modelling with the unified modelling language (UML). In this study, we call the describing models "UML programming." In this paper, we show an educational UML programming environment for science, technology, engineering, art, and…

Geometry students have few opportunities to apply geometric concepts and solve geometry problems in authentic contexts. We developed a Ubiquitous Geometry (UG) system to teach geometry to elementary students by using it to measure common objects in authentic contexts. The instant study investigates the effects of UG on student geometry estimation…

This study is a quasi-experimental research with pretest-posttest control group design, which aims to determine (1) the tendency of students in using various media scaffolding based on gender, and (2) effect of media scaffolding on increasing understanding of students' geometry concepts. Media scaffolding used this study is chart, props, and…

From random interviews of mathematics teachers, the researchers are conscious that students have difficulties in solving problems regarding compound body volume measurement. The researchers found the main factor involved in the difficulties was incomplete spatial concepts. Augmented reality (AR), which is a kind of educational technology, has been…

It is now well known that fractions are difficult concepts to learn as well as to teach. Teachers usually use circular pies, rectangular shapes and number lines on the paper as teaching tools for fraction instruction. This article contributes to the field by investigating how the widely used three external graphical representations (i.e., circle,…

Pierre M. Van Hiele created five levels of geometric thinking. We decided to identify the level of geometric thinking in the students in Slovenia, aged 9 to 11 years. The majority of students (60.7%) are at the transition between the zero (visual) level and the first (descriptive) level of geometric thinking. Nearly a third (31.7%) of students is…

This case study describes and investigates the instructional practices of Grades 1 to 5 teachers and the levels of geometry thinking of the learners, according to the Van Hiele model, with a view to determining whether there is a match between the instructional practice and the learners' level of thinking. The instructional practices of the…