This study aimed to reveal the effects of teaching with concrete learning objects taken from the history of mathematics on student achievement. Being a quasi-experimental study, it was conducted with two grade 8 classes in a secondary school located in Trabzon. The experimental group consisted of 27 students and the control group consisted of 25.…

To understand learners' appropriation of technological tools and geometrical understanding, we draw on the theory of instrumental genesis (Lonchamp, 2012; Rabardel & Beguin, 2005), which seeks to explain how learners accomplish tasks interacting with tools. To appropriate a tool, learners develop their own knowledge of how to use it, which…

The purpose of this study was to investigate the effects of using dynamic geometry software on preservice mathematics teachers' spatial visualization skills and to determine whether spatial visualization skills can be a predictor of success in learning analytic geometry of space. The study used a quasi-experimental design with a control group.…

Between 2003 and 2013, the proportion of California 8th graders enrolled in Algebra or a more advanced course nearly doubled to 65 percent. In this paper, we consider the organizational processes that accompanied this curricular intensification. Facing a complex set of accountability, institutional, technical/functional, and internal political…

In this article, we introduce Sfard's discursive framework and use it to investigate prospective teachers' geometric discourse in the context of quadrilaterals. In particular, we focus on describing and analysing two participants' use of mathematical words and substantiation routines related to parallelograms and their properties at van Hiele…

Since the introduction of the Common Core State Standards for Mathematics (CCSSM) in 2010, stakeholders in adopting states have engaged in a variety of activities to understand CCSSM standards and transition from previous state standards. These efforts include research, professional development, assessment and modification of curriculum resources,…

This qualitative study examined middle school students' performance, solution strategies, difficulties and the underlying reasons for their difficulties in calculating the volume of a rectangular prism. The data was collected from 35 middle school students (6th, 7th and 8th grade students) enrolled in a private school in Istanbul, Turkey. The data…

Geometry students need challenges. They need to apply what they already know to new contexts. As a result, high school teacher Wayne Nirode is always looking for groups of related problems of theorems to challenge his geometry students. He came across one such group or problems when reading Jun's (2012) one-page abstract posted online for the 12th…

Seeking the right level of help at the right time can support learning. However, in the context of online problem-solving environments, it is still not entirely clear which help-seeking strategies are desired. We use fine-grained data from 38 high school students who worked with the Geometry Cognitive Tutor for 2 months to better understand the…

This study is about student teachers' conceptual understanding of shapes. While the National Curriculum Statement stipulates that by the time learners exit high school they should have grounded knowledge of basic geometry and know shapes such as polygons and polyhedrons and their properties, this study finds that the majority of student teachers…

We report on the development and piloting of a method that provides a sufficient condition for confirming that an observed regularity in a classroom is a norm. The method we describe is a refinement of the breaching experiment technique (Garfinkel, 1963; Mehan, 1979) that uses random assignment to experimental conditions as a means to facilitate…

We present a case study that has been developed to inform about the teaching activity of a secondary mathematics teacher in a whole group discussion and the mathematical learning opportunities generated for the students in this classroom context. For data of one lesson we determine the episodes that shape the whole group discussion. For each…

Patterns are commonly used in middle years mathematics classrooms to teach students about functions and modelling with tables, graphs, and equations. Grade 6 students are expected to, "continue and create sequences involving whole numbers, fractions and decimals," and "describe the rule used to create the sequence." (Australian…

In this article Leicha Bragg introduces an open-ended assessment task that gives students the opportunity to access skills and knowledge from the Measurement and Geometry strand. Students take on the roles of cartographer and map user to "hide, map and seek."

Although high school geometry could be a meaningful course in exploring, reasoning, proving, and communicating, it often lacks authentic proof and has become just another course in algebra. This article examines why geometry is important to learn and provides an outline of what that learning experience should be.