Geometry provides a natural window into what it is like to do mathematics. In the world of geometry, playful experimentation is often more fruitful than following a procedure, and logic plus a few axioms can open new worlds. Nonetheless, teaching a geometry course in a way that combines both rigor and play can be difficult. Many geometry courses…

Research has shown that expert mathematics teachers are more effective than novices eliciting and incorporating students' ideas during review lessons. In this paper, we inquire into students' agency in a review. We ask: (1) "What is the division of labor between the teacher and the students?" (2) "What linguistic resources does an expert teacher…

Previous studies on the effects of virtual and physical manipulatives have failed to consider the impact of prior knowledge on the efficacy of manipulatives. This study focuses on the learning of plane geometry in junior high schools, including the sum of interior angles in polygons, the sum of exterior angles in polygons, and the properties of…

From the early nineties, most reformed curricula at upper secondary level choose to give functions a major position and a priority over rational expressions and equations of traditional algebra. The goal of this paper is to introduce key challenges resulting from this choice and to discuss the contribution that software environments associating…

The availability of sophisticated computer programs such as "Wolfram Alpha" has made many problems found in the secondary mathematics curriculum somewhat obsolete for they can be easily solved by the software. Against this background, an interplay between the power of a modern tool of technology and educational constraints it presents is…

We examined geometric calculation with number tasks used within a unit of geometry instruction in a Taiwanese classroom, identifying the source of each task used in classroom instruction and analyzing the cognitive complexity of each task with respect to 2 distinct features: diagram complexity and problem-solving complexity. We found that…

This dissertation builds on and extends research on the relationship between equity-minded mathematics teaching, specifically teaching mathematics for social justice, complex instruction, and project-based learning, and students' learning and identity development. Although different in their structures and strategies, equity-minded mathematics…

Learning mathematics is a complex and dynamic process. In this paper, the authors adopt a semiotic framework (Yeh & Nason, 2004) and highlight programming as one of the main aspects of the semiosis or meaning-making for the learning of mathematics. During a 10- week teaching experiment, mathematical meaning-making was enriched when primary…

Geometry is a major area of study in middle school mathematics, yet middle school and secondary students have difficulty learning important geometric concepts. This article considers Alexis-Claude Clairaut's approach that emphasizes engaging student curiosity about key ideas and theorems instead of directly teaching theorems before their…

Learning geometry emphasizes the importance of exploring different representations such as virtual manipulatives, written math formulas, and verbal explanations, which help students build math concepts and develop critical thinking. Besides helping individuals construct math knowledge, peer interaction also plays a crucial role in promoting an…

In this article, the author presents the Treasure Island problem and some inquiry activities derived from the problem. Trying to find where pirates buried a treasure leads to a surprising answer, multiple solutions, and a discussion of problem solving. The Treasure Island problem is an example of an inquiry activity that can be implemented in…

The purpose of this classroom note is to provide an example of how a simple origami box can be used to explore important concepts of geometry and calculus. This article describes how an origami box can be folded, then it goes on to describe how its volume and surface area can be calculated. Finally, it describes how the box could be folded to…

This research study examined the effect of origami-based geometry instruction on spatial visualization, geometry achievement, and geometric reasoning of tenth-grade students in Turkey. The sample ("n" = 184) was chosen from a tenth-grade population of a public high school in Turkey. It was a quasi-experimental pretest/posttest design. A…

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…

It is our presupposition that there is still a need for more research about how classroom practices can exploit the use and power of visualization in mathematics education. The aim of this article is to contribute in this direction, investigating how visual representations can structure geometry activity in the classroom and discussing teaching…