Geometry students often wonder about the importance of construction techniques. Are they the only way to create geometric figures? What purpose do they serve? How do these techniques relate to other parts of geometry? This article introduces a project used at the high school level that gets all students in a class engaged with construction, gets…

Generating mathematical conjectures is an important mathematical habit of mind for preservice teachers to develop so that they can, in turn, help their students to develop this skill. In this paper we present a classroom episode in which preservice mathematics teachers experience conjecturing in the context of a rich, open-ended task. They also…

Computer simulations have become widely available to support geometric learning; however, the type and amount of guidance, as well as the freedom to engage in self-directed learning that should be allowed for children from differential socio-cultural backgrounds, have not yet been clarified. On the basis of the cognitive theory of multimedia…

The purpose of this article is to better understand how proof is introduced into the study of quadrilaterals and triangles in high school. To do this, we designed a grid to analyse mathematics textbooks in Cameroon francophone subsystems (7th Grade and 8th Grade). The Anthropological Theory of Didactics and the paradigms in geometry served as a…

A common goal for mathematics teachers at any grade level is for "all" students--not just future mathematics teachers--to develop deep understanding of the mathematics they are learning and using. To that end, this lesson can be used in an upper-level high school mathematics course to introduce the concept of a radian in a way that…

The use of concrete objects in a real-life situation is one of the effective ways for teachers to teach and students to explore and learn transformation geometry. The present study, which used a local wisdom or learning context (called Malay woven motif of Kepulauan Riau), focused on developing the reasoning of transformation geometry with…

Every object we think of or encounter, whether a natural or human-made, has a regular or irregular shape. In its own intrinsic conceptual design, it has elements of mathematics, science, engineering, and arts, etc., which are part of the object's geometric shape, form and structure. Geometry is not only an important part of mathematics, but it is…

Proof and proving are important components of school mathematics and have multiple functions in mathematical practice. Among these functions of proof, this paper focuses on the discovery function that refers to invention of a new statement or conjecture by reflecting on or utilizing a constructed proof. Based on two cases in which eighth and ninth…

Two thousand four hundred years ago Socrates gave a remarkable lesson of geometry, perhaps the first detailed record of a pedagogical method in vivo in history [Plato. (2008). "Apologia de Socrates. Menon. Cratilo." Madrid: Alianza Editorial]. Socrates asked Meno's slave 50 questions requiring simple additions or multiplications. At the…

Analogies are known to foster concept learning, whereas discovery learning is effective for transfer. By combining discovery learning and analogies or similarities of concepts, attractive new arrangements emerge, but do they maintain both concept and transfer effects? Unfortunately, there is a lack of data confirming such combined effectiveness.…

The implications of Earth's ocean being little explored may not be immediately evident to individuals who are not ocean literate. For this reason, initiatives to improve ocean literacy must articulate compelling reasons for ocean exploration. A lesson plan that addresses this issue has been developed as part of the education and outreach program…

The author and his first-year algebra students explored the quadratic behavior behind the parabolic shape of fountains at the local family splash park. This hands-on discovery project has three main parts: (1) gathering data by experimenting with and photographing the fountains; (2) analyzing the photographs to obtain numerical data; and (3)…

We describe exercises in which students use PascGaloisJE to formulate conjectures about certain binomial identities which hold when the binomial coefficients are interpreted as elements in the cyclic group Z[subscript p] of integers modulo a prime integer "p". In addition to having an appealing visual component, these exercises are open-ended and…

In the monograph The Math Teacher (following the Third International Scientific Colloquium Mathematics and Children in 2011), the term "teacher" designates a person who teaches mathematics, and the context of each article reveals whether this implies the teacher at a pre-school institution, a school or a university instructor. In…

Children possess a genuine curiosity for exploring the natural world around them. One third grade teacher capitalized on this inherent trait by leading her students on "A Geometric Scavenger Hunt." The four-lesson inquiry investigation described in this article integrates mathematics and science. Among the students' discoveries was the fact that…