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.…

Discussed are several possible methods of teaching a geometry lesson on angles and arcs. (CT)

The process of investigating some of the properties of diagonals and other geometric concepts with a group of 11-year-old girls is presented. Possible changes that could have been made in the lesson are discussed, and examples of individual student work are provided. (MP)

This study was designed to investigate the effects of discovery and expository methods of presentation on the immediate acquisition and retention of geometry concepts by seventh graders. Four geometry concepts, "quadrilateral,""rhombus,""trapezoid," and "parallelogram," were presented in written lessons which used either an expository or a…

To discover a generalization from a pattern of data, students need to know how to analyze the data. This is a description of how high school students can find a formula to predict the number of spherical fruits in a piling by using differences. (JP)

Outlines a guided discovery activity for ascertaining the conditions which allow for the correct tracing of networks. (JP)

Finding patterns in the relationship between the number of sides in a polygon and the total number of diagonals is used as vehicle to discuss discovery learning. (DT)