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…

The authors describe their approach to teaching a course on finite fields and combinatorial applications, including block designs and error-correcting codes, using a hybrid of lectures and active learning. Under the discussed classroom model, there are two lecture days and two discovery-based discussion days each week. Discussions center around…

GeoGebra is the most well-known Dynamic Geometry Application (DGA) in the world. Many researchers are interested in GeoGebra as a tool to make interactive mathematics resources. Here we focus on a snapping function in GeoGebra, which is a kind of general feature of DGA: the mouse cursor is attracted to a specific position or a specific object and…

Integration of history of mathematics (HOM) in mathematics education is emerging as frontier endowed with utility to stem decline in uptake, enhance performance and alter the negative perceptions about the subject. This case study sought to explore the influence of history of mathematics on grade eleven girls' perceptions of the Theorem of…

Planning a mathematics lesson plan is a complex process. Its quality contributes to the effectiveness of mathematics instruction. Given this significance, improving prospective mathematics teachers' lesson planning ability is essential for teacher preparation programs to produce effective teachers. This study examines how a lesson study within a…

Motivation and math anxiety are crucial in performance and satisfaction, and augmented reality (AR) may be a useful tool in enhancing these factors because it provides users with interesting visual experiences. Since related empirical research is limited in investigating the effects of using free mobile AR apps integrating Keller's ARCS…

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…

This study aimed to improve the van Hiele levels of geometric understanding, proof-construction performance and beliefs about proofs of the research respondents: future mathematics teachers exposed to the traditional (instructor-based) method and the enhanced-group Moore method. By using the quasi-experimental method of research, the study…

This article presents an instructional approach to constructing discovery-oriented activities. The cornerstone of the approach is a systematically asked question "If a mathematical statement under consideration is plausible, but wrong anyway, how can one fix it?" or, in brief, "If not, what yes?" The approach is illustrated with examples from…

"Principles and Standards for School Mathematics" (NCTM 2000) proposes that mathematics instruction provide opportunities for students to engage in mathematical inquiry and in meaning-making through discourse. Mathematics teachers are encouraged to build on student discoveries in designing subsequent instruction. In this article, the author…

The path taken and the turns made as a turtle traces a polygon are examined to discover an important theorem in geometry. A unique tool, the Angle Adder, is implemented in the investigation. (Contains 9 figures.)

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)

Presents a question designed to launch a discovery journey through conjecture, research, serendipitous encounters, proof, answers, and new questions. Reports some discoveries and suggests ways in which to incorporate this strategy into classrooms. Presents a geometry project that incorporates this problem-solving approach to mathematics. (JRH)

An approach is presented that is based on modifying the standard axiomatic system found in high school geometry books. Such changes start with the introduction of a side-angle-side (SAS) postulate for similar triangles. It is shown how the new system can prove existence and uniqueness of parallel lines. (MP)

Several methods of numerical mappings other than the usual cartesian coordinate system are considered. Some examples using parallel axes representation, which are seen to lead to aesthetically pleasing or interesting configurations, are presented. Exercises with alternative representations can stimulate pupil imagination and exploration in…