In my capstone class for future secondary math teachers, I ask my students to come up with ideas for engaging their students with different topics in the secondary mathematics curriculum. In other words, the point of the assignment was not to devise a full-blown lesson plan on this topic. Instead, I asked my students to think about three different ways of getting their students interested in the topic in the first place.
I plan to share some of the best of these ideas on this blog (after asking my students’ permission, of course).
This student submission again comes from my former student Caroline Wick. Her topic, from Geometry: defining the term segment bisector.
How has this topic appeared in high culture (art, classical music, theatre, etc.)?
A segment bisector is a point, segment, line, or plane that divides a line segment into two equal parts, according to the math dictionary “intermath” (A1). This geometric term has been used throughout history to create art, even before the term was eloquently defined. The people of ancient Greece would use all sorts of geometric ideas to build their vast architectural structures and sculptures, and almost all of these structures would require segment bisectors. According to the Metropolitan Museum of Art page on Greek Architecture, “the vertical structure of [their] temple conformed to an order, a fixed arrangement of forms unified by principles of symmetry and harmony” (A2). The Ancient Greeks prided themselves on their beautiful structures that were pleasing to the eyes because of their symmetry and balance.
Take this picture above, for instance. The columns on the right are perfectly symmetrical to the top beam, and the middle column perfectly divides the top beam. It would be considered a Segment bisector.
Other examples of segment bisectors in high art can be seen in renowned artists work like Picasso who used geometry to paint/express the world in a way that one might not normally see, and other painters have used this geometrical interpretation in their works as well.
A. Applications: How could you as a teacher create an activity or project that involves your topic?
Segment bisectors could be used in a number of projects or activities. One activity could be showing the use of segment bisectors in origami, or the art of paper folding. Origami requires multiple strategic folds of paper that must be perfect if the shape is to come to fruition. One often has to fold the paper in half perfectly many times, which is the definition of a segment bisector. Students could learn how to use geometric concepts in a concrete and fun way that is applicable in the real world.
The picture above shows just how much segment bisectors are used in the art of paper folding.
Another project could be using the information above on ancient Greek architecture to create their own little architectural temples or structures. The students would use basic materials found around the house, and their knowledge of geometric definitions to create these structures. Not only would this project apply to geometry, but it would also help students see how geometry plays a role in architecture; another real-world application of school knowledge.
How can technology be used to effectively engage students with this topic?
Segment bisectors do not really sound like the most exciting topic for students to cover. Sure, they can be used in a lot of different applications, but when a student hears that they will be working with the definition of a segment bisector, they likely will not get terribly enthusiastic. However, if students learn these ancient concepts in the context of new technology, it might stick in their brains as a more interesting topic. Geogebra is a website that allows you to construct geometrical shapes and objects as if you were using a ruler and compass. Students could very easily spend hours on the site just finding different ways to construct a geometric shape. They could use the site to create and define multiple geometric concepts, including segment bisectors, so that they discover the words’ meanings for themselves.
The picture above was taken from a youtube video that shows you how to construct perpendicular segment bisectors using a ruler and compass. And though it may seem like it a more advanced subject, students will be able to see the reasoning behind the definition, and might be able to use this website and knowledge for later geometric use.