Assignment 3: Analyze a Project Idea and Develop/Extend

Group: Gigi, Paul, Stanley, Erwin

Handouts and Sample Tilings:

Reflection for advantages, disadvantages and modifications from each group member:

Gigi:
Teachers and students will need to know how to separate a line segment into different equal number of parts. I had to look this up in Google but the instructions are not always intuitive. I had to recall how to copy an angle. Not everyone has learned how to copy angels, create a perpendicular bisector to a line.
Another problem we had was with creating the star of David. Students may place the triangle intersections in different spots. Students may have to draw on the copy of the tessellation analyze the different shapes that are used to construct the larger shape. Students may need to draw on the copy of the tessellation to see the symmetry or see how the shape is constructed.

Stanley:
After attempting one tessellation I realized that the concept of 4-fold symmetry is key to the tessellation. What a fantastic way to introduce the concept of symmetry. Can easily expand the project by first asking the relatively intuitive question of whether or not any 2-D object with n-fold symmetry can be used to tessellate the plane(the answer is no when n is infinite, as the only object with infinite number of symmetries is the circle which cannot tessellate the plane). Also with this type of construction it is not so important to enforce 'straight-edge and compass' rules of construction as this type of construction is only 'sacred' because of Greek influence.

Paul:
In terms of evaluating the benefits of this project, I think this project caters to the student's artistic flare and mathematical prowess. The first part (drawing the pattern, describing the pattern in words) appeals to those people inclined towards art, not requiring any math skills (except trying to keep things in proportion). The second part (recreating the repeat shape with straightedge and compass, making minor modifications) caters to the mathematician. It requires visual analysis of the shape to look for patterns that can be recreated using the geometry knowledge that students have thus far. Teaching analytical skills will be helpful not just in math but in so many other areas of life. One weakness of the project is that it could be overwhelming for students who cannot see the pattern that can be recreated with the two simple instruments. Tessellations are covered in the Math 8 IRP. Some of these might be difficult. (I will admit: I got a bit frustrated that I could not recreate the hexagram in the middle.) Of course, this problem could be alleviated by choosing simple tiling patterns for the students. I would not modify this too much, but I would pre-select some not-so-challenging tiling patterns or at least have two sets of patterns (medium and hard). One constraint of using this project in my classroom would be time. I might not know how long to prolong this project or how many class sessions to allocate for in-class work. Overall, I could see this being used in my class to get their creative juices flowing.

Erwin:

I was excited about this project. By mixing art and mathematics this was a nice departure from the regular math problem solving typically done in a class. All throughout the assignment, I was unsure with how far I needed to go if I imagined myself as the student. Some students might scrape only the surface of the project and others may go very deep into much detail. The construction is very mathematical because it doesn't follow the usual math problem. By trying to find an object from basically experiment is more real and connects with the individual. I needed to look back at my geometry math book to remember some simple constructions.

Benefits:
-Gets students that are not particularly excited about math a bit more engaged
-Gets students to apply what they learn to out-of the box problems ike finding minimal parts of tiling
-Assessment of mathematical ability can be made

Disadvantages:
-Students will not achieve the same outcome because the instructions/expectations are not clear enough
-The project may in fact take too long for individuals and it might not be able to be applied to groups of people. The project is based heavily on the discovery of shapes not inpendent steps.
-Harder to evaluate, giving a letter grade on effort of the final presentation.

Modification:
Break up the assignment and assess or evaluate each of the steps. This gives clearer purpose to the assignment and is better for time management of the assignment.