Because my post last week delved into this topic in the beginning the first paragraph is mostly a restatement from last week.
I am teaching the last section of math 3, which is the name for 8th grade pre-algebra at Thurston Middle School. This is largely an introductory unit for the students so much of the content is laden with tough vocabulary that becomes easily muddled due to all of the minute differences between key terms. Ironically some of these terms came up in my math methods course last week, and 6 graduate students preparing to be math teachers had trouble recalling definitions of specific terms. From my personal experience I think this is largely due to a vocabulary list approach to this content. These lists were mostly disconnected with their physical meanings for me and so they didn’t stick past whatever test I had to take. As an educator I view the real purpose of learning these terms as a way of identifying like angles in order to answer geometric questions without needing to measure angles, which is often unavailable anyway. The vocab meanings are much more important than their sometimes confusing words. My lessons will be packed with images to and examples to show the relationship with much less stress on the terms. If a student can explain why two angles are equal in measure, but can’t remember that we call them corresponding angles I feel that the goal has still been accomplished.
The two competing ideas on how to teach this content that I know of are the vocabulary list memorization approach and then the more conceptually focused approach. I find the conceptual focus much more valuable as I explained above. It is also my opinion that if students begin to really understand these relationships now, then the names of such relationships are more likely to stick when they see them again later. By asking students to simply drill and recite the vocabulary meanings now doesn’t allow for them to actually attach the words to anything meaningful. My approach will hopefully give students a stronger foundation of knowledge to attach names to in the future. I also feel that math, especially units like this, are extremely valuable in developing strong reasoning skills. Math can be used to help students view the world in a more analytical and logical way, much like critical thinking is often stressed in history classes. Memorization largely takes away this component in a math curriculum, so it is my goal to help students further develop this way of viewing their surroundings.
One of the most important applications of this content is in design or drafting. I really like the idea of having students design a new school or community center. This connects well to technology if design software is available for students to use. It would also make an ideal final project based assessment for this unit. Students could be responsible for different sections of the building and be required to identify important angle relationships used in the design process. I would try and bring in a guest speaker who works in a related field to give students a chance to see someone using these skills in their career. On top of the technology connection inherent in creating the project students could give a presentation on their work, which brings in oral and written communication. I think tasks where students are asked to explain their thinking is important to enriching their understanding of the content, especially since later on in math being able to explain your thought process is the most important skill.
Another potential project or activity I could do in relation to their history class. Depending on their current unit it would be easy to take architecture or art from the civilization they are studying and analyzing its angle relationships. Egypt, for instance would be extremely interesting because I know enough about their geometric tools to make an interesting history/math lesson about how Egyptians formed angles in their architecture. I designed a project for Tech 2 in which students had to take images from the internet and analyze the angles as well as present their findings to the class. To connect it to history I could have students find pictures relating to their current unit. A project like this would be extremely useful in showing students how important mathematical concepts have been throughout history, as well as giving them further insight into the amazing accomplishments of the people they are studying.