Meanwhile, I'm still teaching Elementary Geometry on Saturday mornings. One of the most important aspects of the course is teaching proofs. While there is a subset that will use the geometry itself, there is a larger group that will require training in the type of thinking that these proofs use. Anyone working in the legal field, for example, will need to know how to put together a proof. Yet, the traditional way of writing proofs seems backwards to me.
This is how I typically present on proof on a test:
Notice that the statements are on the left, while the reasons for those statements is on the right. That is backwards to me. Americans read left-to-right, and that puts the statements as something that comes before the reasons when you read a proof. However, the reasons are the connections between that line of the proof and the lines that precede it. Formally, you take the prior information and the reason, put them together using a law of logic or two, and produce the statement.
Of course, the design is traditional. One of my retirement plans is to write a good textbook for teaching Geometry at community colleges (they have good texts for Pre-algebra, Algebra I, and Algebra, but Geometry seems to be confined to high-school texts. In today's world, that would mean creating video segments and an on-line interactive homework system (our college uses MathXL, but they have no Geometry test listed) as well as writing the book with a little less flash and a fewer pictures of kids. When I do, I think I will write the proofs with reasons on the left, and maybe moved up a half-line.
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4 comments:
Okay. I don't know what to do with that. Look. I've come here to discuss with you the God illusion.
While I can't supplant the geometrical insincerity therein I do happen to know that the challenges therein are superfluous in comparison to the video game you dwell over in jest.
Jehovah. Discuss Jehovah. You and I.
Sure, I'm open to that discussion. What did you have in mind?
As always, you get everything wrong. We are human. We believe theories. Proofs are not necessary, and if supplied at all, are always consequential.... dependent exhibits.
In the Bible, JHVH represents the character who visited Adam in the Garden, who told Noah to build the Ark, and who came down the dusty road to dine with Abraham before destroying the cities of the Plain, and who wrote the Ten Commandments.
David thought the Messiah would sit at the right hand of JHVH while waiting for his enemies to be destroyed. Psalm 110:4.
Daniel though Jehovah was Adam, "the Ancient of Days", who would sit to render the final judgment, at which time Jesus would be brought before him and made the Prince of the Kingdom, the heir.
We all got confused when this valid theology got mixed with Greek lore and logic, and somehow came up with the notion that God had to be the First Cause, the originator of OB's Universe, the master of time travel and various other modern magical notions trending to reinforce our individual notions of grandeur.
But no. Adam was brought here from another world a few billion years ahead of us in developing the wondrous phenomena of Life.
babe,
There is no mathematics without proof. That's the nature of a formal system. It has nothing to do with Jehovah/Yahweh/Yehovah or any other deity.
If you want a better understanding of how I see this division, I suggest:
http://lifetheuniverseandonebrow.blogspot.com/2009/09/my-first-hour-in-geometry-class.html
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