Thursday, October 7, 2010
Thursday, August 5, 2010
Friday, December 11, 2009
Sunday, November 22, 2009
Proposed Math Project
Counting Systems Through the Ages!
Grade Level:
8-10
Purpose:
To gain a more thorough understanding of number systems.
Activities:
1. Research a counting system that we don’t use in class.
2. Create a poster showcasing their research.
3. Compare and contrast the researched number system with our modern system.
4. Write a word problem with this number system.
5. Present findings to class.
Sources:
1. A nice website on ethnomathematics: http://www.tacomacc.edu/home/jkellerm/Ethnomath/
2. A website on Egyptian numbers:
http://www.eyelid.co.uk/numbers.htm
Time:
Two class periods where many resources will be made available. Students would spend approximately two hours outside of class working on this project.
Marking:
60% for content (shows understanding of number system and its relationship to modern counting systems, evidence of research, word problem), 20% poster aesthetic (well organized, information is displayed clearly and creatively), 20% for in class presentation (showmanship).
Grade Level:
8-10
Purpose:
To gain a more thorough understanding of number systems.
Activities:
1. Research a counting system that we don’t use in class.
2. Create a poster showcasing their research.
3. Compare and contrast the researched number system with our modern system.
4. Write a word problem with this number system.
5. Present findings to class.
Sources:
1. A nice website on ethnomathematics: http://www.tacomacc.edu/home/jkellerm/Ethnomath/
2. A website on Egyptian numbers:
http://www.eyelid.co.uk/numbers.htm
Time:
Two class periods where many resources will be made available. Students would spend approximately two hours outside of class working on this project.
Marking:
60% for content (shows understanding of number system and its relationship to modern counting systems, evidence of research, word problem), 20% poster aesthetic (well organized, information is displayed clearly and creatively), 20% for in class presentation (showmanship).
Project: Recreational Mathematics
Martin Gardner
Martin Gardner was born on October 21, 1914. A prolific writer, Gardner has published 70 books to date on topics including: recreational mathematics (our interest here), pseudoscience, magic, philosophy, literature, and even a couple works of fiction. His most recent work of fiction is a story about Oz involving Klein bottles. Gardner is most fondly remembered for his column Mathematical Games, which ran in Scientific American for 25 years.
Gardner has no formal mathematics training outside of high school and even had a hard time passing his high school calculus course. His background is in philosophy, which he studied at The University of Chicago. When asked what he likes about mathematics Gardner responded: “There is a strong feeling of pleasure, hard to describe, in thinking through an elegant proof, and even greater pleasure in discovering a proof not previously known.”
After serving as a yeoman in World War II he became a contributor to Esquire magazine. His first submission was a short story entitled “The Horse on the Escalator.” From Esquire he became assistant editor of the children’s magazine Humpty Dumpty (Humpty was the head editor). After submitting a piece on flexagons to Scientific American in 1956 he was asked to head a monthly column focusing on recreational mathematics.
Gardner claims that the number of puzzles that he has invented could be counted on one hand. He could often be found scouring Manhattan bookstores for books of recreational mathematics that he would use for inspiration. Gardner believes that his column was so successful because of his lack of experience. While writing the column he would also be solving the problem for the first time.
In 1981 Gardner retired from Scientific American to focus on his other passions, mainly debunking pseudoscience. Gardner inspired many a future mathematician with his column which lives on in various collections that have been published since his retirement.
Martin Gardner was born on October 21, 1914. A prolific writer, Gardner has published 70 books to date on topics including: recreational mathematics (our interest here), pseudoscience, magic, philosophy, literature, and even a couple works of fiction. His most recent work of fiction is a story about Oz involving Klein bottles. Gardner is most fondly remembered for his column Mathematical Games, which ran in Scientific American for 25 years.
Gardner has no formal mathematics training outside of high school and even had a hard time passing his high school calculus course. His background is in philosophy, which he studied at The University of Chicago. When asked what he likes about mathematics Gardner responded: “There is a strong feeling of pleasure, hard to describe, in thinking through an elegant proof, and even greater pleasure in discovering a proof not previously known.”
After serving as a yeoman in World War II he became a contributor to Esquire magazine. His first submission was a short story entitled “The Horse on the Escalator.” From Esquire he became assistant editor of the children’s magazine Humpty Dumpty (Humpty was the head editor). After submitting a piece on flexagons to Scientific American in 1956 he was asked to head a monthly column focusing on recreational mathematics.
Gardner claims that the number of puzzles that he has invented could be counted on one hand. He could often be found scouring Manhattan bookstores for books of recreational mathematics that he would use for inspiration. Gardner believes that his column was so successful because of his lack of experience. While writing the column he would also be solving the problem for the first time.
In 1981 Gardner retired from Scientific American to focus on his other passions, mainly debunking pseudoscience. Gardner inspired many a future mathematician with his column which lives on in various collections that have been published since his retirement.
The problem will be presented in class.
Thoughts on the project:
This project is a good way to show students that math problems exist in popular culture and can be done just for the fun of it. It’s also a chance for students to pick a problem of their own choosing that will hopefully be a fun challenge for them and not just another problem where they aren’t interested in the answer (except that it’s correct). One of the great things about the problems in Scientific American is that they are phrased in a way where you are actually interested in finding the answer. During class it’s hard to make questions that are interesting for students, and showing them that they can actually find math problems that are “fun” will hopefully improve their opinion of math and willingness to engage in the learning of it. While I was finding the solution to the problem, I wondered how easily I would be able to find the solution if I were still in high school and didn’t have a degree in mathematics. If I assigned this project to students I would worry that the problem they pick might be so hard that they get the impression that math is just something that they will never be able to understand and use fully. On the other hand, picking problems for the students doesn’t allow them to find problems that are interesting to them and takes away a lot of the benefit of the project.
I would most likely use this project as an enrichment assignment to be completed between units, since there is no specific topic that is being used or learned here, it’s simply a general interest project. It would be fun to have everyone present their project, but I don’t know if I would have the time to spend doing in-class presentations. Instead, maybe I would have them create a poster and put the posters up in the classroom. Another thing I could do if I had one class to spare is make this the basis of an in-class math fair where everyone would create a booth and go from group to group trying to solve the other problems.
To put together a math fair I could modify this project so that the end result is a booth rather than a report and poster. If the students were not in grade 12, I could adapt the project so that I choose a number of problems that I know are solvable for their grade level and allow them to choose only from my selection of problems. Another idea would be if I had a grade 12 class and a lower grade class (grade 8-9) I could assign this project to the grade 12’s, have them make a booth with tools to allow anyone to solve the problem and bring the finished projects to my grade 8-9 class for the students to work on. I could make part of my evaluation of the grade 12’s that they present the problem in a way that is understandable and solvable for a grade 8 class.
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