Thursday, July 25, 2013 Immersion Resources
Thursday's Schedule | |
File Size: | 87 kb |
File Type: |
Session A: Rational Tangles with Bob and Katie.
Rational Tangles was a dance with three simple moves. This activity involved seeing the world with mathematics and then using that mathematics to predict and make sense of what we were seeing. Some of the leaps were tough, but we untangled them in good time. This work was started by one of the most intriguing living mathematicians, John Conway.
Ambitious Circlers and students who like puzzles might want to investigate John Conway and his puzzles (PDF). Another good source for interesting puzzles? The work of the late Martin Gardner. His mathematical puzzles, many posted in the Scientific American over three decades, are a good resource for teachers who want places to go to find challenging problems. Many of his puzzles are published in inexpensive books by Dover Press.
You can see Tom Davis lead the Tangles activity here. Excellent Middle School Mathematics Teacher, Fawn Nguyen wrote about using this with middle grades students here (highly HIGHLY recommend this read!). You can read papers on Tangles here (PDF from James Tanton) and here (Tom Davis PDF).
We only scratched the surface! But the work we did is related to an important topic of mathematics called Knot Theory. "Important?" you say? It's helping to unravel the mysteries of human DNA among many other things and it begins with a pervasive theme in mathematics at all levels: "How do we classify things that are the same in one way or another?"
Rational Tangles was a dance with three simple moves. This activity involved seeing the world with mathematics and then using that mathematics to predict and make sense of what we were seeing. Some of the leaps were tough, but we untangled them in good time. This work was started by one of the most intriguing living mathematicians, John Conway.
Ambitious Circlers and students who like puzzles might want to investigate John Conway and his puzzles (PDF). Another good source for interesting puzzles? The work of the late Martin Gardner. His mathematical puzzles, many posted in the Scientific American over three decades, are a good resource for teachers who want places to go to find challenging problems. Many of his puzzles are published in inexpensive books by Dover Press.
You can see Tom Davis lead the Tangles activity here. Excellent Middle School Mathematics Teacher, Fawn Nguyen wrote about using this with middle grades students here (highly HIGHLY recommend this read!). You can read papers on Tangles here (PDF from James Tanton) and here (Tom Davis PDF).
We only scratched the surface! But the work we did is related to an important topic of mathematics called Knot Theory. "Important?" you say? It's helping to unravel the mysteries of human DNA among many other things and it begins with a pervasive theme in mathematics at all levels: "How do we classify things that are the same in one way or another?"
Session B: Pencilcosa with Bob and thanks to Chaim Goodman-Strauss of Mathbun.
We took a brain break to build a pencilcosa, designed by Chaim Goodman-Strauss, Chair of University of Arkansas Math Department. But this was what Sherry Turkle called "Evocative Objects: Things we Think With." While we were building our dodecahedron, we were thinking (subconsciously or consciously) about number of faces, pencils, rubber bands, intersections, how it holds together, pentagons, etc.. These pencils were drawing connections. Hey! wasn't that one of the Standards for Mathematical Practice? So was persisting in the face of a challenge, as we discovered!
The pencilcosa template is below.
We took a brain break to build a pencilcosa, designed by Chaim Goodman-Strauss, Chair of University of Arkansas Math Department. But this was what Sherry Turkle called "Evocative Objects: Things we Think With." While we were building our dodecahedron, we were thinking (subconsciously or consciously) about number of faces, pencils, rubber bands, intersections, how it holds together, pentagons, etc.. These pencils were drawing connections. Hey! wasn't that one of the Standards for Mathematical Practice? So was persisting in the face of a challenge, as we discovered!
The pencilcosa template is below.
Pencilcosa Template | |
File Size: | 823 kb |
File Type: |
Session C: Exploding Dots with Daniel Showalter.
Dan shared with us a discovery of the wonderful James Tanton. James found out that his machines that exploded dots could help us to understand the algorithms we use in arithmetic AND in algebra (cool connection!). Moreover, these machines allowed us to do this in bases other than base 10 with relative ease. James Tanton's videos, books, and twitter feed are a great resource for thinking not only about GOOD Problems, but also for thinking about GOOD approaches. His work on exploding dots can be found in the following PDFs: Instructor's Notes, and Student Notes.
Dan shared with us a discovery of the wonderful James Tanton. James found out that his machines that exploded dots could help us to understand the algorithms we use in arithmetic AND in algebra (cool connection!). Moreover, these machines allowed us to do this in bases other than base 10 with relative ease. James Tanton's videos, books, and twitter feed are a great resource for thinking not only about GOOD Problems, but also for thinking about GOOD approaches. His work on exploding dots can be found in the following PDFs: Instructor's Notes, and Student Notes.
Session D: Closing paperwork and the LMT
Thanks to all through suffering so graciously through our evaluation and research. You are contributing to something great and helping not only to build a community of problem solvers, but a body of research that should help us determine if what we're doing is having good effects. That, in turn, may help us to win more grants to keep doing this work.
Thanks to all through suffering so graciously through our evaluation and research. You are contributing to something great and helping not only to build a community of problem solvers, but a body of research that should help us determine if what we're doing is having good effects. That, in turn, may help us to win more grants to keep doing this work.
Want to add something? New results? Further thoughts? Did you try some of this in a classroom? Let us know so we can share. Email us at [email protected].