The Talking Stick Blog

News, Updates, Program Recaps, and Homeschooling Information

Functions: Crescendoing to Proof

(May 16 and 23, 2017) I thought that this course was about functions. We did a great exploration of them for the first four weeks. But in the last two weeks, something magical happened. Our math circle transcended a single topic to arrive at an exploration of the essence of mathematics, a near-visceral experience of true mathematical thinking. I’m so…

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USING MAPPING DIAGRAMS TO DEFINE FUNCTIONS

(April 18 and 25, 2017) We spent most of our third session creating mapping diagrams, which are a visual way to present and evaluate functions. The students were surprised, after several weeks of numerical function machines, that functions do not have to involve words. They can involve words and more. We mapped students to their drivers, students to their ages,…

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Bill Cipher, Racamán, and Lightning (Functions 1)

(April 18, 2017) The goal of today’s session was to get everyone familiar with what typical functions look like. Over the weeks we’ll be ramping this up. Today, though, was the first session of a six-week “Picnie Math” course on functions designed for students approximately age 10-13. We had a circle of 13 students ages 9-14 picnicking on the grounds…

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Pushin’ Too Hard? (Problem Solving 4 and 5)

(March 30 and April 6, 2017) I’ve had the song “Pushin’ Too Hard” in my head for the past two weeks. Math Circle is to blame. (Or to credit – I like that song!) The students seem to want to really challenge themselves. Especially since they’ve been acknowledging their feelings about problems and said (several weeks ago) that the Balance…

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PROBLEM SOLVING #3: Domains, Ranges, Sheep, and Apples

(March 23, 2017) “What’s that,” asked L, the first student to arrive for math circle. It was a balance scale. I showed him how to calibrate it, then, as the others trickled in, showed everyone how to use it to weigh things. Once our group was assembled, people wanted to get right to work on function machines. A went first,…

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PROBLEM SOLVING #2: Progress on the Ogre Problem

(March 9, 2017) “The math circle teacher is here!” announced S to the other students who were playing outside, as I walked onto the Talking Stick grounds. I was early, but before I even had my bag open and the whiteboards set up in the classroom, everyone was sitting on the floor waiting to start. So we started. Immediately everyone…

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PROBLEM SOLVING #1: A New Group of Students

March 2, 2017 As I prepare for today’s math circle, I realize that I am in a privileged position of utmost responsibility: only one person in this group of six has ever been to a math circle before. For years, the majority of students in our circles have participated for years. I hope I am up to the task. FUNCTION…

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FERMAT 3 and 4: Proofs Proofs and Proofs

WHAT IS THE MOST IMPORTANT NUMBER IN THE WORLD? The students came up with a list that includes just about everything that mathematicians say is important. (Non-mathematicians have a completely different list, though!) What would a mathematician say is the most important type of number in the world? This was tougher. Lots of conjectures. I finally used some leading questions…

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Fermat 1 and 2: From Trial and Error into Proof

(October 31 and November 7, 2016) “What are the greatest human accomplishments in history?” I asked at session one of our teen math circle. The students generated a list on the board. “What made them great accomplishments?” I asked. The students gave reasons for the greatness of each accomplishment listed. We did the same for a narrower version of the…

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Rational Tangles Weeks 3 and 4

WEEK THREE Voting on How to Proceed with Conjectures: R wasn’t here last week, so the students did a brief recap for her of what we did last time, which was testing their conjectures for which mathematical operation the move “Rotate” represented. “I’ve been thinking about the rotate thing, and maybe it’s multiple operations, not just one thing,” M mused….

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