A bit about me

Go Bruins (and Grizzlies)!

It is a pleasure to be teaching mathematics at Gardiner. I am a graduate from The University of Montana and was born and raised in The Northwoods of Wisconsin. I have two passions, the first being almost everything out of doors. Second, and a very close second, is learning, especially reading and studying mathematics. Indeed, my most cherished possessions are my backpacking gear and my library. The history of mathematics is messy and fraught with mistakes and disagreements. As such, making mistakes and having the freedom to navigate situations is integral to learning.

“Making mistakes is what is expected in order to learn, being wrong about math isn't wrong, but actually right only if we correct it.” Dr. David Erickson

Forget the mistaken idea that an answer in math is simply right or wrong. We are to learn to think mathematically and concentrate on the process.

“It is the story that matters not just the ending.” Paul Lockhart.

Tuesday, December 12, 2017

When we study the interactions of events, we sometimes run into places where our intuition fails us. This is especially fertile ground, albeit sometimes uncomfortable. When we have mathematical models in place, we are asked to trust the math. To the extent that we are able to take this leap, our understanding grows and the previously counterintuitive becomes obvious.

Dr. Jones and the physics class recently ran into such a situation while studying the mechanics of dynamic motion. The context was an object being pushed across a flat surface in such a way that the object moves with a constant velocity. Noting that constant velocity implies an acceleration of zero and applying Newton's Second Law of Motion, we reach the conclusion that the net force on the object in this direction of constant velocity is zero. For many of us, however, this is counterintuitive. How, our rational minds insist, can the net force be zero when the object is moving? Once we take the aforementioned leap of trusting the math, this fact becomes a more palatable. Indeed, after sitting with the idea for a while, it becomes obvious. The frictional force between the object and the surface is exactly counterbalanced by the force pulling or pushing the object. The net force is zero and the object is not slowing down or speeding up. 

Another example that lies somewhat comfortably in the zone of proximal development of high school mathematics students is the Monty Hall Problem. In his game show, Let's Make a Deal, Monty had three doors. Behind one of the doors was a desirable prize, behind each of the two others, a goat. The contestant would choose a door. Monty would then have one of the doors with a goat behind it opened. The contestant was then asked whether they wanted to stick with their original choice or switch to the other unopened door. The door of the contestant's choosing was opened revealing their choice. The question is what is the best strategy. Should one stay with the original choice or switch? Does it even matter? The answer is counterintuitive to many. Indeed, the mathematician Paul Erdos refused to accept the answer as did thousands of viewers. Erdos was ultimately convinced when showed a computer simulation of the game. Gardiner's Python Programmers are investigating this question. We started with writing programs to simulate the game. Then, we will write additional programs to investigate the strategies of sticking with the original choice versus choosing. Once we have the answer, we have the opportunity to align our intuition with our findings. 

In the fast paced world of Secondary Education we need to take advantage of the opportunities to wrestle for prolonged periods with questions that are not easily answered. When the counterintuitive becomes the intuitive, we have truly shown how flexible and inventive our minds can be. We are taught to really examine and consider carefully the evidence and the argument. There is a healthy place for doubt and speculation, even in the confines of our own certainty. It is not so bad, we discover, to admit that we are wrong about something. To learn to marvel at your own growth is a worthwhile endeavor.

Monday, December 4, 2017

Python Programming

The Python Programmers will start meeting on either Monday, December 11 or Tuesday December 12. Stay tuned for details. We welcome people of all ages and experience!

Wednesday, February 15, 2017

The Algebra I class will attempt to offer a answer to the following question:

Is it possible to predict  a person's height given their shoe size?

Stay tuned for them to submit their findings.

Saturday, February 11, 2017

The Python Programmers have recently investigated code that generates the first n terms of the Fibonacci Sequence. The following discovery was also made:

If n is the nth term in the Fibonacci Sequence and n+1 is the nth plus one term, Then as n goes to infinity, the ratio of n+1/n converges to the Golden Ratio. We also found that this is the case with the Lucas Sequence.

Under current investigation is the question of what types of numbers must be our first and second term in the sequence for this surprising property to hold. That is, does always hold when the first terms are positive integers? integers in general? rationals? irrationals? transcendentals?

Ask a programmer about these questions, they are exploring some good stuff!