Education

The Rubik’s Cube and task completion

Part of my shtick as a Geometry teacher is the Rubik’s Cube. I have a 3^3 and a 5^3 in my room; I’d had a Void as well, but it’s wandered off (perhaps due to my own doing). The students…

Education

The Six Basic Trigonometric Functions

I read an article today on the six basic trigonometric functions, and I thought there was a particularly important insight that I wanted to present in my own words. When I was in school, we learned the six basic trigonometric…

Modeling in GeoGebra

Introduction In this entry, I’m going to demonstrate the use of GeoGebra to estimate a value for a fairly tricky trigonometry problem, then illustrate how to find the value using trigonometry and an appeal to WolframAlpha. In so doing, I…

Intersecting Secants

In this entry, I’m going to be discussing how mathematicians tend to approach the world, and why we need better PR. I’m currently teaching High School Geometry. Here is what the book has to say about the “Segment of Chords…

Numerators and denominators

I remember as a child studying fractions, being told that the top was called the numerator and that the bottom was called the denominator, for reasons that were not made clear to me at the time. In retrospect, it’s possible…

Just forget my Dear Aunt Sally

The purpose of a mnemonic is to make something easier to remember. Roy G. Biv represents the major colors of the spectrum (Red, Orange, Yellow, Green, Blue, Indigo, Violet); it has the weakness that most people tend to think of…

Listening to students (reflection)

One of the greatest benefits to my current teaching position is its small class sizes, which affords me a significant amount of one-on-one tutorial time. I know fairly well how I think about numbers; I don’t know how other people,…

=

When I was a lad studying mathematics, the equality sign seemed particularly simple: The stuff on the left is equal to the stuff on the right. However, I have since been developing a much more sophisticated perception of the simple…

Expressions as Names

One basic concept in mathematics that I see students struggle with, and with which I struggled myself, is the notion of expressions. However, when we remove the mathematical component, we can see that expressions behave much like a concept that…

PEMDAS and negative numbers

By standard mathematical convention, $$-1^2=-1$$. At the same time, students are taught to refer to $$-1$$ as a negative number. A friend recently led me to realize that these two conventions are at logical odds with each other, as discussed…

Well… is algebra necessary?

Except for the final grades, I’ve just wrapped up teaching six weeks of credit recovery for Freshman Algebra. It’s tough enough packing nine months’ of material into six weeks, but consider these are the students who didn’t do well enough…

Introduction and purpose

As of this summer, the summer of 2012, I am qualified to teach mathematics at the high school level in the state of Michigan. I am expecting to be doing so full-time this fall. I am also qualified to teach English,…