## Welcome

**SolidAngl.es**! My name is Bill Shillito, and I'm a math educator living in Marietta, Georgia. I've been helping students learn mathematics since 2009, and every day that I teach, I learn as well. I decided to start this site to share what I've learned and my thoughts on how to make math education even better.

## My Philosophy of Teaching

#### Teaching Techniques

There’s a lot of debate these days on the “right” way to teach. Should one be a “sage on the stage” or a “guide on the side”? My answer is “yes!” I spend a lot of time and energy both learning the inner workings of the math my students encounter and investigating better, more intuitive ways to teach and learn it. Lecture, as cringe-worthy as the word is these days, has an important place in teaching. But that doesn’t mean I just stand at the front and talk out of the book. It’s no secret that I get excited about mathematics – my voice and my motions convey the enthusiasm I have for teaching math as well as math itself. And that enthusiasm is often contagious! That being said, at the end of the day, it isn’t about me – it’s about my students, and it’s important that I enable them to take charge of their learning. They engage in productive struggle as they investigate the world of math, and they experience the thrill of discovery as they see why math works the way it does. Of course each student is unique in his or her abilities and learning styles, and I differentiate my instruction accordingly, designing my lessons and activities so that every student has the opportunity to attain understanding and succeed.#### Seeing is Believing

The technology available today provides me with a unique opportunity to make math come alive for my students. Gone are the days when students could only imagine what a given curve or surface might look like. With software like GeoGebra, my students can see it with their own eyes, but even more importantly, we can play with it, explore it, tweak it … really get to know it. Figures are no longer confined to a textbook, but instead gain a life of their own. A trapezoid camouflages itself as a triangle; an ellipse’s focus goes to infinity and comes out the other side; a curved line zooms in until it appears virtually straight. I encourage my students to uncover the relationships between seemingly disparate objects, and in doing so, they create knowledge that is meaningful, knowledge that is their own.#### Solve for “Why”

Give a student a formula, and they can do math. Teach a student where the formula comes from, and they can*understand*math. Never do I teach a topic without delving into exactly why it works. Rote memorization and mnemonic tricks can only get students so far – to excel in mathematics, students need to truly understand the concepts and procedures. I’m not interested in having my students regurgitate the sine of an angle. I’d much rather have them know what the sine of an angle is and be able to visualize the location of that angle – that way, not only are they more likely to correctly compute the value, but they know what it means and can see how it relates to other problems. It’s even more important that students learn to connect the dots, to approach a problem from multiple viewpoints. The distance formula, the absolute value function, the Pythagorean theorem, and the graphs of a circle and of a sphere may seem on the surface like a multitude of things to have to remember, but when students realize that they’re all manifestations of the same concept, each one explains and reinforces the others, ensuring that students never forget any of them.

#### The Faces behind the Formulas

All too often, math is viewed as a collection of expressions and equations, facts and formulas. In my classroom, I emphasize an all-too-often-forgotten element of mathematics – the people who discover and create it. Behind every formula and equation is a story, and no story can be told without its cast of characters. Students don’t just learn to factor polynomials. They feel the excitement when great Italian minds engage in a battle of wits over who can solve the cubic and the quartic first. They feel the pain of a young French romantic who can prove that the quintic can’t be solved with basic operations, yet can’t prove his love to a young woman, dying in a duel at only twenty years old. The friendships and rivalries, the failures and the triumphs … they all show students that mathematics is a human endeavor, pursued by men and women from every part of the world, from the beginning of recorded history to the present day. Maybe one of my students will even write the next chapter in the story.#### Communication is Key

There’s another important point to take away from the human aspect of mathematics – the fact that, since the beginning of recorded history, mathematics has been a social activity. This is a fact that many classrooms seem to have forgotten, as many people equate “math class” with students listening quietly and taking notes while the teacher talks. Real mathematicians don’t do math this way … so why should students? I treat math more like a conversation. My classroom is a place of inquiry and discussion, of conjectures and justifications, of points and counterpoints. Every student brings a different perspective to the table, and I challenge them to share those perspectives for the better understanding of everyone. In an increasingly connected world, the ability to communicate ideas is essential, and so this is a key skill that needs to be emphasized in education.#### What’s the Point of it All?

So everything above has explained*how*I teach mathematics, but the question still may remain …

*why*do I teach mathematics?

- I teach because I love to teach.
- I teach because I love what I teach.
- I teach because mathematics is everywhere.
- I teach because mathematics is more important than ever in our increasingly complex and connected world.
- I teach because I want to inspire my students.
- I teach because I live for that fabled “light-bulb moment.”
- Most importantly, I teach because I believe in my students and do everything I can to prepare them to succeed, not just in my classroom but also in life.