What is Rational About an Exponent?

I have been helping a friend paint his house this week so I have not been able to write as much content for my new website as I had hoped. However, I was able to work on an article about a method of introducing rational exponents. It is not complete, nor completely edited (my editor a.k.a my wife, has been working insane hours this week) but it will give you an idea about the content I hope to create. Let me know what you think.

Associate With Me?

Eventually, I hope my math teaching website will include a comment section so I can get feed back from teachers on how they teach each topic. Unfortunately, that involves a much more dynamic type of website construction than I am currently employing. Luckily, I am helping a friend paint his house this week and he happens to do web design as a career so I should be able to pull it off eventually. For now, however, I am going to use this blog to get some feedback on different topics.

Todays topic is: Associative and Commutative Properties

I am interested in your thoughts on how you teach students about these properties. Obviously, the properties themselves are pretty simple to illustrate, but is it important to make students name the illustrations or is it more important for them to just understand the properties but not know their names?

The Latest Project

As I have talked about before, this past year I began creating single page websites called "lenses". One of the features of Squidoo, the website where I created these, is that it has a stats page. On this stats page I can see every word/phrase typed into a search engine that is used to find my site. From looking at these search terms I came to find out that a lot of teachers were finding my websites looking for resources and ideas on how to teach a topic. This has led me to create a new website designed for teachers. If you visit this website right now you will see that it is far from complete. I am daily adding resources and contributing to the discussions on the different topics. My goal is to finish Algebra 1 by the end of the summer.

Please take a look at the site and let me know what you think. Thanks.

http://www.how2teachmath.com

The Slope of My Life

As a line changes over time so has my life recently. For various reasons that I may blog about in the future, I began looking for a new job in April of this year. I found three schools that I was very interested in and were very interested in me. They were the Sycamore School, Herron School and the International School of Indiana. I was excited about all three schools and believe each would have been a very good place to work.

While in middle school I competed in a great math program called MATHCOUNTS. As an 8th grader I was fortunate enough to finish 3rd at the state competition. This allowed me to compete for Indiana at the national competition. The coach of that team was a teacher from Terre Haute named Bob Fischer. From that trip and other experiences with MATHCOUNTS I have a tremendous amount of respect for him as a coach. This is relevant because the job at Sycamore gave me the opportunity to assist him in coaching their MATHCOUNTS team. While at Franklin I found out I really enjoyed coaching academic teams, so the opportunity to work with someone with his experience and record was very appealing to me.

Thus, with this in mind, as well as other considerations I have accepted a position at Sycamore School in Indianapolis. There are some huge changes for me as this will be a middle school position (though I will be teaching Geometry and Algebra 2) and it is a private school. My other two jobs have been at public high schools. As well Sycamore is considered a "gifted and talented" school. This will also be a big change for me because I have always taught regular/low level classes. This is the change I am most comfortable with because I have always desired to teach high level classes.

I decided this year to break my summer into two parts. The first part was reliving my glory years on the golf course by preparing for and then competing in the Indiana State Amateur Tournament. It went very well as I made the cut(top 60 out of about 500 that attempt to qualify), made a hole-in-one and finished 51st. Unfortunately, I played very poorly in the 4th round or I would have finished even higher. The second part of my summer is going to be focused on creating online math resources. This past semester I worked on creating Squidoo pages on Algebra 1 topics(See top right corner). I am going to continue that work, but I am also creating a website more geared for teachers. I will post more on that tomorrow.

How Do You Factor That?

I recently finished another squidoo lens on working with polynomials. One of the goals of the lens is to teach students how to factor quadratic expressions. I was taught the guess and check method to factor quadratics and have always held the belief this was the best method to factor quadratic expressions. One of my fundamental theories on math education is the importance of teaching the why along with the how. The guess and check method may not always be the easiest "how" but I have always thought it was the best "why".

I will confess I have not worked much with the other more algorithmic methods of factoring quadratic expressions. If you teach/use this method, I would love to hear why you think it is the best way to teach the concept?

What Math Should I Teach?

I have recently finished two more Squidoo pages on Quadratic Equations and Square Roots. Both of these, as have the others lenses linked to the right, force me to face the question "What Math Should I Teach?" In my mind, the Squidoo pages and the acccompanying videos I have created are designed for a regular 8th grade/freshman Algebra 1 class. But as I have learned from teaching those classes the curriculum can vary widely from class to class, school to school and state to state.

Indiana, my home state, has created a list of standards for us to follow. The Algebra 1 standards are the governing list of concepts for me to cover in an Algebra 1 class. And I use them as such. However, even with those as a guide there are many choices to make on the depth and breadth that each topic is covered. For instance, I am currently teaching basic trigonometry concepts to a high school Geometry class. The class is what FCHS refers to as a "lab" class, which means the students background puts them in a category of needing extra help to pass Geometry. Thus I am left to ask the question of how in depth do I teach the concepts to them. The Indiana Geometry standards state:

G5.4 Define and use the trigonometric functions (sine, cosine, tangent, cotangent, cosecant, secant) in terms of angles of right triangles.

G5.5 Know and use the relationship sin2(x)+cos2(x) = 1.

With this in mind I look at the two days it has taken the students to begin to grasp just the basic 3 trigonometric functions and I wonder if I can possibly cover both of those. Especially in light of the fact that I still need to cover quadrilaterals and circles before the end of the year(under 8 weeks left). I have more to say on this, and will at a later time, but I would love to hear any opinions that other teachers have on how they decide what they are going to cover.

Exponent Properties

I recently finished my squidoo lens on exponent properties. I have enjoyed the process of creating these single page sites. It has allowed me to accomplish two important things:


1) The actual building of the site is very simple and easy to do. I had to work a little bit to figure out the html need to create exponents, but overall the process of creating a website on squidoo is pretty painless.


2) Squidoo is well recognized by Google. Within the first week of publishing the exponents lens I am average 15+ visits a day from people searching on google. Considering how specific the topic is that is pretty cool. It is nice to know that people are finding and benefitting from the work I am doing. Yesterday nearly 100 people visited the four lenses I have on squidoo.


The lens I am creating currently is on simplifying square roots. It should be done some time next week.