Graphing Basics

My plan tomorrow is to work on the discussion for graphing linear equations. I am always amazed at how many of my students are able to graph equations one day and then look at me blank faced the next. When I teach students how to graph from the beginning I emphasize its meaning. Thus I think it is appropriate to spend a considerable amount of time having students graph using T-Charts. Other forms of graphing are important for various reasons, but it is very important for students to view a line as a collection of solutions. In my opinion, the best way to accomplish this is to work with T-charts. Eventually, I teach the intercept method and obviously the slope-intercept method, but conceptually I think it is essential that students have a concrete understanding of the relationship between solutions and a graph.

What are some of your best tips for introducing graphs? I will be talking about slope later on, so I am just looking for ideas about how to graph using T-charts.

Google Knol

Google has jumped head first into the content creation business. There new platform is called Google Knol. It is very similar to squidoo, which I have discussed before and is what most of the sites listed at the right were created with. I decided to created a "knol" on euchre to try it out. The process of creating a "knol" is much easier than creating a squidoo. However, there are a lot less options. If you are a teacher looking to publish something for your class, knol would be a pretty easy place to do it. It will be very interesting to see how the knol project goes. Will google rank its own pages better in its search engine? I haven't decided if I will contribute any math content there or not.

30+ and Counting!!!

My math teaching website is coming along nicely. I have added over thirty resources and have begun to write some of the articles. I am very excited about the site and the relationship this blog is playing in its creation. I know two things for certain about it:

1) I have some good ideas about how to teach Algebra 1.

2) I have SOME good ideas about how to teach Algebra 1.

I definitely know that I don't have all the ideas about teaching Algebra 1. Thus I am very thankful for the contributions of some of the readers of this site. I believe collaboration with other math teachers is the best form of professional development and I appreciate those that are engaging in that with me. It is my goal this blog turns into a community of math teachers discussing very practical means of teaching math.

What's the Function of a Function?

While watching a 53 year old golfer winning the Brittish Open I decided to tackle the discussion on functions. I feel pretty comfortable with how to teach about functions. What has me struggling a little bit is the "why". I understand the value of functions, especially as they relate to Physics. As well, I understand the importance of one-to-one and many-to-one concepts in Abstract Algebra and the importance of domain and range. But my question is:

Why is it important to teach an Algebra 1 student if a relation is a function or not?

Any takers?

Should Teachers Avoid Social Networking Sites?

From 2005-2007 I went to Indiana University as a full-time math graduate student. In the timeline of my life this was 3 years after graduating from the University of Evansville. Thus, I essentially missed out on the Facebook revolution that took over college campuses. However, the majority of my classmates at IU were fresh out of college and were all on Facebook. Accordingl they coerced me into setting me up with an account. During grad school I pretty well ignored it except to use it as a means to identify students that I tutored at IU.

Fast forward to the last two weeks. I figure if I am going to create these resources I might as well try to market them to as many people as possible. Through my research on how to internet market, I was told sites like MySpace and Facebook were usually reccomended as one option. Thus I dove into Facebook and have been an active user the last two weeks. I am very glad I did because I have reconnected with an old college roomate and a friend from Brazil who studied at UE for a semester. Her whole family was at UE that semester and they were some of my favorite people I met at Evansville.

The question I have is what is the appropriate behavior of a teacher on these sites? I am of the inclinationt that I would not accept "friend requests" from students that are currently at my school and would definitely be careful what is posted on my page. It is an interesting question and one that more and more new teachers and schools are going to have to deal with...Let me know what you think.

And and Or

The latest article I have been writing for my website deals with combined inequalities(or compound inequalities). One of the difficulties in teaching this topic is helping students understand conceptually the difference between "and" and "or". I try to accomplish this by developing real world examples. For example I give them the statements such as:

"The sky is blue and the grass is green."

"Peyton Manning is a Colt and a running back."

"Barrack Obama is running for president or he is a math teacher."

I then ask them which of the following are true and why. The goal is to get the students to understand that both statements must be true for an "and" inequality to be true. And that at least one must be true for the "or" inequality to be true.

What are other ways to help students understand combined inequalities?

What Does It Mean to Be Equal?

I am currently working on the Algebra 1 standard "Equations and Inequalities" for my new math teaching website At the core of teaching Algebra is an understanding of equality. One of the major obstacles for students is realizing the differences between an equaiton and an expression. I usually try to make the connection by explaining that an equation is a comparison of two expressions. I emphasize that most equations are actually questions. What value of the variable(s) make the equation true?

The above is more of a conceptual understanding of equations. But just as importantly students must learn how to apply the properties of equations (and inequalities). I introduce them by setting up an equation of two numbers. For instance, 20 = 20. I then add a number to one side and ask them the question, "what must I do to the other side so the equation is still true?" I then use this general method to try and generate the properties of equations.

What are some ways that you introduce and reinforce the properties of equations to your students?

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.