## 6.25.2007

### Algebra + Geometry + Technology = Student Success: Math Technology

This session is one that will be showing a model math lesson using various pieces of technology. I am sure that some of this will be stuff I have seen before, but there is always something new that will come out of a session like this.

As I am sitting waiting for the session to begin, all I have to say so far is "Wow!" I have been able to visit two vendor booths so far: Apple and TI/DLP. Both were giving various demonstrations on various topics. I learned a little about TI Nspire and some more on TI Navigator, but unfortunately they are only for Windows. I guess I could always push for parallels on my cart of computers to be able to run these. Or, I could just survive without Nspire and Navigator. I do want to stop back for a presentation on Nspire to see how it works. They are also offering training and hardware for \$225 at various times and places around the country. It's an idea...

*NOTE: This session is being video-taped, so you should be able to watch it at a later date.

Let's begin. This is set up as a model lesson, where there are people on the floor acting as the class, while those of us on the sides and back are passive observers. We start out by trying to solve a problem:

A rectangular kitchen table is three times as long as it is wide. If it were 3m shorter and 3 m wider, it would be a square. What are the dimensions of the rectangular table?

A volunteer comes up to the interactive white board to explain the problem. The gentlemen who solves the problem also points out that the table is quite large. We move into working with Geometer's Sketchpad (I assume to help solve the problem...) I open GeoGebra on my computer since I don't have Sketchpad. We start by drawing a line segment, then finding the midpoint. We then draw a circle where the midpoint is the center. It seems to me that it's a bit easier to do this on GeoGebra than it is on Sketchpad, and this is the first time I'm doing most of this on GeoGebra. I need to play around with labeling. That's something to play around with.

But we labeled the circumference and diameter of our circle, and then showed how as we move around the endpoints of the circle, the circumference and length of the diameter changes. We use this data to graph a line that shows the relation between the two variables, which gives us a direct variation, where the slope of the line is pi. A question is posed: "Have you ever thought about teaching the concept of pi as a line?" Very interesting question. But from here, we know we can show the slope in a label that shows the relationship as pi! As further proof, we take the data and tabulate it to show that no matter what we do with the diameter, we will get the same relationship. I guess we shouldn't say "further proof," as we're are only looking at examples that support the construction.

This is a nice look at how to use Sketchpad in a somewhat constructivist approach. One thing I noticed is that the teacher is just talking us through the process. Why aren't the students leading the learning? Isn't that what we're aiming for with 21st Century Skills?

Now we are moving from working with the circle to looking at patterns. There are four different patterns that are squares (3 X 3, 5 X 5, 7 X 7, and 9 X9). We are asked to find the side length, area, and perimeter and to see if we can find the pattern that exists. While we do this, the teacher walks around the classroom to make sure everyone is on task and working through the task.

We next go to enter the info into a graphing calculator (she is using TI-Smartview for the TI-84 Plus Silver). Someone comes up to show how to enter the info into the calculator. Now we're working through some of the basics of entering lists. We are warned to never it DEL when trying to clear a list because we will "lose our list!" That's not true, as you can always run the SetUpEditor to bring back the list (as long as it is listed in L1 through L6). I hate to say "never do this" to a student, because it is inevitable that there will be a student who does it! But it is nice to know that you can retrieve the list.

But we are entering the sides, area, and perimeter into the lists and finding equations by plotting two of the lists and using the LinReg function. For anyone who has used the TI's in class, this is most likely second nature.

Oh, no! She is using the terms x-axis and y-axis. I'm not a fan of that, as I prefer the horizontal/independent and vertical/dependent axes, as I don't like having my students thinking of it as just x and y. They need to be able to understand why the variables are what they are, at least in my opinion. It leads to better understanding of what they are doing. I have been doing this type of teaching for as long as I have been teaching (four years now!), so I will be stepping out at this point.

One piece of software that was mentioned is CPMP Tools. This is a java program that offers some free tools. I'm not sure how they work, but I did download it to play with it.

Overall, this was a good sample lesson, as it is similar to what I do in my classroom and have seen in others. I would have liked to have seen how to make it more student-centered instead to the teacher just walking them through it step-by-step.