Mortgages

While listening to the radio last night there were a ton of stories about the hike in long-term interest rates here in Canada. These stories generated a lot of buzz around mortgages. Many experts were saying that homeowners should lock their variable rate mortgages into a fixed rate mortgages.

One of these brokers caught my attention. He suggested sticking with a variable rate but making the payments as if you were on a five year fixed mortgage. This would pay down principal a lot faster. Here's the math...He said that on a $300 000 mortgage this method would result in a savings of $8000/year. My first thought was 'I wonder if that means that on a $150 000 mortgage your savings would be $4000'. It was a very simple question as I was driving, but I quickly realized how useful it could be when talking about exponential functions and to see how much students have understood. It's also a nice way to show students how the math they're learning relates to everyday life.

The question could simply be: Would a mortgage of $150 000 (or $600 000) result in a savings of $4000 (or $16 000)? Why or why not?

Cluttered Desk or Something to Ponder?

I've been teaching for a decade now. Today I had a moment when I realized just how much things have changed in that decade. This is a picture of how my desk may have looked on a given day:

This is what my desk looked like by lunchtime today:

I did have to group everything so that it fit into the shot, otherwise there would have been a whole lot more clutter in the picture. I notice two things about these pictures.

1. My desk looked a whole lot tidier back then. I hate to imagine what this picture will look like 10 years from now.
   
2. The tools I use have changed dramatically.

Point #2 had me thinking about the tools I will use in the future. Just to be clear I still use most of the tools I used 10 years ago and today's display was unusual. However, I do see myself using more and more tools. My hope is that by expanding my toolbox I can  make math more interesting and engaging for students. I think this is working since one my students made a comment along the lines of "I usually hate math, but this is a lot of fun" as she was leaving today. I also hope that I can provide my students with skills that will help them in the 21st century. I want them to be able to blog, edit images, participate in online communities, etc. If we don't teach them these skills who will?

What tools do you think teachers will be using in the future? What 21st century skills (if any) should we be teaching students in addition to the curriculum?

Let Them Create

I asked my students to create a public service announcement for math class. They had the choice of doing an audio or video file. Much to my surprise all of them chose to do a video. I was a bit nervous about having students create videos in a math class. I was concerned that their videos would be entertaining but wouldn't have a lot of mathematical content. I set some guidelines for them and much to my amazement they are using the math in their videos. In fact many of them are doing more calculations and including more math than I had expected.

My students are just loving the project. It's such a departure from what they're use to. It nice to see them coming to class eager to do math and work on their videos. I'm definitely a convert and will have to do more projects like this.

iPods in Class?

I am extremely excited about using the iPod Touch in class. I think they can be an incredible learning tool to all students in all subject areas. I see iPods as a way to bring the outside world into our classes at a very reasonable price. I have been trying to convince my school and district of the value of these devices, but as of yet I haven't had much luck. I managed to get a couple of iPod Touches from Apple on loan for a period of one month. I'm hoping that in that month I can show students, teachers, administrators and parents the value of mobile devices in the classroom.The best thing about these devices is that we don't have to buy an entire class set. Many students are coming to class with this technology. Let's provide some to the students that don't have access and put the ones that are already in students' pockets to good use.

I have two routes that I am going to pursue.

a) In my low-end math class we've used water conservation as a context for the math that we've studied in this unit. I've decided that I'm going to assess the unit by having students produce a public service announcement (PSA) in either audio or video format. The PSA will have to contain some mathematics to show that they have understood the content. Students creating audio PSAs will use the iPods to do it while students doing the video PSAs will use video cameras. I know that I could book a computer lab to do this but it seems like such a waste given that the different groups will be at different stages at different times.

b) I teach in a province that has a province-wide literacy test for all grade 10 students. I will prepare audio/video tutorials that can be loaded onto the iPods to help students prepare for the test. The students can use this material as they prepare for the test. They can pause it, rewind it (do you still call it rewinding on an MP3 player?) or listen to it again. The iPods can then be handed out to students who need some remediation. I think that the real bonus here is that the delivery method will be engaging.

If you have any other ideas about how to use iPods in a classroom please feel free to share.

A New Take on Slope

I haven't taught the basics of slope for a few years. Rather than use the tried and true method of drawing graphs on the board and finding their slopes I thought I'd take pictures around the school of lines and we would find the slope of those lines. It was a very small difference but the images seemed to capture the attention of many of my students. Many of them commented on where the picture was taken (Are those the stairs at the North end of the school?), some were even curious when I took the pictures.

After a quick demo of slope using Geogebra I started with just an image an asked how we could find the slope of a slanted microphone. Someone quickly pointed out that we needed a grid. We overlaid the picture with a grid and counted the squares for the rise and the run. On the next image we introduced a coordinate system and the formula for slope so that we didn't have to count the squares. The end result was something like this.

I wanted students to find the slope of the roof for this church. Somebody asked if they had to do both sides. We discussed how they thought the results from both sides would be related. They were then asked to confirm their guesses.

Overall most students were tuned in. I think there were a few that thought I was babbling and wanted me to get to the traditional lesson. It make take a few lessons like this for them to realize that this is the lesson.

Smartboard

I had a Smartboard installed in my class a week ago. Before I get into too much detail I should mention that I've been using a Smartboard on wheels for the past month so it's not as though last week's addition totally changed they way that I do business. I must say that what I like most about having an interactive white-board is having a projector permanently mounted in my classroom. Now if I want to show a quick video or do a quick demonstration I just turn on the projector and I'm in business. Before it was such as hassle (I could go on in depth about the hassle but will spare you the details) that I often decided that the gain wasn't worth the effort.

I think that the interactive white-board is a very neat idea but I'm not entirely sure it's good bang for the buck. Yes my students love coming up to the board to use it. Will the novelty wear off? I'm guessing probably. Yes it's great to be able to capture everything I've done in my lesson, export it as a PDF and upload it to Moodle for students to view. Is it worth the expense? Time will tell.

There are other companies that make interactive white-boards and devices that turn a regular white-board into an interactive white-board.  Mimio is one of those companies. For the price of my Smartboard (and the installation) we could have purchased almost three Mimio systems. Don't get me wrong I do like having a Smartboard but I feel guilty that my colleagues don't have one. I have extended an open invitation to my colleagues to kick me out of my room so that they can use the technology with their classes.

 As a side note we had four teachers in from a neighbouring district to see how our school is using Smartboards and Moodle. They are looking at using both technologies and wanted to learn from our experience. They were very curious about the details of Moodle and to learn all of the ways it could be used. It's great to be able to collaborate like this. Thanks for coming guys.