It's every geometer's favorite: the hierarchy of quadrilaterals.  I've used the most basic version here for simplicity's sake, as well as the fact that my last teaching post was with 6th graders, who wouldn't need any more information than this anyway.

The idea that some polygons can be classified as several different things is difficult for many students, so this type of image can help many of them.  Anything on the map can be called itself, or anything that you can get to by going up the map.  Often, a student will see a square, and not understand that the square is also a rectangle (or for that matter, it can be classified as anything on this version of the map).  This map also leaves an opportunity to introduce a new classification of quadrilateral, and have students decide where it fits in to the map.

Google Maps, once more, with feeling.

My idea for a math lesson that utilizes Google Maps would revolve around rates, and particularly one of the most talked about rates right now, miles per gallon.  After learning about rates, students would plan a long distance road trip.  They would be given a gas mileage rate and gas tank capacity, possibly by random draw (we could all chuckle about the student who got the 20 year old pickup with 10 mpg) or possibly allow the students to pick their own vehicles and look up gas mileage statistics.  Students would then have to plot a course to their destination, using the draw a line along roads tool to track distances so that they can decide where they would have to stop for gas.  For more advanced classes, you could include having to account for speed and time, planning where to stop for meals or for the night if the trip is long enough.  Here's a map from a trip I recently made to a reunion (we went to our inlaws' house and rode from them there, that's why it's so indirect, and I'm pretending we went straight back home to make a different route back), with stops added for theoretical gas stops. Here's the map.

Podcast

Found myself a math podcast, here at mathgrad.com.  It talks about some interesting things and the math behind them.  I can see it as a great way to introduce a concept, or as a way to help explain some of those random questions you get from students that you aren't prepared for, when they're asking how the math works out for some things they encounter.

Some "tasty" links?

Just created a delicious page with a couple of links on it.  More to come hopefully, but I don't have many bookmarks to start with so I'll have to scrounge some stuff up.

Flickr site

Here's my Flickr with all of one picture so far.  More to come when I'm on the desktop which has pictures, as opposed to the laptop which has just the one, and that's because I plucked it off facebook 5 minutes ago.

http://www.flickr.com/photos/65200040@N08/

Let's embed some media!

For any of the musically inclined out there, or even if you just like a humorous video:



The bustling metropolis of Watervliet, where I currently live:


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My wife's favorite picture of our son.  He's 3 now.

RSS

Got the RSS reader up and going.  I'm going to have to check it more often, or else I'll end up with 100 new things every time I go there.  Here are some of the sites I chose to go along with my classmates' blogs:

cnn.com
espn.com
Left-handed Toons
XKCD (VERY occasionally has some adult language)

Wiki

First shot at a wiki for me, although I should have enough experience using Wikipedia to make it at least halfway decent.  http://nruland.pbworks.com.  For some reason I feel like I'm not qualified to put information out in the internet like this, but I guess it's just a wiki and shouldn't be taken too seriously.  I seem to have caught the "Wikipedia is always the truth" bug and am worried people will take my stuff for absolute truth.  I wonder if this is how the (non troll) Wikipedia editors feel?

R/D 1 - Technology to enrich and advance learning v. technology for its own sake

                The Postman article and the Reigeluth & Joseph article seem to give a sort of upper and lower bound for the discussion of the use of technology in education.  On one hand, it is important to realize that simply using technology for the sake of using technology accomplishes nothing except making the teacher feel tech savvy.  On the other hand, there are a multitude of tasks that educators must perform and a plethora of information that can only be organized and easily accessible with the use of technology.  I believe the key is finding a way to balance the two to make sure that students are getting the best quality education that we can give them

                One very important point that Postman brings up is that the transfer of information is not the only, and in his opinion, not even the primary focus of schools.  He argues that “Schools are not now and in fact have never been largely about getting information to children,” and goes on to say that “One of the principal functions of school is to teach children how to behave in groups”.  Unfortunately, this is one place where this article suffers from being nearly 20 years old.  In 1993, you could learn about how to act in society without being surrounded by these technologies, but today every 10 year old has a cell phone and most students are on Facebook by the time they’re 13, the legal minimum age for sharing information on the internet.  I would argue that not incorporating technology into any form of educating would be withholding very vital lessons in how to operate in the group settings of today.  The underlying point he is trying to make is still very valid, it’s just that the world in which it was made was very different from the one we know today.

                Postman also gives occasion for thought when he asks “What is the problem to which the new technologies are a solution?”  He then goes on to talk about how the problem is how to give information to students, and that the problem had already been solved and was also not the main focus of schools anymore, as discussed earlier.  The problem with this is that he is completely missing one problem for which it is a very good solution, and that is managing the great amounts of data that come from today’s ever increasing focus on individual education.  Reigeluth and Joseph, who to be fair have the advantage of almost 10 years of time passing between Postman’s article and their own, bring up the concept of “advancement for all”, and talk about how students will learn at different rates and have different needs in their education.  In order to keep track of where each individual student is would be a monumental task to be undertaken without the help of technology based ways to gather and organize this information.

                Over my two years of teaching, I’ve been able to see some of how this can happen.  All of our students took the NWEA tests in math, reading, and language usage in the Fall and Spring each year.  These tests are designed to gradually increase or decrease in question difficulty in order to try to find the level at which the student is successful.  My experience was with results on the math test, and it would keep information on how well the students answered questions in several different mathematics strands, such as geometry, number sense, and algebra.  This information was available to teachers via the internet, and broken down so that you could find the concepts that should be easy, concept the student should be developing, and concepts that would most likely be frustrating to that student.  We used that information to try to develop individual goals for each student for their development through the school year.  Although tests are not always 100% accurate, with the increasing number of students each teacher has to keep track of, trying to come up with anything close to this for individual students would be terribly time consuming at best and impossible at worst.