So today was the first day of school, and immediately after school let out, I sat down in my classroom and make some “Link” sheets for Precalculus. I actually got this idea from a conference in Albuquerque we went to, and easily the best talk had several great ideas concerning teaching and making more connections.

For these link sheets, you take one problem, typically an algebra problem such as graphing a quadratic, and you break the sheet into four sections. These 4 sections can vary, but I usually use “Equation”, “Written Description”, “Table”, and “Graph”. The students are given one or more of these four sections, and they have to figure out what goes in the other three sections. I am thinking that once they get the hang of it, they will be making more connections than usual, but the problems can be very open-ended, with multiple correct answers for the equation, if only given the graph or description, for example. We’ll see how the students do, but I am certain they will really struggle with it initially. Here’s an example of a LINK sheet:

The students also seem interested in the Participation Points, especially because they get to *choose* how they want to earn their points. I tried to be very careful about the way I worded this to them, to make them as excited as possible.

I also just checked my e-mail in the middle of this blog post and received something from the “Blogging Initiation Team”–a group of great teachers who are also great bloggers, and are trying to get other teachers involved in blogging. They’re the reason I started this blog, so I want to respond to one of their 6 questions and join in on what they are doing. (Thank you!!)

I’ve decided to respond to question 2 and 6 simultaneously which ask:

2.Where does the name of your blog originate? Why did you choose that? (Bonus follow up: Why did you decide to blog?)

6.One of my favorite topics/units/concepts to teach is_____. Why is it your favorite? (Alterna-question: change “favorite” to “least favorite”.)

So the name of my blog comes from a though experiment I learned about in Math Grad School (this is before I realized that I wanted to be a teacher!). The thought experiment is designed to show how infinity really isn’t a number in the normal sense of the word, and strange things happen if you treat it like a normal number. Here’s a link to the story of Hilbert’s Hotel, although my professor told it to us a little differently. (You have to read partway through the article to get to the story.) So I decided to “photoshop” (I really used GIMP) and created an endless hotel hallway as well as an infinitely long school bus–both of which are in the story, and I changed the “bus” to be a school bus since I’m a teacher and all. I suppose I could have changed the hallway to an endlessly long school hallway, but it was hard enough finding a hallway that could be replicated like that *and* was in the creative commons photo database (and yes, I am still a new teacher so I’m afraid of getting sued for the silliest little things).

So, one of my favorite things to teach are lessons which “blow the students minds”. I was a philosophy minor in college and even considered going to philosophy graduate school (well, “considered”… nobody accepted me, however), so I really enjoy getting to teach things that make students go “wow, I never thought of that!” Any kind of math, science, or philosophical thought experiment are so much fun to show students for the first time, and although that’s not in the curriculum, I do find time at the end of some classes to share some of the stories such as Hilbert’s Hotel.

Hi Jonathan! I did follow Steven’s Strogatz column at one time (so behind on my reading) and that’s where I first read about The Hilbert Hotel! Very cool. Love the bus you created for your blog heading. I commend you for starting this post after your first day of school! On behalf of the Initiation Team, welcome to the Blogosphere!! It’s an honor for me to feature your blog on mine at http://fawnnguyen.com/2012/08/21/math-blogger-initiation-week-1.aspx.

Also, from what you described of your Link Sheets, they sound similar to the 4-quadrant Frayer model that I sometimes use. It’s so important to give kids multiple representations of any one concept. Bravo and thank you!

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