Mental Models

As I have been exploring the use of technology to create more effective classroom environments, I have noticed a stark dichotomy in my teaching experience. One the one hand, I have facilitated dozens of independent study projects my gifted enrichment students. These projects were heavily dependent on using technology to gather, organize, and present data. On the other hand, I generally taught Algebra and Geometry with almost no use of digital technology.  We did  a lot of hands on projects with manipulates, measurement tools, etc., but the laptops stayed safely in the cart during math. 

So basically, I am comfortable with using technology to teach a process (project planning, research, organization, etc.), but I don’t instinctively use it to teach content.

Why is that?

The thing is, I am a pretty good teacher. I structure my planning to allow for a lot of exploration activities and real world applications. I am steadily increasing the amount of structured reflective activities that I use for myself and my students. I always assume that I can improve the lesson, or dig deeper, or make assessment more authentic and meaningful. I believe very strongly that students can and should self-select topics of interest to explore at a rigorous level. My entire enrichment program is predicated on that model, and it is commonly accepted as a best practice for working with gifted and high ability students.

And with all that, I am still operating from the framework of traditional instructional models. Teacher. Students. Textbook. Classroom. Even if I am really good within that model, and I can envision spending the rest of my career getting better and more innovative, there are still inherent limits. I am still driving the car, even if I know when to speed up and slow down and go the scenic route, everything has to filter through me.

I am the one that is in the way…but I am still the one that has to lead to way too.

I need to change my mental model. But along the way, I will need to address the mental models of my students, my parents, my administration. Not everyone is going to think it is a good idea (even the students).  Why rock the boat if everyone is “getting A’s?”  That is not an irrelevant question, and each stakeholder group wants a slightly different version of the same answer…because it is worth it to provide a meaningful and appropriately challenging education.

I think this also demonstrates to me the need for a strong professional learning community. I need to see, concretely and in detail, how others are implementing similar ideas, how well it is working, and how people are responding. The more that I explore the digital options that are available, and the vibrant community of teachers that are using them in the classrooms
(including math!), the more I am forced to accept the fact digital applications are the means to the end for both myself and my students.

Doors close….doors open

In other news, I was furloughed today. Very disappointing but not entirely unexpected given my position on the seniority list. Given the budgetary concerns in my district, my best case scenario was to make it through next year before this happened.

But like Dory says, “Just keep swimming!” Time to dust off the old resume and update it. The most grueling part will probably be the endless professional statements on PAREAP.  What is your philosophy on classroom management? What are the component parts of a “lesson plan”? (shudder…)

I have been a busy bee for the past four years, and I have a ton of good experiences that I can leverage to legitimately sell myself. But I definitely do not want to just rush in to the first available job and be in the same, or worse, position next year. I want to find a good fit for my teaching style, and where I want to be as a teacher in 5-10 years. I’m probably going to just take some time over the summer to explore my options, develop my portfolio, and maybe do a little tutoring.

In the meantime, I’ve got to close out the year, pack up my classroom, and finish two grad classes.

Just keep swimming.

Excellent (part II)

The kids took their test yesterday for the solids unit using their custom-built Excel spreadsheets to help them do the calculations. They had complete discretion as to whether or not they used the spreadsheet. A few students preferred to do it the “old fashioned” way, but most used Excel for at least part of the exam.

Most of the kids needed extra time to finish, which I certainly did not anticipate. But in retrospect, it makes total sense. They were basically taking a test in a completely new way, and it noticeably slowed them down. In addition to the normal processing time needed for the content, they were not yet proficient in using the spreadsheet…how and where to enter the data.

By far, the most interesting thing was realizing that they were learning and adapting on the fly. Multiple students had to make adjustments to their formula cells during the course of the test as they caught errors in the calculations. Even better, some students modified the very structure of their spreadsheet, or added completely new formulas to streamline or improve their calculations.

It was a pretty cool experience.



I had a really cool experience today with my Geometry class. My students were supposed to take their test today for surface area and volume of solids. The year is rapidly winding down, and I definitely do not have time to teach another unit. The problem is, I definitely have two or three days where I should be doing “something” before we start the review for the final exam. I really didn’t want to do lame filler work or some sort of pseudo-interesting (to me…) activity.

They were really caught off guard when they came to class, expecting a
test, and I said, “Change of plans! Grab a computer!” You have to
realize that, until this point, I have never used computers in this

I am not totally sure where the idea came from to do a lesson using Excel.  Maybe here.  (Check it out…it’s totally awesome.)


Ok, don’t worry, I didn’t bust out the mullet wig (You shoulda read the link…). But Mr. V did casually mention using Excel during the lesson to run some numbers, and I guess it stuck with me.

Anyway, the grand idea was for the students to learn how to build formulas into a spreadsheet that can solve all of the problems on the test by simply entering the given data. Also handy, they could use the review guide that they already completed as the sample problems

Long story short, the lesson was great. They were totally into it. Exclamations such as “Awesome” and “Wow, that’s really useful” were heard repeatedly. Most of them had never been taught anything more than the most basic functionality of Excel (sum, sort, etc.), which was completely shocking to me, by the way.  I mean, they have had computer classes for at least three years now.  Another example of the danger in assuming that someone, somewhere is actually steering the ship.

But I digress. The lesson was great. The students were engaged. I felt like a rock star. And they learned something that they immediately and instinctively recognized would useful beyond the 40 minutes of class time.

Of course, we didn’t get through it all. One day was barely enough time to model and troubleshoot. Monday during class they will work together to finish building and testing their spreadsheets.

Ultimately, it will probably take them 5-10 minutes to complete their test, and I will be surprised if the don’t all get 100%. Who cares? How often do you really have to calculate the surface area of a hexagonal prism anyway?

Twitter Ninja

 I am a believer folks. #twitterisamazing

This is definitely the breakthrough that I have been looking for to expand my professional network.

Plus, based on my “expert” knowledge garnered from a measly few hours of tooling around with Twitter, I had several really engaging conversations in two different grad classes tonight.

Lessons learned:

1. Just go for it. If you don’t understand it, Google it.

2. A lot of people feel the same way I do about this stuff…interested…but don’t know where to start.