28 October 2014

Pathways to Prosperity - Pathways for Teachers

I had an amazing opportunity to be a part of a program this past year called Pathways for Teachers (the professional development/curriculum writing arm of a larger program called Pathways to Prosperity.) The goal of the program is to pair up gen ed teachers with business and industry to give teachers "real-world" settings and experience that they can take back to their classrooms and use to enhance the relevance of their curriculum. The program was funded last year by+Boeing, through a partnership with +Cooperating School Districts.

We spent 2 whole days in the spring touring different manufacturing and business sites talking to workers and getting a general idea of what STEM-type jobs might look like beyond engineering. (I went to Icon Mechanical in Granite City, IL, Component Bar Products in O'Fallon, MO, Boeing HQ in Hazelwood, MO, and Ameren HQ in St. Louis, MO). During the summer, we had a week-long Pathways Institute that was designed to give us a more in-depth look at ONE site we had previously visited, training in developing project-based learning units, and time to collaborate and write the units.

I spent my externship day in the summer back at Ameren HQ downtown for what I thought was going to be a day of attempting to integrate electrical theory and problem solving into my Algebra class. What I came away with was several next-day applications for statistics and graphical analysis that completely caught me by surprise. Believe me when I say, real people do stats. Excel was EVERYWHERE (as were awesome 3 monitor setups at like every desk.)

After the day at Ameren, I worked 2 1/2 days with two other teachers from my school creating a project-based learning unit integrating everything we had learned at our individual externships. Collaborating on the project was a great experience because justifying decisions to my teammates and bouncing ideas off each other to solve different problems that arose in the process made for a better project. As just a small example, in the unit, students are grouped into teams and each student is given a job with an individual rubric. Giving specific tasks to kids in groups was not something I'd ever tried to tackle on my own, but we became our own support system. Its always harder to back down from makig innovative (hard) changes when you're got a buddy in the trenches with you.

Today I have the opportunity to share my experience with the this year's round of teachers - here are my slides.

Created with Haiku Deck, presentation software that inspires

23 October 2014

The PhotoMath App is Good, and History Says Its Here to Stay

In case you haven't heard about it yet, there is a new education app for iOS and Windows Phone devices called PhotoMath. Most basically, the app utilizes the camera on your device to recognize numbers and letters, runs an algorithm, and then displays a solution on the screen. From there you can follow the solution it generated step-by-step.

Here it is in action.

There are two ways to respond to the Photomath app, really. One is a reaction of fear, and the other one of promise.

This app is really cool,  people! The computational power behind pointing a camera at an equation or expression and having it solved or simplified step by step for me (nearly instantaneously) should really impress us, right? My hope is that the PhotoMath app and it's future iterations will be the disruption in math education we've been looking for. How much longer can classrooms ignore the technology and force students to solve everything by hand (and then stop there)?

Let's look at a brief (and roughly estimated) timeline of math technology in education:
  • 1970s: 
    • Computers are cool and all, but we mustn't let them replace the computational and arithmetic skills of our students. What if the technology goes away?
  • 1980s: 
    • Handheld calculators are cool, but we should only give them to students once they've learned their math facts anyway. What if the technology goes away?
  • 1990 and 2000s: 
    • Graphing calculators are a great tool, but students still need to know how to do it all by hand. What if the technology goes away?
  • 2010s: 
    • That's really impressive that you can make full color graphs on your smartphone/tablet, zoom in and out, change axis scales, and locate points of interest with a swipe and a pinch, but they can't use those on "the test," so they aren't worth the time.
    • Wolfram Alpha can solve equations for you? That's a really cool tool for college students to use as they explore upper-level mathematics. I hope my kids don't find that and cheat. Besides they need to know how to solve equations for "the test."
  • 2014: The PhotoMath app

What side of history will you be on?
As I noted in the timeline above, technology to solve our kids' equations on their homework has been in their hands or laptops via Wolfram Alpha or CAS graphing calculators for years already. The PhotoMath app makes it even easier to access that power, but I think your attitude toward Wolfram Alpha should mirror the opinion you ultimately take of PhotoMath. Will you embrace the technology and lead conversations and work to push for lessons and assessment in your school that expect more of students than x=_____, or will you wait for someone else to make that decision? I think history foreshadows that you'll be dealing with it eventually, anyway.

Special Right Triangles - Really?

What's in the list you keep (internally or physically) of things we still traditionally teach in our math courses that just feel "wrong" in 2014?

Memorizing formulas is probably one of my least favorite things, and I know I have that in common with my students, so wherever and whenever possible! I like to teach them the concept on a pattern level or with strategies that have more than one application. In other words, if the only reason for me to teach it is to maybe get lucky and steal a question or two on a test, then I usually won't stress it.

I was having a good week with my Applied Math class. The kids have been more or less focused recently, and we were all getting along. Kids love Pythagorean Theorem, for some reason. Right up there with "y=mx+b!" It's hard to find a kid who at least doesn't think they know how to use it. Taking advantage of those good vibes, I would have rather rolled on into circles, but the ugly special right triangles lesson stood in my way.

I went through the trouble of having them use Pythag the night before to actually solve the SRTs, and my first example showed them again how they can just use Pythag on any right triangle to find a third side. Good feelings were still flowing, and then our first question from the book had a 60 degree angle and ONE side. "Try and do THIS ONE with Pythagorean Theorem," it seemed to taunt me. I took the bait and walked the class through the relationships. And one by onem my confident students fell to the wayside, and my focused, eager students started to check out. 

So, why? Why invest time in a chunk of knowledge that isn't necessary if you know  Pythagorean Theorem or basic trig ratios?

Here's a note sheet I plan to share with my students tomorrow to articulate the alternatives again.