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.

"We Just Want to Be Comfortable"

I went to the St. Louis EdSurge Summit at Ritenour High School Saturday afternoon. The event featured dozens of #edtech startups with tables sharing their product and passions, and a terrific keynote to end the day from Google Education czar +Jaime Casap, but what impacted me most was the student panel hosted in the auditorium after lunch.

The second question +Chris McGee posed to the group was, "If you had unlimited funds to set up your ideal learning space, what would you include?"

Accounting for my typing speed on an iPad, here are their responses:

• A desk with matching pencils and notebooks, picking where you sit, no desks in rows or columns 
• Students feeling comfortable, couches EVERYWHERE, because everyone loves couches, it's just uncomfortable sitting up in a desk - I can focus better on a couch
• ATMOSPHERE, as inviting as possible, simplicity and complexity in a way to get things done
• We DONT fall asleep on the sofas, it's not just the classroom, it's the teacher too, if we're in a cozy classroom the way we think and work will change
• Availability of being able to choose our tools for what we want
• PAPERLESS CLASSROOMS
• Students interacting with teachers when districts are hiring new teachers
• I think I focus on my work better when I'm working on a computer or tablet
• LIGHTING is a big part of atmosphere for relaxing 
• I can stay more organized with the laptops instead of using my binder.

Do you put as much thought into the layout of your room as you do the color on the walls, the alignment of your posters, or the security of your teacher desk?

I have a couch that I salvaged out of the "surplus: send to plant" storage area 2 summers ago that I put toward the back corner of my room in what I named the "collaboration corner." It's a decent space. I have a rug we were done with at home, a coffee table that I salvaged from somewhere else, and a few clipboards to write on. The only problem with the collaboration corner is that it's in the back corner. I don't feel like I can manage the students there when I'm at the front of the room at the SMARTboard (which is something else to consider anyway; should I be up there enough for it to feel like a problem?) or speaking at a student's desk in the front. So what happens? The collaboration corner hasn't hosted very much collaboration the past year and a few months.

So what's the plan? I'm gonna double down on the commitment to the collaboration corner and move the couch toward the front of the room.

Do you ever feel this way about the things those students shared? You want to believe what they're saying, that they're totally committed to those statements and that in the environment they described they would all be creative, productive little problem solving machines, but your experience with that starts to psych you out.

My hope is that moving the couch out of the back corner will separate the kids seeking the couch to hide out from the kids who just want to get in a spot where they can hunker down and work. The funny thing is, I thrive in the same environment with the same level of trust. I've convinced my curriculum coordinator to let me and a colleague go work at Panera Bread Co. this week on a website for the district rather than sitting at the table in his office. I'll sit there and drink somewhere between 6 - 9 cups of coffee, spread out my things, jam to some music, and crank through that work.

Here's where my put couch on Monday. You've got a week, kids. Show me what you've got.

Algebra on a Chromebook: LucidChart Diagrams

I've heard more than once that laptops or Chromebooks in a 1:1 environment get relegated under the desk during math class because the classroom teacher struggles with finding ways to integrate the technology into what is usually a much more hands-on process with graph paper, pencil, and exercises.

I think the easiest answer is to have kids using the laptops for watching videos, looking up examples on webpages, or drill and practice on websites. The sexy answer is to have kids engaged in problem-based learning, integrating their math work into relevant reports, graphs, images, and presentations, but first you would have to also sell problem-based learning on the teacher.

In between the easy answer and the sexy answer lies LucidChart Diagrams, whose collection of education templates can facilitate note-taking, critical thinking, the problem solving process, organizing and summarizing, sequencing, and concept mapping.

Let me show you briefly how a student could use LucidChart Diagrams to integrate writing and list the steps to solving an equation.

You can find LucidChart Diagrams in the Chrome App Store

After clicking on "Create," this box pop-ups, giving you a selection of templates. There is an extensive "education" collection.

This is the "sequence chart" which you could use for any technical writing task. 

Your next task is inserting an image of a worked out equation for students to write about. Scroll to the bottom of the menu on the left and select the plus icon to add an image. This box pops up in which you can do a Google search or upload your own (student or teacher created)

Here's what mine looks like after resizing the image some and inserting each of my steps. (click to zoom or pop out to new tab)

Other charts you might use - 

• Venn Diagrams
• Cluster/Word Web
• Compare and Contrast
• Concept Map - use to connect similarities and differences in characteristics of functions
• Planning Chart - problem solving or think alouds
• Vocabulary Chart - visualizing unit vocabulary, grouping similar/related words
• T-chart - change the headings and use as guided notes/interactive notebook. students import images of examples and type in on the right side.