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

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.

"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.

That Common Core Subtraction Problem

Its hard to have NOT seen a variation on this problem over the past year.

The basic premise is this: Students are presented a subtraction problem, but instead of performing the traditional stacking/borrowing algorithm, evil public school common core teachers force students to jump through extra hoops. Students add chunks of numbers to the lower value to get to multiples of 5, 10, and then the higher value in an effort to find the difference between the values.

Every time I see this shared on social media its from a politically conservative non-educator using it as a tool to illustrate how big government getting its hands into our locally controlled schools makes things unnecessarily complicated (and ultimately, worse).

Say no to #CommonCore the moron math pic.twitter.com/YWHlJ9Yrg2
— Guardian Of Freedom (@ClownDogGunny) October 6, 2014

Here's the problem with using this ONE standard to characterize and criticize "common core math" - its the same thinking that our students and families use when they say things like, "all I need to be able to do is count my money. I don't need ______."

This question is meant to address a 1st grade standard about operations and algebraic thinking. The point is getting kids to understand multiple ways to manipulate numbers.

CCSS.MATH.CONTENT.1.OA.C.6Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 - 4 = 13 - 3 - 1 = 10 - 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 - 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13). (source: corestandards.org)

Before you're ready to confirm your contempt for core standards, think back to your own math experience. I've found that most "non-math" people often prefer problems and learning environments in which there is more than one "right" answer. The point of this question is to build mathematical thinkers that can adapt their thinking to look for solutions when their first or second attempt is unsuccessful.

2 Exercises for "Relevant" Proportion Solving in Algebra 1

One of the first things I realized after becoming a math teacher in my very first Algebra 1 summer school course was that students love to cross multiply. You stick a fraction on the board and ask something like, "Okay, what next," and you will most certainly get some kids that are dying to cross multiply.

Kids that only know how to cross multiply love to get exercises like this:

And they're probably even pretty comfortable with this:

But things might start to fall apart sometimes when students have to set up the proportions themselves in a situation not neatly laid out for them in "word problem" format.

Here are two such attempts that I used in my Algebra 1 class this past week. One is about troop reduction in Afghanistan, and the other is about "total percentage of weight loss" and trying to win the reality show The Biggest Loser.

WAYS TO MODIFY THESE PROBLEMS:

1. You could increase the rigor in both of these problems if you did not initially give either of the numbers I hand out (8000 and 51%, respectively) and instead, had your students figure out what number would be relevant to finding a solution that would satisfy the problem. After deciding what information was needed and/or relevant, students could do a web search to find the information for themselves. 
2. Have an extension question exploring these ratios in a different way.
1. The Afghanistan troop numbers could be compared to Iraq or previous deployments this century in Afghanistan.
2. The Biggest Loser problem could ask students to compare Jerry to other seasons to see if he would have won those years. You could have students set up "teams" of Biggest Loser contestants and find the proportions of weight loss necessary to defeat other fantasy teams from previous Biggest Loser seasons.

10 Writing Prompts for Exit Slips

Exit slips are, of course, a great means of quick, formative assessment over your day-to-day lessons in class. Writing is a means to trigger students' brain to memory and learning connections. Let's do 'em together!

1. "Describe something you previously misunderstood about _______ that was clarified in this lesson."
2. "Give two tips for remembering how to _______."
3. "Give a title and two section headings to your work/the notes for today's lesson."
4. "How would you describe today's lesson to my five year old when she asks what the kids learned today?"
5. (After putting up the graph of a function with each axis labeled): "What would this graph tell us about the relationship between the variables?"
6. Have students answer any of the unit essential questions (this is good for PLC pre and post data, too)
7. "How did something we learned about ______ help your understanding of ______ today?"
8. (After putting up a solution to an exercise). Evaluate this student's work. If the student was wrong, make an inference about where he went wrong or what he needs to relearn.
9. Did today's class rock or suck? Explain your choice with two reasons.
10. Make a list of as many content-specific words we used today. Define their meaning in the context of today's lesson.

Student Tips for Simplifying, Multiplying, or Dividing Radicals

To wrap up the lesson today, I had my students try to process their learning with an exit slip giving two tips for simplifying, multiplying, or dividing radicals.

Some of them referred to some notes we had written yesterday, some referred to something I'd said in the last couple days, and some used a kernel they'd picked up during class today that helped it click for them. We had a successful day, I think.

The "or dividing" is awkwardly  tacked onto the end of that heading because after I wrote "2 tips for multiplying or simplifying radicals," someone piped up, "Can we do dividing, too?" You win, students - its your class. :)