Sunday, August 19, 2012

In the Name of Efficiency

See anything weird about this?

I started college as a Mechanical Engineer major since some college advisor (who knew nothing about me) thought ME (Mechanical Engineering) would be the most fitting major based on some test I completed coupled with my interest in math and science. As I was taking my prerequisite courses in math and science I switched gears to Electrical Engineering because my love for music swayed me into thinking I could design amplifiers and effects pedals (stompboxes) for musicians. I took a couple of EE classes and really didn't enjoy it. I wasn't passionate about it and saw many others in the same boat who kept making comments such as, "I have to finish this [major] now" or "I can't not major in electrical engineering" or "It's what my [insert parent gender] does." As for me, I really enjoyed my introductory Philosophy classes because they allowed me to explore some pretty radical thinkers and we had all these wonderful debates about logic, God, metaphysics, existentialism, human rights, medical rights, law, etc. I became a Philosophy major and the rest is history... I think. My point is, if anyone (me included) knew me well enough, they should have highly suggested I major in Civil Engineering.
Here's why CE:
I'm one of those people who drives by construction (road, building, bridges, pipes, etc.) and is always trying to figure out what is being built, modified, or enhanced in the name of efficiency. I'm also that person that drives by an area and will vocalize how inefficient the lane configurations are, or offramp, or stoplight sequence, etc. That's usually followed by a suggestion on how to improve it. My poor wife gets an earful at times. I'm also that guy that looks at products and either loves and respects an efficiently designed product or will completely be baffled that a company releases a product so poorly engineered and wreaking of inefficiency. Then, I spend the next 30 minutes thinking of ways to make it a better product or design while restraining myself from emailing the company. I know the latter example isn't necessarily classified as CE. However, I could see myself out there designing things to help improve civilian efficiency. Thank goodness I'm not. Instead, I'm in the classroom with normal adolescent  middle schoolers who are always are in a good mood and never have social problems or woes. Right? One can dream. I love my job. I love teaching those wonderful teenagers. There's never a dull moment with middle schoolers. As their teacher, my objective is to strengthen their young impressionable minds and help them be better critical thinkers.
Enough about me, the point of this post [In the Name of Efficiency] is I have an idea for my class this year. Dare I say 'theme'! And if it goes well, could easily become a staple for the remainder of my teaching career. That's how much I value this idea! We look for products that fit one of two categories:
  1. The product is very efficiently designed. We explore everything about it that makes it a superbly designed product. What math is involved? How is math involved?
  2. The product is inefficiently designed in one or more ways. Identify the area(s) of inefficiency and propose a well-thought out modification/enhancement. Again, how would math be involved? 
Here's a simple one for the first category: efficient.
A modern ketchup bottle.
The ketchup bottle that rests on its lid uses gravity to its advantage and you rarely have to shake the dang thing. Plus, your burger, dog, or fries will actually still be warm when you're done getting ketchup out of the bottle. Why did it take someone so long to think if this, right?
Here's an example that fits the second category: inefficient.
A depleted salt container.
Take that salt container at the top of this post. Granted, it took a couple of years to deplete the salt in the container, and maybe there's a new design out there, but I got to the end and there's still salt in it. No matter what angle I hold the container, or shake the cylindrical container, it won't pour out every little grain of salt. My question would be: How could we better design the spout? Should its location change? What would happen if the spout were closer to the rim? What would be the easiest, yet most effective change?
Companies do this all the time (or at least should). They reassess the efficiency of their products. Why can't a classroom full of students do the same? We/they complain about things all the time. I want my students to bring in stuff: pictures, products, construction site pictures, machines, etc. We discuss it for a week. We make a bulletin board of ideas. We split the board in half for efficient vs. inefficient. I want each student to be responsible for at least one contribution throughout the year. They do a brief write-up. Pick from a collection of modifications/enhancements submitted by their peers. Sketch or draw a new design. I'm ranting here because I want to flesh this out... I want this to work!
I want my students to bring things in that drive them bonkers. Fine, if you don't like it, think of something better. How would you design it? What would you want it to do? On the other hand, I want my kids to bring in things that they absolutely adore. Things they couldn't live without. Things that they take for granted on how awesome they are. This might require them to give it more thought. Usually something that is efficient, well-designed, well-made, and awesome can be overseen because of how great it is. The second it stops working, is gone, or replaced with an inferior product we pine. Talk about an opportunity for students to appreciate many of the wonderful, amazing, and unbelievable inventions of our time. I think this would foster a sense of gratitude for some of the cool things we experience every single day. It's not just about complaining and finding things that could be better. 
This is one thing I'll be doing differently this year. Am I off base here? This wouldn't be the foundation of my teaching, but it sure feels naturally appropriate to a math class. Aren't we teaching our kids to be better problem solvers? better critical thinkers? better contributors to society? I always tell them to better problem solvers and not better problem complainers. Don't we have things that drive us nuts? Within reason. I'm not talking about losing your internet in the middle of an airplane ride. Your life will go on without the internet for a few hours. Yes, it will! Don't even start with me. If you got a problem with losing the internet on a plane, read a book, pay attention to your kid for a few minutes, or talk to the person next to you. Everybody has a story to tell. Ask them what their story is. If you're not convinced, talk to my man Louis CK. Tell 'em CK:


Efficiently,
318

Tuesday, July 24, 2012

Distance, Rate, & Time [Giddy Up!]

Last week I finished Steve Leinwand's Accessible Mathematics. It's a quick, easy, informative, realistic, and applicable read. Get on that!
This week I planned on diving into Standards Based Grading while restructuring some things for next school year. Well, there's still time for SBG. Instead, I've been churning out some new 3 Act lessons with:
  1. Some outtakes to the hexagonal Pencil Cup lesson and...
  2. The beginning of some distance, rate, and time lessons
There's a plethora of resources out there dealing with d = rt. Therefore, I thought I'd try and put my little spin on the whole roundabout. Keep checking my Distance, Rate, & Time album for updates.
Giddy up to summer!


Go the distance,
1140

Thursday, July 12, 2012

Elmo's Microwave Travel

Summer school has been a fantastic testing ground for 3 Act lessons with incoming 6th & 7th graders. I'm constantly reassessing my deployment of the lesson format. If you have any improvements to offer, go for it. Check out Dan's whole catalog. Here's a few I used this summer:
  • Print Job: Talk about rate and breach theoretical v. practical discrepancies.
  • Nana's Chocolate Milk: Ratios, Fractions, Proportions, Equivalencies, do it!
  • Popcorn Picker: Do identical rectangular papers have the same volume?
  • Super Bear: Unit rate, ratios. Discuss Percent Error (genius)!
Dan's lessons are wrapped up in a neat little package, following his own framework for digital media. It's up to us to deliver. Today, I used my Elmo's Microwave Travel lesson. Keep in mind this was with incoming 6th graders. I'm more generous with them than my 8th graders. I continue to learn about the 3 Act lesson format (here's Act 1):


Act 1 (go get that Q):
View and immediately get those Q's (questions) in the air.
I don't perseverate anymore over having at least one student ask the intended Q. Let students ask what they wonder and state observations. If they hit your intended mark, don't jump for joy. Act as if it's just another Q in the mix. Summarize the questions and observations before revealing the Q. I usually say something like, "I'm right there with (insert name) on this and I also want to know (state question)." Luckily, there was at least one kid form each class who wanted to know how many rotations Elmo makes in the microwave. Get that Q on the board immediately along with any other questions that could be answered during the lesson. Have students write the Q's at the top of their paper, notebook, handout (whatever you use). Everyone needs an objective, something to work toward. Once it's scribbled down, encourage your students to make an estimate for each Q and pencil it in near the Q. We came up with:
  1. How many rotations does Elmo make? (They nailed this Q!)
  2. What distance does Elmo travel around the microwave? (Extension of the 1st Q)
  3. Will he melt? (Some students really worried about him melting. How considerate.)
* Using their wording for the Q's, I encouraged them to put it in relation to one minute.
Students do all the thinking, questioning, noticing, etc. but in the past I wasn't writing the Q on the board. Big mistake. Now it's monkey see, monkey do! Get the Q on the board. Go!

Act 2 (muy importante!):
Ask the students to discuss, "What do we already know?" Here are some responses from students:
Elmo travels for a minute. (Me: "How does that help?")
He's on a circular plate. (Me: "What do we know about circles or can do with that?")

Write the facts on the board. Now I ask, "What information would help you answer those Q's on the board?" or "What would you want to know in order to answer the Q's?"
Really make students think here. Don't make it easy. I have to keep working at this tactic. Allow students to struggle with the notion that they need to determine what's relevant before you divulge any new information. This allows students to be better critical thinkers. Here's what they thought:
Maybe we could see how far he goes in 10 seconds (Me: "Interesting.")
The plate is a circle. Can we know the circumference? (Me: "Is that easy to measure?")
Then can we have the radius? (Me: "I'll give you the diameter. How's that?")

Roll Act 2 Elmo. Students, get solving. Start discussing, debating, testing, calculating, etc. If you come up with something let the class know. If we agree on it, we'll write it on the board. If not, we'll erase it. Hey Frank Noschese, now I'm starting to see the importance of those student whiteboards. WWFSD? (What would Frank's students do?) Can we still jot down necessary info at the front while students collaborate? Of course.
This is all student derived. I was simply the scribe.
Okay students, you got a solution? What does that number mean? Does it make sense? Did you check it for reasonableness? Did you give a unit of measurement? Did he travel in miles, feet, inches, millimeters? Does it make sense? I bombard them with questions. I'm almost getting to the point where I forget about Act 3. I want to see their work during Act 2. I want to hear their rationale. I want to learn from my students and their thought process. I enjoy that. Lately, the big driving force for me to actually leave Act 2 behind and attack Act 3 is the discussion that follows after viewing Act 3

Act 3 (theoretical v. practical):
On paper, many 6th graders miscalculated that Elmo travels 37.68 inches for one minute. Even after asking them if it made sense, they stuck with their answer (I let it go). There were a couple who got the correct answer! I didn't tell them; we watched Act 3. The students who had the correct answer and saw that 37.68 inches was quickly ruled out, watched intently as the time wound down. The anticipation on their face was priceless. The video ended and one girl was both happy and confused at the same time as she awkwardly asked, "Is it okay that my answer is one inch off?" Hello! Here's our opening for discussion. Theoretical v. Practical. I was so happy. First we discussed why 37.68 inches was incorrect. They didn't multiply their circumference by the number of rotations in a minute. Then we tackled the theoretical v. practical results. My microwave plate is kind of wiggly. It doesn't rotate at a constant speed the entire time: it slows down and speeds up. That one inch could be accounted for a few reasons. Their world was rocked, but Elmo's world made sense.

[Sequel to come] Dan contacted me for some video footage of Elmo traveling for 30 seconds in real time so he could use it at a workshop. He wanted his attendees to graph:
  1. Elmo's distance from the center of the plate over time [Update: Video]
  2. Elmo's distance from the glass door over time [Update: Video]
  3. Elmo's total distance traveled over time [Update: Video] *My recent addition
I plan on doing the video sequel and will experiment with it in Motion this week. My kids enjoyed the sequel discussion, but missed a video to back it up. Great sequel idea Dan, thanks.

Traveler,
252