What Do You Notice?

Earlier this week, I asked for feedback on the Lens Lab I’d written for physics. Kelly, David, and John helped me focus my thinking with their comments. I want to tell you now about how I incorporated some of the comments. It all began with something I learned in St. Louis at Twitter Math Camp.

The Activity

Given a large magnifying glass, and a look at the image formed of objects located outside our classroom window, I asked kids, “What do you notice? Be specific.” Here is one group’s noticings:

Next, I armed each kid with a marker and sent them on a gallery walk. If they spotted something interesting on another board, they put a check. If they disagreed, they put an x.

Crediting My Sources

This idea is part of a strategy I learned from Max Ray this summer at Twitter Math Camp. From his blog:

The strategy we call Understand the Problem: Included in Understand the Problem is the core activity I Notice/I Wonder, which gives an entry point into the problem to students of all levels, but which can be perfected and improved even by expert problem-solvers (see, for example, the world’s hardest easy Geometry problem). I Notice/I Wonder begins to orient students towards recognizing givens and constraints, identifying mathematical quantities or objects in the problem, and describing relationships among them.

Based on feedback from Kelly O’Shea, I used “I Notice” to open a lab this week. She suggested I begin with a demo, which I did (hold a magnifying glass up to form an image from the window on a sheet of paper). Then, she suggested I move on to:

Ask for observations. You’re not looking for anything specific. You’re just letting them get their brains going. Challenge observations (by putting it back to the group and/or by letting them observe again, this time for that specific thing) that conflict with each other (or that are obviously not true), but don’t try to push them in any specific direction overall.

The check-x system helped the kids challenge each others’ observations in a non-threatening way. It also allowed me to quickly assess what they noticed.

The entire activity took 10-15 minutes during which kids engaged with each other and the material in a meaningful way. Can’t complain about that. Y’all have a great weekend, I’m off to pick apples in North Georgia.

Labs: Something I Want to Do Better

Whenever we enter the physics lab (really, it’s just the back half of my room so I’m talking metaphorically here), I feel the weight of big-S Science on my shoulders. I want to do it right. But I don’t know really what that means.

For one, I know a little about inquiry and know that I want some of that in my labs. Years of traditional education taught me that science and my own curiosity weren’t similar at all. You went in, followed some complex procedure and verified something you already knew and believed. Unfortunately for me, the verification and “proving” didn’t mean anything because the procedure shrouded all the real discovery in mystery.

For another, dispelling misconceptions seems like the most important work I can undertake as a science teacher. I definitely want some of that in my labs.

I think I’m improving at writing labs but they’re still unsatisfactory. Here’s my emotional laboratory roller coaster that often ends at unsatisfying:

I accept the challenge to write a lab that doesn’t feel like a waste of time and that kids actually learn from.

About the Lens Lab

Below is an optics lab I wrote with a colleague. We’ve already studied mirrors and done a little investigation with converging lenses. Kids know the mirror/lens equation:

My focus is on getting the kids to understand 1) the focal length (F) is a property of a lens independent of where you place an object, 2) when an object is placed at near-infinite distance from the lens, the image distance (di) equals the focal length (F), and 3) that the kids already know of real uses for lenses in different configurations. Do these goals come through in the lab?

I’m pretty happy with the final part (bottom of the last page).

Assume I’m not interested in a complete overhaul to modeling physics. What suggestions do you have to make my lab, or labs in general, better?

Solving Algebraically

New hashtag, folks! #physicsteacherprobz. And entry #1 is the student who solves a problem by substituting values first.

What do my kids do when they encounter this?

A simple pendulum has a period of 2 seconds and length of 1 meter. What is the acceleration due to gravity in this environment?

For the non-physics peeps reading, a simple pendulum has a period (T) given by this equation:

Kids are gonna solve for g like so:

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To me, that’s so ugly. Substituting numbers in at the beginning and calculating intermediate answers. Kills me to read tests solved this way.

I prefer my physics students solve equations algebraically before substituting numbers for two reasons. One: compounded rounding errors can blow the result. Two: algebra errors are really hard to spot, making the justification of this answer harder to follow. [Of course, the reason “because your teacher wants it that way” isn’t sufficient. -MHG]

There is long term value is in describing a relationship in terms of any variable, no matter how the relationship was stated when you were introduced. Right? (Right?)

Solving the pendulum equation for requires a student to apply algebraic rules of inverse functions. Maybe the kids aren’t comfortable with this symbol manipulation. Numbers are concrete, so kids like to plug ’em in soon as possible.

In all my time in the math classroom, we never had equations of more than one variable, so I think the kids are stunned when they see that simple pendulum equation.

How do I get the kids to see value in solving an equation algebraically before substituting values? #physicsteacherprobz

Working Examples

My Goldilocks Problem: I need to solve example problems but hate doing it during class. I’m unhappy with the pace — it’s either too fast or too slow. Nothing seems just right for a good chunk of my class. Oh yeah, and a little thing called differentiated instruction.

My resources: 1-to-1 laptops and most kids also have iPhones or other smartphones. I have a HoverCam document camera, a YouTube account, and plenty of notebook paper.

How I am solving my Goldilocks Problem:

  1. Decide what problems are appropriate to film yourself solving. These probably aren’t trivial examples. Recording these examples can be time consuming, so I don’t want to lead you down a path with you thinking it’s all roses and puppy dogs. You could probably scan the completed solution and post it faster.
  2. Crack open a can of Vanilla Coke Zero, gather meaty sample problems, and turn on your document camera.
  3. Start recording, solve problem on paper while talking your way through it. I even have an example to show you.
  4. Post recording to video host of your choice — I’ve used YouTube and Schoology to test this out. Files can be quite large, so storage on something like Schoology may be problematic over the course of a year (64 Mb for approx 3 minutes at a YouTube type resolution). 
  5. Share links with kids. Ooh, storm in brain! What if the titles or video descriptions included a hint as to when the video would be useful? For example, “Solving for frequency when wavelength and velocity are given”.

Advantages of this approach:

  • Pen(cil) on paper is familiar for me, handwriting quality is high, and gesturing to stuff on screen is natural.
  • Students can see me model appropriate calculator use (multiplication in the denominator of a fraction will get ’em every time).

I’m considering a hybrid approach for the next homework set — I’ll solve all the problems and only record the ones I suspect will be harder for the kids to understand. All solutions will be posted as a PDF alongside the recordings.

Foldables: Not Just for Little Kids

I think there’s a notion among teachers of high school students that coloring, scissors, and folding are stuff their kids should have left behind years ago. To them I say “pish posh!” I did a 2 door foldable to highlight how sound waves resonate in closed and open pipes. Helpful, say, if your students are building their own wind instruments.

I know what you’re worried about — foldables take valuable class time that could be better spent. There are ways to speed their creation up. Teachers who use foldables often have names for their favorites (so you can say to your kids, “make a 2 door tabbed foldable”) and names for the folds (such as the famous hamburger fold). I think the time is well spent. My friend Julie Reulbach agrees, saying foldables can “visually slow [students] down”.

Finally: A Chance to Merge Math & Physics

Because my students took the statewide End Of Course Test (EOCT) earlier this week, my school allows me to give a final project instead of an exam. This was a big break for me because my kids are tested out and I have no desire to write a 50 question comprehensive multiple guess test that can be graded within mere minutes of it being turned in so that I can close out my gradebook on the insane end-of-semester schedule we all have.

I’ve included the project below for you to enjoy steal. [Galileo’s Ramp (Word, 622kb)]

I start the kids off with understanding position-time and velocity-time graphs

Here’s a little snip:

Later, we move into understanding how quadratic functions can be transformed

There’s more in the full version (I guess that’s kinda obvious). Hit the link above.

I owe a huge debt of gratitude to @occam98, @fnoschese, and @jsb16 for brainstorming with me via Twitter the other night. Y’all were amazing. I opened with, “give me some phenomena that fit a quadratic function.” Also, I would never have finished writing this project tonight if I hadn’t had a horrible day at work. Something about a lousy day makes me want to do better the next.

This project gets students to understand position-time and velocity-time graphs in a rudimentary way, gets them thinking about the quadratic equations that describe those graphs, and helps them begin to understand how to collect data accurately.