A whole bunch of juniors in high school just left my room, excited to go outside tonight and look up.

Update: Timon made a video that you could use to launch the lesson

I started by showing this:

Which is not all that exciting, granted. It's a table of the day in January 2012 vs how much of the moon was illuminated. The data comes from the US Naval Observatory. I explained what was in the columns and asked them to write down one thing they noticed, and one thing they wondered. Thank you, Math Forum. Their noticings were pretty good: the periodic nature, the numbers of full and new moons in January, the fact that few of the values are repeated. Their wonderings, though, were wallowing in lameness. I was hoping for anything, really, that hinted at making predications past January. But, no joy. This is a direct quote: "I don't really wonder anything about the moon."

Anyway, onward. It got better. I said by the end of class they would be able to predict what they would see when they looked up tonight, and know what the moon was doing on their birthday this year, and would know other days this year when there was a full moon.

They followed some instructions for entering values in a table and making a scatter plot on their calculator. Then sketched the scatterplot, and came up with a function to model it.

Then they were to use their calculator plot of the function to explore some questions:

- Which days in January had a full moon? A new moon?

(This would seem obvious from the table, but once they have an equation graphed, they forget all about the table! It's kind of weird. I put this question in so they could get their heads around what

*x*and

*y*represented in their functions.)

- How much of the moon is visible today? Discussion of how we'd have to change the calculator's viewing window to "see" today. Or what we'd have to plug in where in their function. Once we realized we needed to know today's Julian date, I gave them:

- How much of the moon is/will be visible on your birthday this year?

- On what days this month should we expect a full moon?

It might have started out slow, but by the end of class they were pretty animated. One girl noticed that there was a full moon on both of her parents' birthdays this year (before she noticed they were 30 days apart.) There were some different predictions for tonight based on the slightly different functions students came up with (some of them estimated a phase shift, some of them calculated it by various methods, and some of them pretended there wasn't one.) So, tonight they will look up and see if their model worked.

**Open questions:**

1. How to create a better hook/act one to prompt more and more interesting wondering questions? Or if anyone has ideas about realistic periodic functions that would be more grabbier, I'm all ears.

2. Would it be better to get an equation of the sinusoidal function by using the regression command on their calculator? More accuracy would take out some of the suspense "who was right?" but on the other hand, we'd have a more reliable prediction of what they would see tonight, and maybe if I was lucky a few kids would think that was kind of cool.

Question 1: Maybe if you use a video like this http://youtu.be/3tHVRS2vJi0 it could be more interesting than a table of numbers? I don't have video editing skills, but if you could overlay dates over the correct frames and then cut it off at a certain time, that would certainly "lead" them towards asking what it might be soon/now.

ReplyDeleteQuestion 2:

Do both. See if you can "beat the calculator." There are factors in there that just fitting a sine graph won't be able to do, so see if your method is actually better.

Could you plot the points using GeoGebra and have students use sliders to figure out the formula? You good have one graph which uses a sin function and another using cos with the same data...

ReplyDeleteI appreciate their honesty in their wonderings... It's a professional quandary for me and I vacillate a lot between these three poles:

ReplyDelete-It's good to have honest data about whether kids care about the moon or not; it's not my job to make them care

-It's my job to be more interesting, most of the time, than whatever else is going on around them, and get them curious about stuff, so I need to be as compelling as possible, with lots of videos and prompts relevant to their life, and whatnot

-I need to teach them how to be curious, to show them what math can do for them and invite them to have the kinds of questions math can usually answer (What will happen next? What's fair? etc.) so that when I show them cool stuff they get why it's cool

I suspect reality is at some center between those three poles, in which I would do just what you did -- find a situation that inspires mathematical wonderings in me, learn what it inspires in my students, see if I can make the mathematical questions therein more compelling, and help my students reflect later on the kinds of questions math can answer and challenge them to find more of those questions.

To answer 1, I like David's idea of using the video and overlaying key dates... and a low-tech version might be just to include as the last line of the chart something like "Ms. Nowak's birthday" and then kids might wonder things like "what's your birthday?" "what will it be on my birthday?" "how did you know what it would be?" That might help remind the kiddos that they don't have to stick to the dates on the chart and this doesn't have to be about the moon in the abstract, it can be about the moon in relation to stuff they care about & can witness.

PS -- this comment (& proof of my humanity) is brought to you by 55 nuctober. Thanks capthca!

This is exciting! I'm planning to do a moon journal as a background, non-mandatory project with my regular physics classes this year. How many do you think don't know that sometimes you can see the moon during the day? :)

ReplyDeleteDavid and Max, I like where you're going with the video introduction. I'm not sure I can make such a thing. Do you think iMovie can do that? iMovie is about where my video production skills top out.

ReplyDeleteMax, your three poles resonate with me. You articulate that tension very well.

Kelly - moon journals?

Damon - Me and the mobile lab are mad at each other right now. Even still, I think the slider idea would make it too easy. They wouldn't have to know anything, just trial and error until it matched. Of course, the regression function makes it ultimately easy, so.

Other periodic functions that are interesting (also available from the US Naval Observatory) is day length over the course of a year. It has a different period, amplitude, and vertical shift. The interesting part (I think) is the different amplitudes for different latitudes, and the discussion that can lead to. Also, the data from the USNO actually comes as sunrise/sunset times, so the kids have to do a little more work to come up with day length. It would be a nice sequel to the moon activity.

ReplyDeleteThat's the one I've been using for years. I like the idea of doing it for more than one location. (I've always just used the city my school is in.)

ReplyDeleteBut the moon project is so much more appealing, I think.

I love the video idea! I'd use this one and just add titles at the approximate dates, fade to black, and then just ask them the question "What is it going to look like tonight?"

ReplyDeleteThey don't always have to "wonder" the question that you really want to ask right?

BTW this is awesome! I wish I was teaching/learning this.

What a cool moon phases video, Timon.

ReplyDeleteWhen we've used Noticing/Wondering in classrooms sometimes we use the students' wonderings as the question and sometimes we reveal the full problem (the scenario and the question that we had removed). It depends on a variety of things, including timing and problem solving experience. I admit that in my Wooden Legs videos [http://mathforum.org/blogs/suzanne/suzannes-classroom-videos/] I gave them the question on the problem.

In other cases, though, we ask students to look through all of their wonderings listed on the whiteboard. We ask them, "If you had a test, which of these questions do you think would be on it?" I remember one time the students couldn't make up their minds and so we ended up circling 3 of the many questions. We said that for homework they should pick one of the three to draft some ideas so that they could come back the next day, work in groups based on which question they chose and talk about what they thought. If students get to the point that they do thorough wondering, this is powerful. Students definitely have buy-in and investment if the question they're working on is their own.

Moon Journals—Observe the moon every day. Write down some notes about it. Start to put together a pattern. Eventually, be able to predict when you will be able to see the moon and where it will be in the sky. See what other patterns you notice. Etc. :)

ReplyDelete