Monthly Archives: October 2012

Modeling Trig Functions — The Ripple Effect

I wanted to imitate “bringing alive a lesson” like so many other bloggers have done and been doing, so I’ve got this lesson idea that we’re going to do tomorrow for Precalculus, but I really need to get it set in my mind what we’re going to do, so what better way to do that than blog about it?  (Okay, yes, I could write a lesson plan, but I’ll do that after I have a better idea what I’m going to do…)  That’s one great thing that writing and (even more) following blogs has done to my teaching: I’m now actively looking for connections to phenomena in the real world and tying it to what I’m teaching in class.

I had some students help me create the following video by shaking an extension cord up and down (using the super-nice high-speed camera that my principal got our Physics class!).  We get a nice transversal (why does spell-check not like the way I spell that word?!) wave out of the following video, and we’ll warm-up by freezing it at some point and finding a function to match the image.  I’ll probably try to use Geogebra to show the students the results of their hard work to obtain an equation.  I’m going to try to stick to Dan Meyer’s advice: “Be less helpful”.

So I have several videos I created trying to get “the perfect wave” from water.  First I tried a small “tank” and then finally got brave enough to pull out the big fish-tank that’s been empty for what seems like ages.  Still couldn’t get a very pretty wave, and I’m a bit worried about having to explain transversal vs. standing waves to the students because this is Precalculus, not my Physics class, but regardless, I can still pause the video and have students work on a specific wave. I’ll use one part of one of the following videos:

The goal is to move the students to modeling what happens when you throw a rock into pond.  I’m hoping students will want to test different things like rock size, shape, strength of the throw, etc.  I’ll probably also convince the students that it is very important to tie a string to their rock so that they can retrieve it easily (hehe).  If I can get a video of how goofy they look, perhaps I’ll post that in a followup.

Then, if we still have time, I’m hoping to wrap it up with sound waves, leading to the technology behind sound cancellation.  The sound waves alone will take a long time just to explain, so maybe that’s next week’s lab.  Wow, we are way behind where we were last year in Precalculus, but the students have gotten so many more authentic experiences, and I really think they understand the material better at this point in the year.

Oh, and I called this post the “Ripple Effect” not only because we’ll be observing ripples, but also because I am hopeing to be a contributing part of the “ripple” of teaching who are blogging and teaching/learning from each other.  I have definitely  benefited from other teachers’ blogs, so thank you!

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Parent-Teacher Conferences

Had conferences with parents this past week, and they went alright, considering how exhausted I was.  I like how our school does conferences: there are two days where all the teachers are set up at tables in our gym from 5pm to 8pm and parents can come in and can go find all their child’s teachers in the same close proximity.  Usually it is the case that the parents you need to see don’t show up, and the students who are doing fine have very helpful parents where the conference goes a bit like this:

Me: Well, your child is an absolute pleasure to have in class.  Thank you for having he/she/it at this school.

Parent: Thank you, so-and-so says he/she/it likes your class as well.

Me: Thank you.  I look forward to continuing to work with your child.

The End

Fortunately a handful of parents showed up where their child had F’s, and in every single case, they were thankful for “how many opportunities I give for their child to succeed and he/she/it is going to work harder in the future.”  I believe most of them.  I also exhausted my supply of oxygen explaining participation points, but I think it was worth it.  Here’s the sheet I handed them, which was also hopefully helpful:

I even received very positive feedback from the one parent who sent an angry e-mail just a few weeks earlier.  The parents got on my side once they realized that “Participation Points” were not a subjective measurement and it was simply that their child was not doing work outside of class.

Just curious if other people have more advice for parent-teacher conferences, from experience.  I always try to include something positive the child has been doing and really try to demonstrate that I have a personal knowledge of how much effort their child is putting into my class.  Anecdotes are always bonuses.  But the thing that really helped this time was pointing out, at least for every student with an F or a low grade, at least 3 different ways their child could be doing better, and I hope that the parents truly follow up, as I believe most will.

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Crazy Juggling

Just saw this video online and want to use it:

Not sure how yet, but I think I’ll use it when we get to forces in Physics.

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Cutting a Deal with my Classes

I was disappointed with how poorly my students did on their recent Tiered Assessment quizzes.  In order to get a 0 on these things, you basically have to flop every single problem.  And yet, one of my class’s averages were 75, 45, and 57 on three quizzes they took Friday.  Somewhere over the weekend, I had an idea: I told them that they would have a test on this material next week unless they could raise the class average to over 80 for all of these quizzes through retaking the quizzes.  This was especially effective telling them right before sessions (which are one of the best things I’ve gotten from other teachers’ blogs, and that’s saying alot a lot!), so they were invested in each other’s success.

And the best part is, the quizzes already covered all the material, so they wouldn’t be tested on any new material–instead they are retaking the quizzes and studying for them in hopes that they don’t have to retake the test.  All the while, helping each other study for it and learning as they strive for this.  It’s a win-win-win situation!  Now if I could just get them to think critically…

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Ferris Wheel Fun — Intro to Sine Graphs

I watched Dan Meyer’s TED talk again (here it is you’ve somehow not watched it).

And I was inspired (again) to make better lesson plans.  I really was fascinated how he mentioned that “this is what I do during my 5 hours of lesson planning during the week”.  So I sat down and looked at the book’s introduction to sine waves in Precalculus and decided to create a more fun intro to that.  Here’s what I came up with:

First, I showed them this neat Youtube clip:

My students really appreciated it because it has sounds from (I think) transformers in the background.  Then I asked them “so what’s the largest ferris wheel?”  After blank stares, I showed them pictures from the Wikipedia of the Singapore Flyer and showed them this video.  (We talked briefly why there’s a floating field in one of the pictures… space issues in Asia are always fascinating to students who live in the middle of no-where New Mexico.)

So next, I told them that a small child walked up to them and asked “How far above the ground are we?” (I was going to ask “How high are we?” but I thought that would induce too much giggling.)  I didn’t give them any other information (inspired by Dan to “be less helpful”).  Eventually I had to lead them on and say “okay, suppose it is 20 minutes into the ride”.  They asked for the height of the wheel, which I gave them (165 meters) and they asked how long it took to go all the way around (30 minutes, according to Wikipedia).    They also asked for other things, such as “what’s the diameter?” (some students said  165m, “duh!”) or the speed or acceleration of the “barrels”, which I didn’t give.  (Perhaps I should have given that info to them and let them sort out what was important?  Oh well, they actually had enough info to figure it out, even though it was irrelevant information).

I didn’t realized this beforehand, but requesting that “20 minutes have passed” (out of 30 minutes) actually gives you a 30-60-90 triangle, which we had just learned about, so I was excited for them to use that knowledge.  I was impressed by how quickly some of my seniors figured it out and were happy for them to present their findings to the rest of the class.

Overall, though, I was somewhat disappointed by how slowly my 1st period went (the Seniors), but as disappointed as I was by 18 seniors, I was even more excited by the 4 juniors (yes, half the class was gone for various school functions) who got as far as the seniors did in 10 minutes, AND were able to come up with a generic formula for the situation!  Here’s what they discovered:

h = \sin(360 - (90 + (\frac{t}{30})*360))*82.5 + 82.5

Where t is time and h is height above the ground.

They discovered this before knowing anything about sine graphs.  They have no idea what amplitude, period, phase shift, or the sinusoidal axis means!!  Isn’t that awesome!?!

So yeah, I was pumped, and when the bell rang, even my good math students stated “woah, that was a short class!”.

Take it, use it, let me know what you did differently.  One thing I would have done differently, especially for my seniors, would be to have the students make guesses beforehand.  That would make students, as Dan states, “buy in” to the problem.  It would also help significantly with their intuition once they arrive at an answer.

Next, I’m going to be making a Geogebra file which shows how the height changes over time.  I’ll share that when it’s done.

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Awesome xkcd Exploratory Activity

So I read this post about teaching Calculus students using a date-able range xkcd comic, and I thought “awesome, this has functions, inverses, several domains and ranges (several functions), slapped together with some good old internet research and important technology skills (Excel, Google docs’ spreadsheets), all rolled nicely in a topic that captures HS’s attention.”

So I did this in Precalculus today, during our block (1 and a half hour) period.  One class started awesome and tanked, the other class started even better and soared.

Class 1 are the seniors, so no super-special math ability, but they’re not “bumps on a log”–they’re bright when they are motivated, and I think they were motivated by the questions that arose.  Unlike Mr. Cornally’s class, I had to prompt them with questions like “what do you think, is this reasonable?”, otherwise they would have just stared at me.  However, I was proud how they went in the right direction and some even realized it was an inverse!  Awesome.  When we finally got around to using a Google docs’ spreadsheet, I knew they’d goof off at first.  “Hehe, I just typed so-and-so stinks, hehe.”  They’re seniors; what can you expect?  So I decided beforehand I’d give them 5 minutes to get it out of their system.  However, that wasn’t enough time and they kept going with the dumb comments, so I was very disappointed in their lack of maturity and interest in the problem.

However, my second class, who are juniors, and therefore a bit faster on the uptake, ran away with the problem immediately.  One of my more socially awkward students (he knows he is, so that’s okay) exclaimed “this is important for me to know!”.  What’s awesome is they got this by the end of the class:

Yup, that’s in Google Docs, although I showed them the final step of selecting “Make Graph”.  Still, I was proud of them and they seemed to want to continue this project.  I don’t want to devote a ton more time to it, but perhaps I’ll make it worth a fair amount of participation points and they can have some awesome conclusions about it at the end.

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Teaching Class Without Talking

So I read this blog post from a teacher about how she taught for an entire class without speaking.  I’m not talking about giving a test or lab and sitting back, but actually running a class, where students are taking notes, answering problems, and interacting with me and with each other.  I accidentally tried it today and it was awesome!

Sorry that I can’t give you credit, whoever you are–I looked for your blog post, but couldn’t find it.  Please comment if you are the one who tried this so I can give you credit!!

It actually started accidentally–students were finishing a quiz, and I wanted to start teaching despite not everyone being finished.  I first put some problems on the board, and then got the students to begin working on them silently.  Towards the end of class, I was showing them how to do the problems without speaking (simplifying radicals), and since it was only the last 5 or 10 minutes of class, students commented “Mr. Newman, you should teach a whole class without talking!” so I told that I’d “think about it.”

Well, the very next class was a continuation of what we had started, so it just made sense for me not to speak as they did the warm-up.  Not only was it really fun, but students had to really think for themselves. They didn’t beg me to talk, they simply accepted that I wasn’t going to talk.  If they had a question, once one student understood the concept, I would gesture for that student to share what they learned with the class.  One by one, students began getting the concepts, and reinforcing those concepts because they were teaching each other as I put more and more problems on the board.

The only drawback was the one students who didn’t do as well, and it is because she is a big note-taker.  She’s a great student, she’s just not good at math (yes, there is a difference!): I know she goes back over her previous notes until she understands the information, but she doesn’t pick up information quickly.  Therefore, by the end of class, she was lost, although I hope her notes were complete enough for her to put the pieces together later.

I also had a lot more energy at the end of the period.  I think that when I teach, especially to that class, I get excited easily, and so burn up all my energy talking faster and faster.  I felt like I had plenty of energy to keep working during my planning period immediately after that class (which doesn’t always happen…)

I do not think I could do this with a class like Chemistry, but this Precalculus class was just the right combination of bright students who know my mannerisms well enough to get when I’m trying to communicate something, as well as a subject where you can put problem after problem on the board and have students learn and I increase the complexity of the problems.

**Edit: Here’s a link to one wonderful blogger who preceded me in the “silent teaching” idea.  Much thanks to her and others who helped me have such a fun day in math class!


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