End game

I had the end game in sight. I carefully planned out all my Algebra II classes so that we could learn the very basics of matrices and systems of equations, and have one last quiz on them, before the school’s official “review days” kick in. (No assessments during those days.)

Everything was peachy keen.

Until I learned that, oh, yeah, the school was taking away one of my classes and giving it to an Academic Awards Ceremony. Which is fine, I can deal. But that’s one of those things that get slipped through the cracks in terms of “let’s tell new teachers that the awards presentation is during class!”

The point is, everything had been planned out. I had dotted every i, crossed every t. (The jots and tittles were there, I swear!) Now with that class given up to the awards ceremony, everything gets totally screwed up in terms of teaching. It’s not just missing that one class, but it’s a perfect storm. One consequence is that, get this:

there will be a stretch of 7 days (that’s including 2 weekend days) that I don’t see one of my Algebra II classes, due to something or another.

Let’s go through them in order: there’s the one day that week we don’t meet regularly (rotating schedule), there’s a high school field trip day, there’s the awards ceremony day, there’s saturday and sunday, there’s memorial day, and there is registration day.

There are other issues, in terms of the quiz I was going to be giving them. Normally, this is all no sweat. I roll with the punches, I can jiggle something here and finagle something there. But in end game mode, you have nothing to adjust to make everything work. I’ll pull a Tim Gunn, and it’ll all play out nicely. It’s just annoying that I have to pull a Tim Gunn in the first place.

As an aside, sorry for all the metaphors, or whatever I’m doing (“roll with the punches,” “end game,” “jot and tittle,” “perfect storm,” “slipped through the cracks”). I don’t know what’s wrong with me.

Calculus Projects! Or, How to Combat Senioritis.

The year is coming to a close and I’ve found something to entertain my seniors. They’re taking regular calculus. More than likely, most of them will never take a math class again. If they are going to take math in college, chances are they’re going to be taking calculus over again (I don’t teach the AP calculus classes at my school).

My school treats seniors with the deference that seniors think they deserve. They don’t have to take final exams, they don’t go to classes after May 22nd (don’t ask), and they miss a lot of May to AP exams. All in all, because of these restrictions, May is pretty hard to plan, if you teach a senior class.

I gave my last quiz recently, and I’m having students use their class time to work on a calculus project.

I only have 7 students in this class, so I decided to do something pretty radical. I pretty much gave them free reign on their project. I told them they could do anything they wanted — just as long as they’re passionate about it. They have to do something they’re going to enjoy doing. They could also choose the point value of the project (a large quiz grade or test grade).

At this point, the only way I’m going to get them to do anything is by tapping into things they like.

So I had them brainstorm, we met individually so I could guide them, and they’re off to the races, with some great projects:

  1. One student is doing a study of Newton’s method (we didn’t cover it in class) to find the zeros of a polynomial. She’s going to compare whether Newton’s method to finding zeros is “better” than a more simplistic method of finding zeros. That method, in case you were wondering, has you find an interval where you know there is a zero (e.g. for example, say you know there’s a zero on [-1,1] because the function is negative when x=-1 and positive when x=1). Then you divide the interval in half (into [-1,0] and [0,1]) and you find which of those two intervals has the zero. Then you divide that interval in half, and find which of those two intervals has the zero. On and on and on…
  2. Another student is doing a study of rainbows, which involves calculus. (Awesome resources here and here.)
  3. Another student really liked learning the intuitive version of the chain rule that I taught (post one and two), and wanted to make a lesson for my students next year on that! So she’s making a video tutorial and worksheet to accompany it.
  4. In the same spirit of teaching, one of my students wanted to do something similar by making a video tutorial on the formal definition of the derivative.
  5. One student is taking AP Physics B, but throughout the course, has noted connections between what he’s learned in his non-calculus-based physics class and what we’re doing in calculus class. One connection he made was between Pressure, Volume, and Work. He (rightfully) noted that W=\int P dv. So he’s going to be making a presentation on this relationship by doing a bit of research and bringing application to the class.
  6. Another one wanted to learn something “new” so I suggested he do some research on a hanging string. More notably, if you hold up a string (like a necklace), it will hang down due to gravity. Surprisingly (or not?) the shape is not a parabola. It turns out that it’s this funky shape called a catenary. He’s investigating why that’s the case, and how to derive the formula.
  7. Last but not least, one of my students had difficulty with the sections on surface area and volume, because she couldn’t visualize the regions/spaces being formed. So she’s making two mechanical thingamajiggers out of wire. You bend the wire to be whatever function you’re going to be rotating, and then there’s a handle that rotates the wire. I am so excited about this one — I hope it works out so I can use the model next year in class!

6MMM^3

The 6th Monday Math Madness is online now. This week is actually not so hard, even though there are two different problems… I was able to get both of the answers in about 30 minutes (assuming I didn’t make any huge errors). I especially like the first question, because it can be easily transposed into a slightly more difficult and fun problem…

The first question reads:

  • Start with 500 gallons of mayonaise.
    1) Mix in 10 gallons of ketchup. Stir until completely mixed.
    2) Remove 10 gallons of the mixture.
    3) Repeat steps 1 and 2 until the mixture is approximately 50% mayonaise and 50% ketchup.How many iterations will it take to do this?

Here’s the slightly modified problem:

  • Start with 500 gallons of mayonaise.
    1) Mix in 3 gallons of mayonaise and 7 gallons of ketchup. Stir until completely mixed.
    2) Remove 10 gallons of the mixture.
    3) Repeat steps 1 and 2 until the mixture is approximately 40% mayonaise and 60% ketchup.How many iterations will it take to do this? 

That slight change makes it more difficult! But fun fun fun!

Two cows are in a field…

In math club this past week, we didn’t have anything to work on explicitly. So we just made up a problem, based on a problem we encountered in the previous week.

Without further ado, here it is. You have a circular field, enclosed by a fence. Two cows Antonio and Barry graze in the field. They are each tethered to some place on the circle, tied with ropes of lengths r_A and r_B respectively.

The problem is: come up with a formula for the area of the region that both cows can graze together.

I love that we came up with the problem, and that we’re exploring it ourselves. It’s great that it’s so simply stated, and that it has a pretty tough solution. I love that it’s a generalization of something we did earlier. And I love that even this problem can be generalized further (e.g. we have n cows).

What we did in 15 minutes:

We know we’re going to have a piecewise function of three variables. To start the problem, we make the circle a unit circle, we place Antonio at the point (1,0) and we place Barry at (\cos \theta, \sin \theta).

By the end of our math club meeting, we had one part of the piecewise function f(r_A, r_B, \theta). We found where there would be no overlapping grazing area, where the function would be zero.

I have some sketches of the problem and the bit of solution we got together. I’ll put them below in a bit.

College students might just take the cake

So I got a rather strange email from a parent yesterday, but one of the problems of blogging under my own name is that I can’t quite go into specifics about things like this. But the point is, it made me wonder what the parent could possibly have been thinking to send the email.

With that said, what’s clear from reading the blogosphere is that teachers put up with a lot of strange requests. My favorite place for reading that sort of stuff is on Learning Curves… which aperiodically posts the warped way his college students think about school and grading and fairness.

Which reminded me of being a Teaching Assistant for a number of history courses at UCLA.

I too had a lot of strange requests and goings on… so I comisserate.

An email I sent a student:

  • I am your TA for History 3B. I noticed that you turned in your midterm essay for the class. However you have not attended any of the discussion sections, nor have you turned in any of the weekly reader responses. If you are still planning on taking this class, I think you, me, and Prof. [Professor] need to have a meeting. (I can’t see you passing the course without attending section.)

The students response started

  • I see I’ve been caught. I’m not sure how to respond.

Emphasis mine. That’s one of my favorites.

Another one of my favorites (I have a million of them):

  • I just wanted to ask you a few questions concerning my grade. How far was I from getting a B-, I received a C+ in the course? I would like to mention that I had to take two finals back to back the day of the final. I would also like to mention that I had spent the majority of tenth week and half of my finals week working on a project for my aircraft design class. It was a group project that entailed the design of an aircraft, a presentation, and the review of another group’s project. Like all of the groups in that class, we didnt get our work done until the last minute. As a result, I only had 1 and a half days to get ready for two finals. I was very stressed out those last few days of finals week with all the work I had to cover. I only ask that you please take this into consideration.

If these sorts of things were isolated cases, that’s one thing. But these emails aren’t. And that makes me wonder what they are thinking when they send an email like this, just like I wondered what that parent was thinking. What they think education is, college is, grades are… Because clearly they live in a world totally different than the world I inhabit.

Conclusion: I’m so happy to be teaching high school students.

I wanted to go AAAARGH!

Disclaimer: I don’t intend this blog to be centered about whining. I want this blog to be about practice, about ideas, about improvement and reflection and archiving my first years of teaching. That being said, this post is written by someone (me) who is temporarily frustrated. The good thing about me is that after frustration, I usually come out on the other side stronger. I try to turn my frustration into something productive. That all said, onto the whining!

Here I am, about halfway through our fourth and final quarter, and I’m teaching a gaggle of tenth and eleventh graders about trigonometry. And we’ve been working with radians and reference angles for a long time now. They should be second nature.

They aren’t. I am so fed up with trying to use this book to teach trigonometry that I might just scrap it and design my own homework, and organize it my own way [1]. Heck, I’ll just write my own little book on trigonometry for my students, focusing on the skills that I need them to know.

It’s clear that the students have lost the big picture for trying to memorize procedures without knowing the concepts behind these procedures.

The hard part about being a teacher is that even though I may sometimes decry my students in a moment of panic, I blame myself. I assume every student is working hard at home (if they tell me they are) and then I have no one else to look at, except in a mirror. And I know, I know what you’re going to say: “Thinking in terms of blame doesn’t do anyone any good.”

But it’s my way of keeping myself on my toes, always trying to do better, and figure out what I did wrong. It’s also highly depressing, and leads me to periodically question if I’m a good teacher. Ahhh, to be blessed with the endemic uncertainties that comprise a first year teacher…

It gets hard, though, when I feel like I am on an uphill battle, given a Sisyphean task.

The catalyst for this post? All of this stems from a whole bunch of students in my Algebra II class who asked today why I claimed \pi + \frac{\pi}{3}=\frac{4\pi}{3}. And then a whole bunch of others who didn’t realize \frac{1}{4}\pi is the same as \frac{\pi}{4}.

The really frustrating thing about this is that I saw fractions were a problem when we started trig, so I gave a review worksheet on fractions early on in our trig unit. Clearly, I am going to have to start earlier and come up with a different plan of attack than just a worksheet.

Did I mention that I wanted to go “AAAARGH!”?

[1] I did a bit of rearranging and lo and behold, my students did extremely well on that assessment. It could be that the topic is easy for them, but I don’t think that’s it.