Author: samjshah

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.

Credit Goes Where Credit is Due

I know a lot of people have a lot of things to say about Dan Meyer.

What I can say is that he was the first teacher blogger — though now my blogroll is much longer — who kept me inspired and chugging along in my first year of teaching. (Wow, I’m already writing like the year is over… and we have one more month to go!)

Which is why I can’t but be thrilled for him becoming a winner in the Cable’s Leaders in Learning.

Kudos Dan Meyer! (Hat tip to Dangerously Irrelevant for spreading the word.)

A Scholastic Journal for High School

The high school I teach at has a student-run newspaper, yearbook, literary and art magazine, and even a foreign language publication! One germ of an idea that I had months ago has recently become something I have gotten passionate about pursuing: an online academic journal. (Open source journals exist.)

Seriously.

Think about it. Students pour their heart and souls into research papers. Okay, let me rephrase: some students pour their heart and souls into research papers. These papers are usually only read by their teachers. I think having a yearly, online academic journal for my school could really be a blessing for students and teachers alike.

My vision:

5-8 students and 2 faculty members will be the editors of the journal, which will initially be published once a year. Upper school students will be encouraged to submit year round any non-fiction pieces they’ve written and are proud of. This includes research papers for classes, papers they’ve done for independent studies, or excerpts of their senior theses. I would expect that most of the papers would come from English or History or Art History classes, but I think that research papers are written in both the Chemistry and Bioethics classes. Also, students working on investigative problems in Math Club could submit. Basically any non-fiction piece written by a student would be eligible for submission.

From the student perspective, the journal provides an outlet for students to shine, and showcase work that they’re particularly proud of. Plus, it feels good to have good work acknowledged. It’s too often that we forget to praise the good, and so often that we focus on the bad.

From the teachers’ perspective, an academic journal could act as a pedagogical tool in at least four different ways:

  1. Teachers could recommend that students submit their papers when they have done a particular stellar job. Positive reinforcement does the trick, yet again.
  2. It could also act as a way to get students who did well on a paper to ask themselves “how can I make this better?” before submitting to the journal. It sets a higher bar of expectation for students.
  3. At the same time, creating an archive of strong research papers could provide a set of exemplars that a teacher could direct students to. (“If you are wondering what a strong and narrow thesis statement looks like, see this paper written by StudentX on Invisible Man.”)
  4. The editors’ discussions over which papers to admit and to reject will not only expose student work to people other than the student and the teacher, butit will also force a critical analysis of student work. In other words, the discussion and scholarly debate that will revolve around this publication itself will be a great learning experience

Lastly, this type of journal, allowing non-fiction pieces from any department, would be the first glimmers of cross-disciplinarity at my school, where departments are independent islands which each reign supreme.

Certainly there are kinks that need to be worked out. But to me, in my vision, the benefits far outweigh the costs [1].

[1] This is intended to be a bit of an exceedingly weak pun, because actually, the monetary cost of the journal is negligible, since it will be an online journal.

Update: After reading this post, I really want this journal (if it ever comes to fruition) to have its name change with every volume!