Author: samjshah

Sick again!

I was sick a couple weeks ago, before parent night. I recovered. I got a flu shot last week. I thought I was going to be in good shape.

I jinxed it. Now I’m sick again. I went to bed with a sore throat. I woke up sick. I hate teaching when I’m sick; all day I’m going to dream about lying in bed.

Rationalizing the Denominator, and Comment Writing

We get tomorrow off of school for “Election Day.” Translated, that is the day teachers at my school write narrative comments for all their students discussing their first quarter grades. We’ll all be holed up in our apartments, trying to come up with various ways to say “this student is doing great,” “this student is doing okay,” and “this student is not doing well.” Luckily, I’m pretty fast at writing these, so I’m not concerned.

In other news, I gave my Algebra II students a quiz last week, and one of the skills covered was rationalizing the denominator where there are radicals involved. (Multiplying the top and bottom of the fraction by the conjugate.) My three musings:

(1) Why do we math teachers care so much about this? I know it’s a good skill to teach because sometimes it really does simplify expressions, but do we always want to insist that the denominator is rationalized? I always thought that it was a bit dumb — and no one really has been able to justify why teachers insist on it with such vehemence. Any ideas? [1]

(2) Ummm… in Calculus, we’re starting to work on the formal definition of the derivative and guess what? To find the derivative of f(x)=\sqrt{x} using the formal definition, you have to rationalize the NUMERATOR. Harumph.

(3) For extra credit, for students who had some extra time after finishing their Algebra II quiz, I asked them if any of them could somehow rewrite the following without any radicals in the denominator: \frac{1}{\sqrt{2}+\sqrt{3}+\sqrt{5}}. Although no one got it, I loved watching them work on it. [2]

[1] My high school Algebra II teacher told us: “Why don’t we want radicals in the basement? BECAUSE THEY BUILD BOMBS!” I will never forget that. Love it. I totally use it. His legacy lives on.

[2] Even though I was horrified that some students’ initial step was to rewrite that as \frac{1}{\sqrt{2}}+\frac{1}{\sqrt{3}}+\frac{1}{\sqrt{5}}. Why is it that students NEVER understand fractions?

Water Pistols and Children!

A while ago, I posted about some interesting problems posed in the Technology Review magazine.

  • Jerry Grossman has equipped n children with loaded water pistols and has them standing in an open field with no three of them in a straight line, such that the distances between pairs of them are distinct. At a given signal, each child shoots the closest other child with water. Show that if n is any even number, then it is possible (but not necessarily the case) that every child gets wet. Show that if n is odd, then necessarily at least one child stays dry.
  • Each of logicians A, B, and C wears a hat with a positive integer on it. The number on one hat is the sum of the numbers on the other two. The logicians take turns making statements, as follows:
    A: “I don’t know my number.”
    B: “My number is 15.”
    What numbers are on the hats of A and C?

I submitted my solutions (click here to read my submitted solutions) and lo and behold, one of the solutions got published in the latest Technology Review (click here)!

Video about Fractals

It’s rare to come across math documentaries, so I thought I’d post a link to NOVAs new one on fractals:

NOVA: Hunting the Hidden Dimension

You can watch it entirely online. I watched it on PBS while lesson planning. It was pretty good. I’m not sure how much I buy the importance of fractals, or the arguments about fractals in nature, but other than that, I’m a fan.

Flummoxed! Or emotionally traveling back to my student teaching days.

Today was a really hard day, because it brought back a lot of the emotions that I had when doing my student teaching. Those days were long and exhausting, and I remember that every little thing affected me.

In those days, I took every student comment to heart. A student got upset after getting back a quiz and breaks down? A student got angry at me for reprimanding them? A student came to me crying about how her A- on a test will preclude them from ever going to college? A student talking to me with nothing but apathy even though they’re failing and won’t be able to graduate? I heard their voices bounce around my brain and my stomach would be all fluttery and I would just be emotionally in turmoil. It may have been a throwaway comment by a student — usually it was — but I carried it with me all day. Sometimes for days.

I needed to develop a tough skin. And, as the student teaching progressed, I did. (Although I needed to breakdown a few times to do it.)

Last year (my first year of full time teaching) I really grew that thick skin. I learned to put up with a lot of flak without students phasing me emotionally. Students really really like to test the boundaries of new teachers at my school and I felt like I dealt with that admirably. I still had days where they got to me, though.

This year I’ve been even more adept at dealing with students. One quarter has passed and I haven’t had that emotional breakdown yet. I think it’s largely because I’ve been even clearer and consistent with my expectations, and I don’t always engage in dialogue with students.

If a student doesn’t do their homework, I let them tell me their reasons/excuses, and then I say “Thank you for telling me that. I’m sorry but I’m still going to have to give you a 0.” Last year, I would engage with a dialogue about why I can’t and won’t give them credit. Last year, if a student asked if I offer extra credit, I would say no and justify my reasons. This year, I say “no” and point them to the course expectations handed out on the first day which states that I don’t give extra credit. Only if students want to have a discussion, in respectful terms, outside of class, do I go into that territory. But this year, as opposed to last year, I’m not the one starting the discussion.

Anyway, how did I get on this topic? Oh yeah, so I feel like I can keep a pretty cool head at school. I’m empathetic to students and my own emotions don’t really ever show through. But today, for the first time this year, there was a student in front of me crying. Because of… well… lots of things. But the point is: my chest tightened, I got all emotional and flustered, and his or her words were bouncing around in my head for hours as I played the situation over and over like a movie reel in my mind.

I felt the same kind of heightened, overly-emotional reaction that I experienced when I was student teaching. It is hard to go through the motions of teaching when you’re not steady emotionally.

I’m much better now, and things will be just fine.

Some fluffy part of me wants to say that emotion enhances teaching. But the more honest part of me is screaming: not being so invested in students emotionally might actually serve them better. I don’t mean that it’s okay not to care about your kids. But it’s okay not to get all tied up in their day-to-day feelings towards you, your subject matter, your policies, or your class. I think I’m not expressing myself right and I need to think this through a bit more to articulate it so it doesn’t come across harshly. But maybe other teachers out there have a sense of what I’m talking about? Keeping an emotional barrier between you and your students?