The goal of teaching LD students is to make information, etc., accessible, but there is a risk of becoming too eager to give “help” when these students struggle. The result is a cluster of students who plead for help even when they can succeed without it, who throw their hands up at the slightest sign of struggle, who demand assurance after every thought, who insist that the teacher stand beside them while they work, just in case.
Realizing that I could do more to discourage such dependency, I’ve adopted a new habit of stalling when certain students ask for help with their work. I protest that it will take me some time to finish what I’m doing and that they should solve the problem as best they can without me—even if they’re unsure—and that we’ll discuss how they solved it when I make my way over to them. Or, at the very least, that they should skip that problem and move on rather than sitting immobile, waiting for teacher.
Today is Presidents Day and I am home from work. I did some laundry, played piano for a while, watched last night’s season finale of Downton Abbey, and spent the balance of the day breaking myself in to Geogebra and reading math ed blogs. In the early evening I came across this post by Dan Meyer, What is Thirty Minutes Worth?, and I have an addendum to offer.
Meyer argues that personal time spent on planning lessons pays off in increased student engagement and teacher satisfaction. But as someone who tends toward anxiety, I can’t freely agree. Take today, for example. My online math ed research was highly educational, but the first fruits of my labor are a headache, a tense body, and an irrational certainty that I am irreparably damaging my students. This is not satisfying. The educational bit will benefit my students, but not the bit where I return from the break even more frazzled than when I left. Meyer spent thirty minutes shopping for glassware; in my current mindset I may have spent all evening shopping, re-shopping, and second-guessing the whole plan.
While I cannot freely agree with Meyer, I can agree with the caveat that personal time should be spent on work only in moderation and with care. I am a first-year teacher and no amount of eager planning or online research can turn me into a sixth-year teacher overnight. If I expect that it will, I will fail and my satisfaction will plummet. But if I expect that thirty minutes here and there can turn me into a better first-year teacher, I’m on track for success.
My forays into the math teaching blogosphere have moved me past the initial excitement phase (“Look at all the resources! All the ideas! This is going to be awesome!”) and into an overwhelming sense of inadequacy. To assert a dwindling sense of self-worth I’m forcing myself to come up with my own 3-act math problem. (“See, I can do it too!”) Stay tuned.
The experiment was a success! Students walked into class today asking to know what the inverse trig functions do (they phrased it as, “What does the negative-one mean?”), two students had reasonable theories to explain it, and one hit it right on the nose.
Before going over the worksheet, I teamed up the students for an activity where one student would write a sine or cosine value on the board, indicating whether it were a sine or a cosine; the next student would name one or several angles with that sine/cosine value and draw the angle/s on the unit circle. They were performing the inverse sine and cosine functions without knowing it. Later when a student attempted to explain his theory for the meaning of sin−1, he suddenly came out with, “I think it’s what we were doing on the board!”
Today I’m conducting an experiment in forethought. For homework I gave my trig students a worksheet with problems they don’t know how to solve (arcsine, arccosine, and arctangent) mixed in with problems they do know how to solve (sine, cosine, and tangent), with the instruction that they were to complete as many of the problems as they knew how. At the top of the page is a list of twenty-six possible solutions, of which fourteen are used. (You can find the worksheet online here like I did.) I hypothesize that two results will come of this.
First, the students will be frustrated about not getting clearer instructions and therefore needing to figure out for themselves which problems to solve.
Second, after seeing sin−1 sandwiched between regular old sin, cos, and tan problems with a list of possible answers, the students will come to class tomorrow with ideas about what sin−1 means . Some may go beyond having an idea and may understand it quite well. If so, my experiment will have been a success by allowing a little forethought on the part of the students to ease the introduction of a new function.
In a class of nine geometry students, I am assigned to work specifically with three tenth graders. They attend lectures and class activities with the other students, then typically leave to work independently or go over homework with me. This allows students in both groups to get more attention from a teacher, and provides me with a sort of teaching apprenticeship. The students, like their classmates, have learning disabilities that cause me to continually reassess what I think I know about how they think.
My latest realization is that I’ve been overusing the whiteboard. At the beginning of the year we introduced angles (acute, obtuse, right and straight) and I found colored markers a great asset as we practiced identifying angles on the board. The students enjoyed working problems on the board with such a small group and even grew comfortable enough to work on the board in front of the whole class when the groups were together. Based on that experience I continued to use the whiteboard each day, expecting that a good method in one case would be good in all cases.
Only this week I accidentally let the students sit down and get to work on their own without rolling out the whiteboard. They worked at individual paces, and I was soon circulating to answer questions on paper instead of addressing each question with the whole group. I was able to see how each student progressed from question to question and was pleased to find them frequently succeeding. Clearly the whiteboard is an invaluable tool but should be given a rest from time to time.