Opinion Changes

It's always nice and surprising how my first impressions of students and students attitudes in class improve (generally) as the year starts rolling. I guess they get used to a new teacher and how tests are given and what's expected of them. They get out of their summer mode of thinking and start actually doing work and coming in for tutoring.

So far I can think of these students:

"M" was twice absent on calculus test days. When he made them up, he complained about the difficulty and how I didn't give a formal review sheet (I told them what was on the test and they had old homework and answer keys to study). I told him that I didn't want to hand hold him, and if he needed to review, then he had to put out an effort. This last test he VASTLY improved his scores, and in class he's actually been participating.

"R" was goofy in class and talked talked talked. He was not doing well on precalculus tests. Lately, he's been coming in for tutoring and zeroing in on specific things he was having trouble with, and he's grasping things much better.

"E" has a surly haughty expression in calculus class and always seemed annoyed with everything I did. And yet, she advocates for herself: can you repeat that? can you wait a bit? can you explain that another way ("in English" another student pipes up). She really wants to grasp things, and now she has started cracking the occasional joke.

"M2" is STILL absent frequently in precalculus class and he's still constantly sleepy in class, but he makes up all his work and when he comes in for tutoring, he asks intuitive questions and has unique, clever ways of solving problems.

There are more, but I love as the year goes on how my kids grow on me.

Take 4

1st period/time through the spaghetti sine graphing activity:
me: read the instructions, they're clear, and you can follow them, and you'll be amazed at the results of graphing y = sin x without a calculator or ruler.
them: help. help. help. I don't get it. help. help.
me: running around helping everyone with the same questions over and over.

2nd period/time through the activity:
me: let me give you an overview of what you're doing here. overview. read the instructions, they're clear, you'll be great.
them: help. help.
me: running around helping.

3rd period/time through the activity:
me: here is a detailed overview with hand puppets and motions on the overhead of what you'll be doing. let me do it slowly and clearly. the instructions are VERY CLEAR. Read the instructions before you ask me any questions.
them: help.
me: I help. Class, ... so-and-so is now an expert on instruction 4. If you have questions on #4, ask so-and-so. ... So-&-so is an expert on instruction 5. Ask him/her.
them: so-and-so, help.
me: (nothing to do).

4th period/time through the activity:
me: (see 3rd time through) with the addition of: the instructions are VERRRRRRYYYYY clear. You'll be great. I expect great things from you. Did I mention that the instructions are clear? Here, look at my hand puppets.
them: help
me: (post-help) so-n-so is an expert on #4, etc. Ask so-and-so.
them: (scurrying over to student to get help)
me: (do dee do dee do ... nothing to do but walk around and watch them work)


oh! and a joke I read on You Tube:

What did "0" say to "8"? ..... "Nice belt".

Linear Speed Reteach

It turns out too many of my students STILL could not successfully work linear and angular speed problems. You'd see this look of abject fear in their eyes if you even showed them such a thing. While I was stressing about it one morning when I couldn't sleep, I remembered an old conversation with a science teacher that mentioned using little cards that the kids could manipulate and turn around and change one unit into the other.

I made up 6 little cards (I fit 4 x 6 on one sheet of colored regular paper) of approximately the colors above (color coded), and handed them out to the students. In about 30 minutes or so, we worked through 4 or so problems of graduating difficulty. At the end it looked like all of them could successfully switch from one set of units to the other. We'll see on Monday. Next time, with more prep, I may even have homework for them on this day!

My problems in order:
1. 200 in/min to convert to miles/min.

I made up some picture of me on a bike and what I was doing yesterday and had them write this down in their notes with a big space between the first and last statements. Then their pencils went down, and they were to pick the appropriate cards in the appropriate orientation to do the conversion, and "place them so I know you know what you're doing".

At first only 40% or so had the right cards in the right orientation. It was easy to walk around the room and spot check and ask if the inches canceled or if you got inches squared. Then they had to transfer that to their notes, and we discussed how how to put the numbers in the right places. Some kids still resisted writing the units, and they invariably put the "12" or the "5280" in the wrong places. We fixed that.

2. 10 mi/min convert to in/min.

Same process. This one was a kid's name riding a unicycle with the appropriate goofy picture. It also helped that the final answers came out really unrealistic - cause for more laughs and stories.

3. # feet/sec convert to miles/hour

Now there was some whining, but we talked about doing distance first, then time. They got it. (power walking? tricycle?)

4. #rotations/sec convert to feet/hour

(Human wheel like in cirque du soleil? Again a kid's name, and radius needed)

Anyhow, I think there was much joy in linear-speed-ville at the end. Hopefully, this will translate to understanding and accuracy on problems.

Never Assume

Two cases:

1. A student was asking me about a linear speed problem in precalculus, and in the problem statement I had that the radius = 14". When I was probing him for the units of circumference, he hesitated a long time, and I pointed to 14", and he said, "oh, that looked like 14 to the 11th power." I KNOW I didn't even mention the notation for feet (') and inches ("). I didn't think it would be an issue.

2. In calculus, a student came in to practice for our next test. We have just covered the quotient rule and the product rule among other things. He was asking me when we know to used the quotient rule, and I was taken aback. I asked him what quotient means, and he didn't know. And this has been about a week or so since we started it. I KNOW I didn't expressly mention that a quotient was a division problem. I thought it was obvious from the statement of the rule.

Notations in my planbook reflections for next year.

Memory Wheel

In calculus, we just finished learning the derivatives of the trig and inverse trig functions, and in the learning log, one student asked if we could make something to help memorize all the formulas. We had gone over some tricks in class, but now they're faced with the daunting fact of memorizing (gasp) 12 things.

I came up with making a wheel like the one above, and after a trip to a craft store for some card stock and some small (are they called?) rivets, I made the one pictured. I quite like it, and it wasn't too difficult.

Steps:
1. Use a compass to draw 2 different size circles on card stock and make sure to mark the center.
2. Cut a "window" out of the small "top" circle (I used cuticle scissors, but I guess an exacto knife would work).
3. Join the circles with a rivet (it was doable with a hammer).
4. I used a sharpie to write the functions on the outside circle. I could fit 14 things with my handwriting. It seems more are possible.
5. Write the derivatives (or whatever the answers are) inside the window as you rotate it around.
6. Voila.

Now let's see how much class time I want to devote to this, or how much I can make them do at home. Everyone has hammers, right?

Yay (Yeah?) Learning Logs

These are my "overhead projector" hands that cause lots of interesting conversations along the vein of "Ew. Take a shower, piggy."

I've tried the Learning Log for all my classes just once now, and I love it. I left 5 minutes at the end of class to quickly say why I was doing this (I get a chance to answer questions that may not otherwise be answered and I get a chance to "converse" with students that never say a word in class). Then I after I explained the procedure, they had at it, and I collected it before they left. It didn't take me too long to look through them and respond to everyone - either a "check" or smily face if there were no questions, or a "good job in class" message to the quiet kids who always do the right thing and are not squeaky wheels and who sometimes get ignored, or an explanation to answer their questions (either on the paper or on an attached large sticky note).

That day in trig we were learning how to "draw pictures in your head" to quickly without writing anything down be able to calculate sine and cosine of special angles all around the unit circle. And in calculus AB they were learning derivatives of trig functions. And in calculus BC they were learning implicit differentiation.

Here are some of the trig questions/issues:
How do you place 3pi/4 on the circle?
How do you tell when the answers are positive or negative?
Is your hair naturally blonde?
I'm still not getting the "quick" special angle calculations...
I liked learning the fast way to do this ...

Here are some of the calculus questions/issues:
Could we have more practice?
Slow down!
Do you always sprinkle dy/dx anywhere you have a "y" in an implicit function?
Is there a way to figure out "y" in an implicit function if you find dy/dx?

I'm hoping as this becomes more of a routine, more of the kids will use it effectively.

Learning Logs

Some of my students are still falling through the cracks of learning in my class, and they're not coming in for tutoring, and they're getting further and further behind, and I'm not catching it in time. I catch it after a test or after I send out official reports every 3 weeks. So I'm going to try something new starting this week.

In the last 5 minutes of class, they're to quietly read over their notes and process what we did that day. Then they're to fill out this form (enlarged and "weird" to get it in here):

I will collect them and respond and return them the next class to start the process all over again. Hopefully, this way I can nip some problems in the bud, and it won't be too cumbersome to grade since it's short and many of the students won't have concerns. Also, I can connect with kids I that never talk in class. I'm printing this sheet front to back and stapling 3 sheets together for a 6 weeks grading period.

We'll see how it goes and adjust as needed.

Learning Trig with Special Triangles