Holiday School Holiday Sandwich

We went to Idaho Falls, Idaho and Jackson Hole, Wyoming over Thanksgiving break. Here is a picture taken after the "lighting of the elk arches" in the town square of Jackson Hole. Apparently, there are vast numbers of elk that migrate around the area, and their antlers just drop off like matchsticks, and people collect them, and, hey, let's build 4 arches made of elk antlers to welcome people into the square.

We also hiked around the Grand Tetons for 3.5 hours, the first 2 hours of which were great, but then (no names mentioned) someone started getting hungry and cranky and did NOT want to hike to the 2nd lake because it impeded their eating schedule.

Now it's back to school, and I was cranky about that - just the rush rush rush feelings of "am I going to get everything done" and "will they successfully learn what I want them to learn", but then I get to school, and the kids are funny and it's good to see them and talk with them.

They are learning my annual fraction song, and today I quizzed them on it, and maybe we'll put it on YouTube because I think it would be a riot. I don't know if that's kosher to tape them and put it on there, but it's not kiddie porn or anything, and the students think it'll be a hoot, so we'll see.

Nonmath Moment

Last Monday in one of my classes a student asked, "if my dad dies in debt, am I responsible for paying everything off?". She was worried because apparently he has never sent child support and apparently has debt, and she didn't want to have to pay. Then my other students started piping up with, "yes you have to pay" in so many ways and how they were so sure that was the case and they'd discussed it with so-and-so and basically you were responsible.

Ew. I didn't know the answer, and we went on with our math. After class I looked it up, and no, you are not responsible, so I sent out a quick e-mail note to my students with the links just so they wouldn't stay under the false impression.

Well, I sent this via our gradebook program that allows you to just send notes, and one of the parents sends back: What are you doing looking into our debt? You shouldn't be teaching this! ...... So I sent back a note explaining the situation, and he calmed down, with no apology of snapping at me and assuming we were all going online and doing credit checks on parents and making big charts to show to the class. Oh my.

Continuity...(it never ends)

Blach! I'm having the hardest time getting the bulk of my calculus students to follow a (seemingly simple) recipe for proving continuity. Come on people, it's 3 steps. I've given you worked out examples. We've drawn pictures. We've modeled it with our hands. We've talked ad naseum about it. I made you write about it. Three steps! It's all I ask. Don't make me hurt you.

Identifying Coasters

I know I have kids in class that are polite and quiet and pay attention (or look like they do) in class, and attempt the homework, and yet are just not getting it. They don't come in for help. They don't ask questions in class. It's easy for them to just not be actively involved in the learning in class and coast and "pass" (though maybe not on tests).

I have various strategies when students answer questions in class to get everyone to participate: talk to someone next to you quietly about ..., help someone or have someone help you with ..., give me a thumb vote on the answer to ..., write down your answer to ____ and I'll walk around and check.

But as I'm walking around or waiting for them to talk to each other or ask questions, there are still kids "fake" doing it. So I debate whether to call them on it or not. I don't think I can do this every time and reach every student because the lesson has to go on and that seems like it would take too much time and maybe have a negative effect. Students can just look busy or look like they're working, and maybe they are, but they're not done by the time most others are done with the current task.

Today I was starting the calculus class, and we were going over homework on the "1st derivative test" to identify maxes and mins. I asked the class as a whole, what were the steps of doing the "test". The usual suspects started to answer, and I stopped them and did something I hardly ever do. I picked on a random student by name. "I don't know". I picked on another (making sure not to pick the kids that got it). "I don't know". So I stopped class and said, "look over your notes from last class, and I'll pick on random people to answer various questions about this topic". Well. That got the motivation up. Everyone was looking through their notes and discussing things with their neighbors and one student was so excited, "I GET it, it's this and this and this". Then I picked by name random students to answer the remaining questions.

I don't do that enough. I've gotten set in my ways and rely on the strategies I mentioned way above, thinking that everyone would get a chance to discuss and learn things before someone called out the answer, and I failed to notice that there are kids not participating too many times, and that it was easy to just sit and vegetate.

Helicopter Parents

I just read this term the other day, and then had an experience with it myself soon after. Apparently, these are parents that hover over their children and are super involved in their school and other activities and help run the kids' lives without letting the kids figure things out for themselves and make mistakes and learn and fend for themselves.

I just gave a 2 question, short quiz in calculus. I thought it was doable. The related rates problem involved a right triangle, so I expected the students to look at it and think, "hmmmm, right triangle, what sorts of equations do I know about right triangles" and then go from there. Well, oh my god, you'd have thought I asked them to prove Fermat's last theorem. One girl immediately started hounding me about it. Then after class she hovered and said that I shouldn't count that question as a grade. Then 20 minutes later I notice my message light is on for my phone, and it's her mother saying that E. was upset about the test and didn't feel prepared and could I please call her. Ewww. It creeped me out.

Cheating

I want my precalculus students to know (at least) sine, cosine, and tangent of all the special angles (at least) in the 1st and 2nd quadrants by heart and quickly. Therefore, I told them early last week that they will have a daily timed quiz with 14 questions that they know in advance, and they have to answer ALL correctly in a set amount of time. I took the 1st one with them and told them I'd double my time and that would be their time. It turns out they have 2 minutes for 14 questions. Doable. I keep giving them a pep talk. You can do it. It's not brain surgery. I'm not smarter than you, I've just been doing it longer. Study. You only need to be able to do each question in just under 10 seconds each. And so on.

They get a 0% until they get all right in 2 minutes, then they get 100%, and they can take it as many times as they need to in the remaining weeks of the 6 weeks. I've already had 3 kids pass in the first few days, and many are close.

Then there are those that seem to make no progress. They don't study for it, and they don't memorize (yet?).

Then there are the 2 boys I caught cheating with the weird "oh, let me look at my palm while I'm taking the test. What a fascinating life line I have." ... or "oh, let me look down at my lap, what a great leg I have.". I stared hard at the boys. I stood by the boys. I didn't say anything directly to the boys. They did not pass, and were nervous while I was standing near or looking at them. Why didn't I say something? But now I can no longer trust them. I also mentioned to my OTHER 2 classes about the cheating without naming names, and discussed how that was trust lost and very hard to earn back.

Blach. I should have a palm check before the quiz, or a stand up and let me look at your lap check. But how silly and weird.

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

Angular Speed

We started working on linear and angular speed, and I presented a few examples of what you would calculate and how to calculate, but some students still struggled. Today in one class this seemed to work. I was looking around for something familiar to link their knowledge to, and lo and behold, THE CLOCK. So I asked them to quietly ("let other people figure it out for themselves") find the angular speed of the second hand of the clock (I had to call it the "red stick" for the students that didn't know the term). "Ahhhhhh". Then we worked on the angular speed of the "long black" stick (minute hand) and the "short black" stick.

I also handed out colored paper that had a large unit circle on it (I bought it special for you at the store) and thin spaghetti (everyone gets one especially chosen for them). We worked on initial and terminal sides of angles in standard position. Then to start discussing reference triangles, I said that they were joining a math cult today, and every time we passed each other in the hall we had to repeat our special phrase: always drop the perpendicular to the x-axis. We practiced our cult voices for a bit. Then I assessed their reference triangle knowledge with the spaghetti. Hopefully, this will prevent students from drawing their reference triangles incorrectly as some have before.

Learning Greek

Last year in precalculus I had each student pick a Greek alphabet letter out of a hat, and they were to make a small (8.5" x 5") colorful poster with the capital letter, the lower case letter and the pronunciation of the letter. Then I hung those around the room, so we had a reference when we were using the letters as variables in trigonometry. I liked the activity, but then the students only got familiar, for the most part, with one letter. This year I made an "elementary school" type sheet where they have to trace over the capital and lower case letters 4 times each while simultaneously saying the pronunciation. They'll get bonus points if they can recite them all in order by memory. I'm liking this activity, so now I have to possibly make the letters myself because I still like them displayed. If anyone wants a copy of the activity, I'll send you one via e-mail (math_mambo@yahoo.com).

I'm also excited about my teacher website. Whoever suggested weebly.com and google calendars, Thank You. They were both easy to use and link together, and in just one weekend I created a usable site. I made it as a homework assignment for the students to have their parents visit the site and either send me e-mail or call that they did so. Yay technology.

Em(pi)nadas

We started trigonometry at the end of last week, and I know from past experience that my fraction-phobic students have trouble with placing pi/3, pi/4, pi/6, etc. angles in standard positon, so I tried something new this year.

I drew a semicircle (flat-side down) and made up some story that involved having and "em(pi)nada" for lunch and said it was so delicious that other teachers wanted to share it with me. I had them draw 4 em(pi)nadas and draw how they'd slice them in pie cutting fashion into 2, 3, 4, 6 equal parts to share and eventually they shaded the 1st piece (thinking of angles in standard position). They had no trouble slicing them equally, and I think it helped later on when I linked pi radians to 180 degrees, and they then drew pi/3, etc angles around the circle.

Then I introduced radians by first saying that for so-and-so's birthday I gave her a circle, and her mom gave her a string, and so-and-so was SO bored that she decided to do math by cutting the string the length of the radius, and she wanted to see how many times it would go around the circle. They were then to discuss how many times they thought it would fit. I got various responses, 3, 4, 6, 10... We finally got to the fact that you're just measuring the circumference. They then proceeded to equally tell me the formula for circumference was pi*r*r and also 2*pi*r. So then I had to sing them a song a student taught me, and then we all sang it together a few times:

Twinkle, twinkle little star
Circumference equals 2, pi, r.

Lovely (it brings a tear to the eye). We then defined radians.

Anyway, after I used my math tools (thin spaghetti to sweep out angles on the overhead), and we practiced placing various radian angles in standard position, we called it a day.

An interesting side note: another teacher friend mentioned a while ago how he linked the clock with the unit circle and that seemed to help his kids place 30, 60, 45 degrees more successfully around the circle. Well, I also brought that up, and in a side note, one student mentioned, "you know, I have a hard time reading analog clocks. I never learned, and now it takes me a while to process it."

Quick Assessment

Last week with about 8 minutes left of class, I handed out scratch paper that was cut into 4ths, 1/4th to each kid, and put 3-4 quick "pop quiz" questions on the overhead (3 math, and 1 "spell my last name" since they always mess it up and it eased the tension of a "pop"). They could use their notes but not talk with anyone. We happened to be studying function composition. I told them to write down the problems, show their work, and box their answers.

They took it seriously because it was for a grade. I liked it because I could walk around and scan their answers and see who was getting it and who wasn't. After a couple of minutes anytime I saw a wrong answer, I quietly mentioned to the kid that they should check that problem. That way, later I had an easy time to grade them, the kids felt better about the "pop"ness, and I then could concentrate on the 3-4 kids that I saw just weren't getting it and help them through quickly or suggest they come in for tutoring later.

Sleep Deprivation and the Modern Teacher

1. We were supposed to calculate (for a grant) how much extra time we spent after school last year tutoring students. So I figured on average I spent 3 extra hours per week at about 30 weeks that year. Wow, I calculated, I spent 900 hours tutoring! I rock (though apparently not at multiplying 3x30).

2. As the week goes on I get more and more sleep deprived (that's my excuse preamble for the following). I also daily wear my wedding ring that I never take off, and many other silver rings that I take off at night and put back on daily. So on Friday I get to work, and to my classroom, and I instantly feel and see that I have all my rings on except my wedding ring (of almost 13 years). Gasp! Oh no! Did I get too skinny (cough) and it slipped off on my way from the car to my classroom? I obsessed about it all day. That night, I went home and saw that it was in my ring tray. I don't even remember taking it off. I don't remember realizing it wasn't on all morning. I don't remember seeing it and sifting around it in the morning while I'm putting on my other rings.

3. I had this lesson that was working really well on symmetry of functions (even/odd/neither) on Friday (remember, in my defense, I'm TIRED), and I divided my overhead slide into 3 rows and would graph, describe, give the rule, and give an example for each type before moving on to the next type. I was running out of room on my slide, so I slid (tee hee) it over to the left and continued writing on the overhead glass to finish up the EVEN example. I then used my spritzer bottle and rag to clean the glass before moving on to the ODD example. I got through the graph, the description, the rule, slid the slide over, and then looked above at my EVEN example, and realized that, Oh no!, I forgot to give an example for the EVEN function, and here I am on the ODD example. So I start walking them through the steps of the EVEN example, and I'm patiently waiting for them to continue, and a student asks, "didn't we just do this?". Oh my.

I'm Scary

School has been in session for almost 3 weeks now. I've given my 1st test, and there have been about 5 homework assignments, and I've passed out current grades. Therefore, various students with low grades came in after school today to get tutoring to boost their understanding and their grade. I keep mentioning in class that I'll work with the students and they're welcome any time and if they make improvements from whereEVER they are in their understanding, they'll pass (or better) my class.

It's been my experience teaching precalculus and calculus that the students are finally, "oh, NOW I have to study to actually get a good grade. ... oh, NOW I have to actually do and do properly my homework ... oh, NOW I have to come in for tutoring to make sure I get it."

There were about 8 students in my room after school, and I'm circulating around, and I'm helping this one girl with domain and range. We were working through a problem. I'm prompting her for answers. I don't think I was rushing her. I paused and waited for her responses without any physical gestures of impatience or interrupting. At one point, as I'm waiting for her response, I could see she was flustered, and she said, "oh, I'm so nervous."

Wow. I didn't think I was that intimidating. My perception of myself and how new struggling students must see me are apparently not in line. I made a joke of it, "I know. I'm scary." and we went on. But it made me remember that just because I think I'm a nice and patient teacher, a student that's just meeting me for the 1st time and is struggling sees a different person.