We have finished all of the transformations for sine and cosine graphs, and soon I want to have an application day where they can write models for various data: blood pressure, tides, weather, oscilloscope readings.... but first I assigned them the following homework:
Think of a city in the world, maybe you want to visit, or it's exotic, or it's far away, or it's a place you have never heard of but searched for online. Then find weather data for a 12 month period for your city. We quickly logged onto desmos.com and they got accounts and we practiced making/plotting table data and changing window settings and such. They were to come back with their city weather data entered and saved.
The next class, we practiced on paper with "weird data":
I made them just draw a generic sine graph with no axes or numbers around it. I then prompted them for numbers, and then got (say) the "28" for the top x value and the max (71) and min (-31) y values. I made sure to wait until I heard things I wanted before I committed them to the paper.
Then they had to find the amplitude/vertical shift/horizontal shift/period. We talked it through and then got an equation. We did it again for a cosine graph.
Then we went on the laptops and they brought up their weather data. I asked them to do what we just did to find an equation that would model their weather data. Most importantly, YES they could guess and check, but it would be WAY better to think things through and come up with an equation first and some justification for the 4 key values as we practiced and then play around.
It made for some interesting conversations about "not normal" data points (I picked Timbuktu, Mali, and the year's data had a cold snap for 4 months that should have been hot) .... and about north of the equator and south of the equator cities (one student's data was warm in January and cold in August) ... and cities that were near the equator (all the temperatures stayed basically the same all year).
My Prague data worked out better than my Timbuktu data:
I have nothing to blog about, so here I go blogging. Isn't that how it works? Is there a point in every year/blog/person where you start to think of something to expand on and then go, eh, been done, not interesting, navel gazing, ....
Some things I've learned so far this year:
* My "if you want help, you need to ask for it" policy was NOT working for all kids. Shocker! In my mind, I was all, "You're 11th and 12th graders! Ask for help!" But in reality, for whatever reason (apparently, I'm scary??), there were kids that were just fine with sitting there in class or after school and being stuck but not asking for assistance. When I finally picked the brains of some kids, I got various responses: well, I don't know how to phrase the question specifically .... well, you were busy .... well, I feel you judge me .... etc. This has caused me to reevaluate how I run class. Now I purposely stop at each table and kid and ask how it's going. It seems that if I'm the initiator, then I get more responses.
* For precalculus, I have a 100% or 0% quiz I give to the students so they learn the values of sine/cosine/tangent of special angles in the 1st 2 quadrants. They initially have 2 minutes and 10 questions, and if they get any wrong it's 0%. They can take the quiz as many times as they want in a grading period. Usually, this is enough of a motivator for my groups of kids to study. This year, not so much. I had the idea of having MANDATORY 15 minute conferences with me about 2 weeks into the grading period. I made a sign up sheet that basically said: morning, lunch, after school with 3 name slots for each and told the kids they HAD to come in at some point in their time frame. I loved it. This allowed me to talk to kids that would NEVER come in for help. I could see how they were tackling the problems and give tips on speed and patterns and strategies. Of course some kids were already fine, so I could just validate their awesomeness in this arena and move on. I'm thinking of having such a mandatory conference for all my classes (on what?) and all my kids at some point in the year. Am I the only one that hasn't ever done this? Some things I like about it are that I talk to kids I may never talk to in class. I also get to see their thinking and pick their brains one on one on how they are doing. I also get reminded that they are humans and not math-receiving vessels.
* In AP Calculus AB, the learning opportunities NEVER stop. I hear my kids learning AFTER an exam when I make them come in to do corrections one on one. I see them learning when they go through my detailed answer key where I give them extra tips on how to do things and what to watch out for. I sense them learning when they are helping each other through hard problems. Yay math.
* Humans are prone to be happy AFTER something is over and they realize it was not so bad after all. I saw some kids that were in calculus last year, and they are unsettled with the math they are learning this year. They said they "missed calculus" and they were surprised. Hah. I take this more as, now that calculus is over and they saw they were successful, they want that comfort level again because they know how it turns out. Now they are in a new situation with a new teacher and it's an unknown, which everyone knows equals SCARY. I'm guessing next year, they'll be all, "oh, I miss last year's math class!".
* I'm turning 50 this school year. Oy! So that's occupying a large space in my mind. I've decided to make this a year of "trying new things". So far that has entailed going out to eat at DIFFERENT restaurants, ordering a DIFFERENT smoothie than usual, cutting all my hair off into a short cut not seen since 1985, .... that's it so far: food and hair. Go me.
Okay, maybe I did have some things to blather on and on about.