I’ve found it useful to give junior PreCalc H students time to work together on take home “exams” in class because it builds some fantastic community and teamwork skills. I instituted new rules to their work: Non-permanent work only. If they work on paper, it has to be tossed. No pictures either.
My thought process is that when they go away to write up the problems that they worked on together, there will be some good things going on in their brains to try and rethink the (upwards of) 20 moves that had to be made to solve these problems (IB questions). What do you think? Does this idea have any basis?
This activity also stands in nicely for a trig review thing that I used to do quite differently.
This post is mostly for myself, but maybe there is some value for you too (isn’t this the case for all blogging)?
I gave out this 2nd quarter feedback form to my Precalc honors and AP Calculus BC classes:
My comments will be in italics. The rest will be verbatim or summarized.
Similarities for Q1: What activities/methods/strategies have we done in class that have worked well for you?
- Standing Groupwork on Whiteboards (HUGE positive response here. Loud and clear, at least for those who like it.)
- (PreCalc H) Take Homes (they enjoy working together on tough problems. The students actively liking this is a new one for me, I think it’s because I’ve given more classtime for these takehomes).
- Marbleslides (A set of Desmos activities) (We didn’t do many other Desmos activities this quarter, the topics didn’t warrant the need.)
- Writing down examples in notebooks and having the classnotes in a shared google drive. (There is a significant group of students who would rather work on paper than whiteboards, I’d put it at 1 in 5 students. They find some solace in printing out my written notes from the tablet, or at least having those notes available, but I think they’d rather do everything on paper.)
Similarities for Q2: What activities/methods/strategies have we done in class that have NOT worked well for you?
- Writing more things down in notebook (This is nicely paired from the last bullet in Q1)
- Seated Whiteboards (They really do like the standing aspect!!)
- Desmos Activities (This was a small amount of feedback, but they had some great points. A lot of their feedback is talking about my custom activities, so this is not a shot across the bow for Desmos, only for my custom activities. Quick take: I think I make them too dense for some students. There is a high load that they’re being asked to lift on some of these, and there are students who don’t thrive in that environment, depending on the timing of the activity and their (random) partner).
- Not going over homework consistently (Yep. Not too much volume on it, but it’s dead on. I think their volume was turned down because I figured it out in December and have been improving on it in January).
Similarities for Q3: What can we do to help you learn better in this class?
- Scattershot mostly, but hand back work quicker. (Yep.)
- Some requests to slow down. (This is a hard one. I know where we need to be to put the majority of students in a good spot for May of their senior year when they’ll take the IB or AP exam. I don’t have a great response for this. Do you?)
Excerpts from Q4: Anything else you want to say about class to me? Suggestions?
- I enjoy the music keep that up.
- I love whiteboards and take homes!!
- It would be nice if reassessments could be done on other days than just Thursday or during school study halls.
- I really like this class. It is fun and interactive. Cool music btw.
- I enjoy doing whiteboard work and take home work in class.
- Nothing additional other than stand is great.
- Love the background music when we work.
- Great learning efficiency, but sometimes comes with dreadfulness from repetition or notes.
- Its actually quite enjoyable
- Are there any good videos to explain some of the methods? Even if they were just linked to classroom that’d be good.
Hey teachers, if you don’t do some sort of feedback form, consider it. Some fantastic feedback, a nice mix of stuff for me to chew on, and some nice motivational stuff from what is working well too.
I often like to wing it when coming up with examples. I like the messiness that occasionally happens. We had 3 different answers for the length of the missing side. Their homework? Find out which one was correct (spoiler alert: none!). What a great accidental lesson.
We tried something different today in Precalc H. I gave the students 8 minutes to work by themselves on the feedback quiz by themselves, and then 4(ish) minutes to work together. These are difficult topics, so I wanted them to know where they stand (the 8 minutes should give them a pretty good idea), and then I wanted supports built in (the 4 minutes of partner time). We went over questions and the key after these two sessions. Worked well, would do again. Two thumbs up.
Very short post just noting that solving trig graphs with technology like desmos. Without prompting they are using restrictions to cut off the part that is unnecessary (pretty sure they learned that from marbleslides). Good stuff.
We covered the midterm exam today (40 multiple choice) in groups today. They knew their grade but not which problems that they got right/wrong. In groups of 5 problems, they tried to find the correct answers, and after a couple minutes of discussion for each group questions, I gave the answers and showed solutions for those who had questions.
Worked quite well. Lots of natural discussion and students helping students.
Next the students worked on finding trig graphs that went through given points. After fiddling with it on their whiteboards, they wrote down a set of steps to themselves in their notebooks.
Super interesting seeing the student thinking here. Will continue.
Some great projects this year (out of only 5 blocks of in-class time).
As an introduction to transformations of trig graphs, the class worked individually on Marbleslide Periodics. We did wrote down their conclusions for what the a, b, c, and d do for the transformations and gave them specific trigonometric terms (period, amplitude, and frequency). Then the class, in pairs this time, worked on my Match my Trig Graph desmos activity. I had the basics setup on this activity last year, so I tweaked it this year with some goodies. There is now a feature to stop them from just making a “trig” graph with 0 amplitude or 0 frequency, and a feature to show a picture when they’ve succeeded. It’s good practice for them to have to enter in an exact value like π/4 instead of an approximation like 0.7854. Really successful activity this year, students were into trying to find all the pictures.
It’s also fun to see the students working in the activity builder:
A fun activity to try with your Precalc/Alg2 class when they’re working on proving trig identities is to have them create their own trig identity.
Have them start with a true statement, then modify it by doing much of what you might ask them not to do during a trig proof (work across the equal sign). When they’ve made it properly obfuscated, have them write down the last line on a post it, erase their work and then ask them to prove their identity. If they can prove it then you can switch post-its with other students in the class to try and prove someone else’s “identity”.
Some students always get REALLY into this, and will probably not be able to finish before the block ends. Here’s a student plugging in his identity into desmos to verify that it’s true before he attempted to prove it.
These type of students often come back after a week having worked on some monstrosity of a proof. Honor them!
We’re working on power series in Calc. Every year I love setting them up with the following series to find the convergence/divergence of:
They work on whiteboards, wander their way through the tough algebra and to the answer (converges everywhere), and are (generally) very happy to have made it through a tricky problem unscathed. Inevitibly, a student asks what the power series looks like. YES.
It all leads to an amazing conclusion. That mess of a series with alternating terms, odd polynomials, and factorials leads to …… (check the graph to see!)!
And then it also leads to my favorite desmos graph (ever??):