Calculus Extras...

One of the fun things about learning calculus in high school is that as a student you get to refresh your memory and pull from your memory and create sweat droplets from all the extra work in juggling the things you have to know in addition to the new crazy great topics you are learning at a breakneck speed.

There's algebra! geometry! trigonometry! rational functions! ln x! fractions! It's like all your years bundled up into one. 

My students this year do not as a whole instantaneously remember the trig values in any quadrant of any of the 6 special angles. I am also not doing my daily "IR" quizzes this year (immediate retrieval) because of the other things I am implementing, and I just don't have the time. I am trying to put basic trig questions on many homework sets, but that is not always possible or enough. So, my next attempt is the following: (can download HERE).

 

 I have created a practice sheet for them to use at home. All triangles are such that they can be reference triangles in Q1. I am hoping that the repetitive nature will help. Then on the back, I have the same set up, but the side values are omitted. 

My thinking is that after this is perfected (maybe I should have a quiz they must answer in a set amount of time), then the next installment is a picture of the xy-plane with a terminal side marked in Q1 with the angle given. Then the final installment is just the statement given.

Hopefully, this will work to keep things stuck in their brains.

Make It Stick Changes

I finally had life/brain/school space to read this game-changing book (Make It Stick). The fuss is now crystal clear. Because of this, I am changing how I do homework and flipped lessons and tests and reviewing in my Calculus class. I will also change other classes, but this is the one I am most worried about right now. 

tldr: there is a linked document above the first picture with next year's baggy problems and a notebook insert.

I felt I was doing a good job teaching them, and maybe I was, but after my results on the AP exam this year, that were DRASTICALLY poorer than the previous years, I reflected on what I did differently. I know I had a different population of kids. I know they had life issues that were so enormous, it's a wonder they still came to school and functioned semi-normally. I know their time was pulled in all sorts of different ways. I know all that. I also know I am a good teacher, so I am not fishing for praise (hah! or maybe I am one of those people who thinks they are one way but are really not). I just also know that this year's results were a big suckfest. Boo. The one thing I did change was that I made a copy of the homework key all worked out, every period, for every kid. I was trying to be helpful. 

I wanted them to see how the problems were worked and be able to learn from examples and skip happily into the sunset in their new-found calculus knowledge. Homework doesn't count for much of a percentage in my class, and my thinking has always been that homework is for practice and students shouldn't be penalized for trying or for making mistakes. I know there are a ton of different theories and ways teachers approach homework, and obviously, everyone should do what feels best for them and their students. I see now that potentially a certain portion of my students did not use the key as intended. 

There are always those students who do the right thing and have an effective way of "studenting", and they used the system wisely. They also passed the AP exam. I also know that there are students who half-heartedly (that wasn't the first body part that came to mind for that adverb) "attempted" each problem and put something down all in the mistaken belief that, "oh, Dadmehr will just show me how to do it next class. I don't have time for this calculus nonsense."

Rinse that and repeat all year, and you have a math student who does not know how to solve problems. Sure this isn't the first time I thought that's how they were attempting some (all?) problems, but I thought that the incentive of test grades would lead them on the right path. Silly me. 

Also, I always knew that I should do cumulative or spiraling of concepts both in review and on homework, but I could never make myself adhere to this consistently.

Fast forward to now. I will change my world. All things will now work perfectly and all students will get 5's and I will be continually doing a happy dance. Thank you "making it stick" and AP Conference. ... Or maybe not, but I have high hopes about these changes.

My first thought was how to effectively (for me) get the students to do interleaved practice (as they call it) so that they can interrupt forgetting of concepts from long ago. The following is what I have latched onto. I will have a large baggy that stays in the class. Students will each buy and keep in the baggy some index cards (2 packs?). I will have them put the shown insert in the bag, copied on pretty paper (that will make all the difference), and they will put their name on one side largely on the inserted instructions: (can download here: word pdf).

Each class day, or every new concept day, I will have them create at least one new problem. They can follow the examples I have given, but the numbers or something should be different. They will follow the format from the insert. I want only the problem on the front (nothing about the answer or what unit it is from). Then on the back, they will work it out, and on the top will list the answer and the concept.

I will collect it at the door and correct and hand it back next class, and put the baggy back in our storing place. Eventually, they will have a wide range of practice problems. Now, periodically, in class, I will say, pull out 3 (2? whatever) cards and BY YOURSELF WITHOUT NOTES OR HELP do the problems on a separate paper (notebook?). Also, put a check mark on the top to indicate you have done this. Then check your work and/or refer back to the appropriate notes to fix your weaknesses in this topic.  I feel like this will interrupt their forgetting. It will also give them a hint as to what they need to work on.

I also see that potentially, they could swap temporarily the cards or they can search for certain topics or they can see if they haven't done any of the problems since there are no check marks and then attempt those. They also are working blind and potentially don't know what topic it is, so this mimics the AP exam, and helps them distinguish key words/phrases that will help with recall. A thing I still need to think about: how can I make them have a variety of easy/medium/hard problems?

Also, I am still not finalizing how I will do homework. Based on the book, I see that certain students were not struggling effectively with the content, so it wasn't sticking in their memories. I will no longer provide any key. They can come in for tutoring. I will have worked out examples available. I always have an answer bank at the bottom, so they know if they did it right mostly. I need to take this worked-out key crutch away from them so that they use their brains more. I will also mix up the work and not just have it on the current content. So this was all my plan before I went to the Houston conference. Now I have some different ideas rolling around in my mind that I haven't solidified yet, but anyway, here is the insert for their notebooks (see above the other picture for the links):

I want to go over this with them and discuss learning and all the reasons why I am teaching this way. I want them to have this to refer back to. I will also start moving my videos to edPuzzle, based on something else I learned in Houston! Apparently, on edPuzzle, you can insert questions for the students all through the video, and, get this (!), the video will not progress until they answer them, AND apparently, the students can't go to another tab or whatever and pretend to watch the video because it will stop. So excited to try this! 

This will make it a more active learning process when they are taking notes.

I am excited to try these things this year and hopefully make my students learn more effectively.

Functions and Rates of Change

Some students in calculus get confused when you are comparing a function and its derivative and second derivative. I get various creative answers of "if a function is positive, then its derivative is positive" .... "if a function is increasing, then its derivative is increasing". I am hoping that this activity will make things gel for more students. Who knows. Not me, but I am willing to try. 

Here's to wishing me luck. One day I will have more perfect moments than not-completely-successful topic teaching and EVERYONE will get it. And cute puppies will bark and wait to be pet and flowers will bloom and I will get enough sleep.

Here is a link to the PDF.