Thursday my school had an art and music day. No one goes to any classes and instead spend half the day listening to their peers create music in the theater and spend the next half creating art in workshops. I couldn’t believe I was getting paid to listen to surprisingly talented students and paint and chat with a bunch of interesting world traveler students.
I knew that I would fail miserably at teaching my students real math Friday before Spring Break. Half of the class was gone visiting exotic countries such as Japan, Samoa and Colombia as part of a global link program and Mock Trial State Championships and the ones who were left didn’t want to be subjected to learning things that everyone else was missing out on anyways.
After tossing around a bunch of ideas in my head about possible math art projects I came up with the perfect plan at breakfast. We would play math pictionary. I would give them a function, a concept, a number like pi, or a random math word and they would have to get the class to guess it with graphs and anything else allowable in pictionary.
It was disheartening to see my best students unable to graph much of anything without a calculator and for it be easier for the calc students to draw a pi over four dots than a 45 degree angle on a unit circle but it was an incredible amount of fun that probably let to a bit of learning as well. One of my favorites was the “golden ratio” picture that involved a picture of gold coins and the ratio symbol from middle school. The quadratic formula involved a picture of someone’s leg and acceleration was indicated with an alien because some of my students started using the mnemonic “Alien V Predator” to remember “Acceleration Velocity Position” in the order that they are anti-derivatives of each other.
In 8th period all of the girls were gone, leaving me with a class of 8 boys on the verge of being let free for Spring Break. I’m not sure any of them sat down the entire period. I need to hide the yard sticks from this crew. They picked them up and started dueling while we were passing back tests. Finally after jumping up and down saying “look at me, look at me” in some sort of mockery of all I know about how to classroom manage we focused their energy on the wildest most competitive game of math pictionary I have ever seen. At one point they two teams are so angry at what they considered cheating that they all turn to me, some of them still with yard sticks raised, asking me to arbitrate on the cheating. There is so much wild drawing, guessing and general mayhem that I really have no idea what to say. So I plead the fifth, in the sense that siding with one team or another leaves me left with 4 wired boys who violently disagree with me. And I know this sounds like flashbacks to my all boys algebra class but the energy was directed more or less towards the board, and most of the pictionary involved math. Thankfully when a tour came by to observe they were busily trying to prove the Pythagorean Theorem for a bonus point.
The last day before a vacation are notoriously hard to teach and I think this is the first time I’ve felt successful. I’m inspired to go off into Spring Break and think of new ideas.
I’m trying to figure out what kind of goals can unify my students in the last, senioritis, post college admittance 6 weeks of school. Some of them are still totally unwilling to do anything but memorize procedures and formulas. They do not like being asked to think critically or to apply knowledge on a higher level of bloom’s taxonomy. One girl proudly told me that she finally understood physics because a physics student had helped her memorize the position, velocity and acceleration equations for free fall due to gravity on earth. I knew this was a bad plan for multiple reasons. First she had the position equation memorized incorrectly. Second, I’d made the question on the test about freefall on “Planet Janet” where g is 15 ft/ sec squared so that memorizing physics formulas doesn’t help anymore.
I tried to no avail to convince her that she knows the power rule and all she has to do is anti-differentiate acceleration to get velocity and position but she wanted desperately to memorize it instead. I wonder if I can reach her by talking about how she doesn’t need to have these formulas memorized to be successful in college. She needs to know to to synthesize knowledge, to seek information from peers, the internet and books. She needs to know how to problem solve. How can I message that to my students? I’ve thought of asking all my friends what mental skills they used most in college and what made them successful. I wonder if I can lead us bravely through a whole bunch of rotating functions around the x-axis to find volumes of strange shapes. My boyfriend who happened to go to my high school in 99(small world) says that the kids are really going to struggle with that unit based on what they did in Pre-Calc. My boyfriend had the same Pre-Calc teacher as my current students so he is surprisingly helpful at lesson planning.
I’ve also been thinking a lot about differentiated instruction. I have huge gaps in ability and desire to learn math in my classroom. I can’t make class hard enough to challenge everyone without stressing some people out incredibly. If it’s too easy then some people are not as productive or learning as much as they could if they were more challenged. I’ve started to notice that kids are really good at self-differentiating and that almost everyone who is capable chooses to do harder problems over easier problems if given the choice. I’m thinking about having choice built into almost all of my assignments next year where I give kids the option of doing one harder problem instead of two easier ones. I figure if they can solve the harder problems then they don’t need as much practice with the easier ones. I haven’t been doing a great job following up on the solutions of the challenge problems. Frankly, I don’t have the time to solve and understand all of them when I spend so much time making sure that I know very well what the homework is, and what prerequisite skills we need for it and how it fits together. Calculus is deceptively challenging to teach.
My final idea that I’m really excited about is to create my own Calculus website. There are quite a few Calculus websites with cute lesson plans, interesting applets, and more, but I’m not convinced that there is one site that is exactly how I would teach it. I want a site that my more advanced students can go to and learn and seek and find out about math in the fun, not too stressful way that I love to do. Wikipedia and YouTube have so much to offer, it’s kind of amazing. In Special Topics we’ve been watching videos about the world and trying to analyze it mathematically. Math is in so many places, good, interesting teaching is just a function of finding the places in the world that apply to the concept you are trying to teach. I’m so lucky to be working at a school without standardized testing where I’m free(as soon as I’m well respected) to experiment and learn and share the beautiful world of math with everyone. I just need to message it to students to invest them in my vision. They are used to math being solving a number of similar problems out of a textbook. If they don’t buy into the idea that it can be something else then they are resistant to put effort into it. I’m just not convinced that solving a bunch of textbook problems is what most of my students really need.