I spent this year in an effort to transition my students from a the tradition lecture, example, home work model they were comfortable with to problem based, discussion model. The transition also involved moving from away from a traditional text book for students to follow and to problem sets designed to invite students to develop their own mini text books for reference. Looking back at their work from the fall, its great to see how far they have come. Ultimately I wanted the students to be able to learn the material from problem set. Ideally, the topics of these problem sets are integrated, but this year I didn't get to that point. The problems sets this year consisted of 30-36 problems. At first they were topic specific and progressed from foundational to complex applications. For example, one set focused on the log properties and the next set on solving log equations, while another set focused on graphs and transformation of log functions. In the beginning, these sets resembled problems at the end of a section in a traditional text. As students got more comfortable developing the material from the problem sets, they became a little more integrated. The problems were still themed by a topic, but resembled more of a traditional chapter review. I also incorporated a few mini projects that usually lasted about three days. I was pleasantly surprised with the outcome of these projects. Ideally I'd like to take all the problem sets and shuffle the deck to produce a sets that don't lock students into one particular idea or topic. Instead, I want the problem sets to evolve into a more integrated approach. Class time was spent with students working on problems and asking questions. Sometimes we were at the board and other times hovering around another student. Many times different solutions and problem solving strategies surfaced. My roll as a teacher seemed to be to listen carefully, try to steer them in the right directions, and help them make connections to previously learned material. I had to be on my toes for each class because regularly students came up with different approaches or ideas to solve these problems that I hadn't thought of before. Resources for their learning came from a variety of sources. First and foremost the best resources are everyone you see in this class. Everyone will have an impact on how each student learns. On the first day of class I told them that there is a huge supply of mathematical content available to them for free on the internet. Don't be shy to go see what's out there. I gave them the usual Khan Academy, Wikipedia, etc. suggestions. On our class page, I posted links to specific video content, solutions to worked problems done in class, appropriate geoGebra applets, and solutions to the problems before each test. The unit structure came out of our daily schedule and school calendar. Each unit lasted six weeks and corresponded to one quarter. To have enough assessments for each quarter, we took a test every two weeks. Each week we meet for three days. This ultimately broke down as follows.
With some pressure to conform to other teachers, we had a final exam. As we prepared for the final, we discovered that the review materials were already created. Because we had a test every two weeks and before each test we created a one page problem set summary, we had a nice explanation of all the topics. Also, bi-weekly test provided a start for students to create their own review problems. Additionally, I created three integrated review sheets, with no more than eight problems that highlighted the material. We only have one hour for our final, so it will consist of no more than eight problems.
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Author"Your only as good as your record collection." -DJ Spooky Archives
September 2020
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