I thoroughly enjoyed reading the book Why School by Will Richardson. I don't know that I can effectively incorporate all of his ideas into a mathematics classroom in my current student teaching situation because we are so far into the school year and changing the format of the class so drastically would have its own set of difficulties regardless of how the format was changed. One question I had throughout the book was why he seems so against the new Common Core. From what I've learned about teaching mathematics in the Common Core manner, it seems as though many of his ideas are already present. I began to wonder if many teachers are implementing Common Core in a manner inconsistent with ideas I've seen at the CMC South conference and NSTA/CSTA conference for math and science respectively. The idea of having students discover the curriculum in groups instead of having it delivered is a main tenant of math common core practices. This is often done through mathematically rich problems that present a need for the concept to be learned and an opportunity to discover it on their own. Often, this is wrapped up with a teacher facilitating presentations on what each group discovered, and potentially giving students the tool or concept that would help them to solve similar problems in the future. This already uses the idea of communication and using others as resources. In order to also incorporate Richardson's idea to have students using the internet in class to find their own resources and learn how to recognize reliable sources, I could replace the "recap what useful tool we've discovered" piece an instead give the resource manager of each group time to use the internet and find a rule, formula, theorem, or other information that would provide the useful tool for the day. This would make the "share out" portion of the lesson include an assessment and critique of each source, and encourage students to be able to find mathematical resources when necessary. They would learn important skills for our modern time, like the ability to refine search terms and quickly assess many resources to find what they are looking for. It would give them the opportunity to create their own curriculum without concern that nobody would notice a pattern or rule, because high school students tend to be digital natives who already have a sense of how to search the internet for what they are looking for. I fulling intend to implement this for at least one unit I teach next year in my own classroom to see how it works out. Additionally, in my next unit with my current class I intend to have students create their own wiki on wikispaces as a class resource. To encourage student participation and discourage myself from creating tests that gauge whether or not students have formulas memorized, I might allow students who participated in the creation of the class wiki to use the wiki as "notes" on their test. This way, students would be creating their own contribution to the global mathematics community and doing work for a real audience, it would encourage students to communicate and collaborate on a classroom resource, and it would allow them to practice the skill of finding and taking note of important information. The first thing I need to work on is creating real world problems that encourage critical thinking skills and require students to analyze information in order to solve them. This is something that has been largely missing from the curriculum I've been asked to teach and I need to create more opportunities for it in the future. If you are interested in hearing some of Richardson's ideas, his TEDtalk is below.
TLDR: Loved this book! I want to use wikispaces in my classroom, and have students create their own online classroom community to create and share work. Looking for other ways to do this in a math class.