So as I said in a previous post, Spring Break is my chance to take a moment to reflect and see what I can do better. Thanks to all of you sending me articles and my network of resources, I have had no shortage!
One theme that mysteriously keeps coming to my attention is the lack of richness in our curriculum. In one of BrokenAirplane's earliest posts, I encouraged all of us to aim for the highest level of application as the end result of our student's learning. Now in the last couple of weeks, I am seeing great posts from thoughtful writers about how shallow our textbooks and assignments are.
In this one, Frank speaks about how the Khan Academy is actually reinforcing our shallow model of education. I agree with his point if teachers are allowing these "tools" to be the complete math curriculum. It would be like going to a cooking class and spending weeks learning about the mixer, the oven, baking soda, etc. and never actually making a cake.
While on the other hand, I teach at a school which does not track and I have 9th grade students who are ready for Trigonometry and others who never understood Elementary Math. Using ALEKS and Khan Academy occasionally (<20% of class) has dramatically improved their confidence in their skills and participation in class discussions.
Another source of this mathematical meme came from Republic of Math and describes the difference between contrived and real problems. Contrived problems are a poor attempt to compel the student to care when the only purpose of the word problem was to wrap a story around a calculation problem. Kirby Urner has said before that we need to tell better and bigger stories and we will find that math is a part of that bigger story without having to make some contrived reason up, and just a couple of days ago, Dan Meyer spoke about the need for strong narrative to drive critical thinking.
The other part that keeps rattling off in my mind comes from my "Is Calculating Math?" post about Conrad Wolfram's exhortation that we stop the trend of 80% class time teaching/learning to calculate. I agree 100% and yet I am now finding myself overwhelmed. I am asking you out there for help at getting better at mathematical modeling. If you haven't watched the TED Talk, check it out here.
According to the Mathematics for Teaching Blog, mathematical modeling breaks down into 4 categories: