Winter term has started here at Cal Poly. In fact we are in week 3. This winter quarter I am teaching two sections of Math 330 Algebraic Thinking with Technology for future elementary school teachers. The course title isn't the point of this post, though I may talk about this course in the future. What I want to get to is that I taught this course last term for the first time. This quarter I am at an advantage as an IBL instructor, since I have laid out the course materials once. For the second time around I can now review my notes, look for problems that did well and try to fine tune problems to get students into the learning zone, where the problems are not obvious and not out of reach.
A hidden "side" advantage of IBL is that we become much more efficient as we repeatedly teach a course. So prep time declines with each iteration until it reaches a steady state. Moreover, we gain valuable insights into the learning issues. This is part of Math Knowledge for Teaching that helps instructors help students.
Example 1: Let's say students really struggled with Problem N last term. They tried it, but no one got it and things stalled big time. Some extra time and special cases were needed to get students going. This time around I can put into the problem sequence an exploration, where students investigate some given special cases and are asked to build several more examples. Then using what they learned from this experience, they hopefully are better prepared for Problem N. I don't want to make Problem N too easy or give away too much, but want to get the core ideas out into play through investigating related examples.
Example 2: Problem K was way easy for nearly all of the students. This time I'll leave Problem K as is, but add in a few more challenging problems after Problem K to ramp up the level. (Note: In math finding really hard problems isn't the issue. The issue is finding appropriate challenges for the developmental level of your students. This changes with each class, so one is always getting things "in the ballpark" and adapting to each situations.)
It's Jazz. You have Rhythm Changes in mind, but it's not the same every time.
