While reading the glossary, I was surprised to find that there were so many different inquiry-based approaches. Before this, I has assumed inquiry-based approaches included things like research essays, projects that students would be guided towards in terms of questions posed and of course allowed to ask the teacher for help, but otherwise left to do the work on their own. I was surprised to see Project-Based learning was actually more structured than this to ensure students are learning the class content. The case method also interested me because, although it is about the individual learner, it is also an exercise of group work and realizing not everyone will agree 100% all the time. Design-based learning is an interesting distinction from project or scientific inquiry (although I'm sure they could overlap) and I particularly liked the idea of finding the restraints in a design. For example, maybe students could create different representations of Pi and discuss the limitations they encountered (one idea I had was maybe playing music so that each note is held for 3.14 seconds, for example, and discuss the limitations in accuracy or with technology that they encountered. In this case, the "product" would be the song. I wonder, if the song was 3.14 minutes long, would it count as a fractal as well?).
Mapping out the pathways of math was more difficult than I thought it would be. I thought back to the presentation I was given in high school for the different paths we could take and I remember there were allowances even within the chart they showed us so I took a similar approach of creating the chart but keeping in mind that further explanation would be needed. For example, I decided to have the Workplace Math 10 route lead to Geometry 12 and Computer Science 11 as well as Workplace Math 11 and History of Math 11 because I believe students would still be able to succeed in those courses with their background. I drew on personal experiences working in Workplace Math 11/12 as well as my experience taking Computer Science 11 and looking at the Workplace Math 10 curriculum when doing so. I took the recommendation to make Statistics 12 follow FOM11 or PC11 based on other school recommendations found online and by looking at the curricula for Workplace Math 11 and Statistics 12. If the school offered this option, it would be a good idea to mention to students they could inquire about Stats 12 through teacher recommendation if they were on the Workplace Math path. In terms of the three main pathways (Foundations, Pre-Calc, and Workplace math), if a student decided to switch pathways, I'm sure they could work out the best course of action with their school counselor.
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