The sidekick supports the superhero behind the scenes and doesn’t generally get too much recognition. But the sidekick is SO important; the superhero is nothing without him/her. There are some topics when I started teaching that I just never really saw much importance for in the standard K-12 curriculum until I realized they were super important as sidekick topics.
The sidekick topic that just dawned on me how important it is is inequalities. I mean I always knew that they show up later on, but their true role in comparing two quantities is enormously widespread. I just never thought of this before until I was coming up with a test item today aimed at getting students to understand the connection between definite integrals and area.
When I first started teaching I felt that inequalities were just another boring topic that I didn’t really see the importance of. But now that I know the big picture much more than I did before I really see the importance of students understanding what inequalities are really about and how pervasive they become in so many other concepts.
I still have lingering questions here – How can I better approach it in Algebra 1 to feed into their sidekick role later? What other topics feed into similar roles and how can I do the same thing for them? Any ideas?