Optimization was the topic when I observed this week, which is basically about finding the x value that makes the maximum or minimum y value given two equations with one other variable. This makes for 3 total variables with two equations, and since the students know they need 3 equations to do substitution for 3 variables, they're all lost when they start. The key is explaining to them that they can use calculus to eliminate the variable being optimized, and then they can treat most of the work like basic algebraic substitution.
It's interesting to see how the students will create a mental block when something looks extremely complex, and start asking questions about things they learned a month ago. They tend to let a lot of variables overwhelm them, so I have to be patient and make sure to re-explain older concepts when they get confused. However, it's actually pretty entertaining sometimes when I ask a student "...and what does y equal?" and they can't answer me, even though in the typed question itself it is stated that "y=3". Once again, I'm just seeing some of the struggles that math teachers frequently experience. It's good practice, and I'm still enjoying it each week.
It's interesting to see how the students will create a mental block when something looks extremely complex, and start asking questions about things they learned a month ago. They tend to let a lot of variables overwhelm them, so I have to be patient and make sure to re-explain older concepts when they get confused. However, it's actually pretty entertaining sometimes when I ask a student "...and what does y equal?" and they can't answer me, even though in the typed question itself it is stated that "y=3". Once again, I'm just seeing some of the struggles that math teachers frequently experience. It's good practice, and I'm still enjoying it each week.