Section 34.4 Closing Ideas
There was once a time when teachers would tell students, "You're going to need to learn these things because you won't always have a calculator in your pocket." It turns out that those teachers were wrong. Almost everyone these days has a cell phone on them most of the time, and so they almost always have access to a calculator. But the existence of those calculators has not changed the fact that people still need to develop mathematical reasoning.
As we saw in this section, there are sometimes problems that calculators can't to perform. And even if you have a calculator that does scientific notation, that doesn't mean you can actually use that functionality. So there are still cognitive gaps that need to be covered in one way or another. An unhealthy approach is simply to say "push these buttons to do scientific notation" and turn math back into another rule-based structure. The challenge is that for the majority of students, you will only see scientific notation in science classes and then only a few other times in the rest of their lives.
If we isolate scientific notation to a set of rules that will only be used in a few circumstances, then the most likely outcome is that students won't remember it at all. But if we connect it back to a conceptual idea (combining like terms), there is a greater chance that student will not only remember, but also have a better chance of re-understanding it if they forget. And this is an important benefit to thinking about math as a body of connected ideas instead of individual skills. It creates opportunities for students be able to use their experience and reasoning to rebuild lost knowledge, instead of simply being stuck at "I don't remember this."