Arbitrary and Necessary

 Hewitt has put into words with this article something that I have thought about before, but not exactly gathered together into coherent meaning.  Previously, I have learned through various tutoring and TAing that we often want to push students to figure things out themselves while perhaps helping them through guiding questions if they're not getting it.  This appears to adhere fairly closely to how Hewitt describes presenting "necessary" information to students.  On the other hand, "arbitrary" information brings back a memory for me from one of the previous articles we have read where the author proposed that so much of definitions are needless, something I took exception to.  Hewitt captures my thoughts on the matter much better- in math, we do have set definitions for things that we have essentially made up, but they are unlikely to change and so must be conveyed as is.

In terms of how to bring this article into my lesson planning- I think that what it brings to mind is the necessity of scaffolding for students at different levels.  I already had as a general concept that I would want to have students try to connect dots themselves if the situation allowed, but in thinking more specifically about lesson planning, I would likely want to prepare for the case that the students wouldn't necessarily all be able to do that.  Hewitt discusses this, saying that something being "necessary" information doesn't mean that every student could figure it out, just that somebody could, which of course seems obvious in retrospect, but I hadn't considered how I might adjust to that in terms of lesson planning.  For example, incorporating review of a subject previously learned before going into a subject that builds on that could be helpful or coming up with different levels of questions to get students at different levels to think about the subject more.  These are things I do while I'm TAing, but I think they are relevant to lesson planning as well.