We've Reached the Halfway Point for the Homeschool Academic Year

Now that we're just past the halfway point of a year of homeschooling, I have some thoughts to share, some of which will be cliche and [hopefully] some will be novel.

I did teach as both an undergrad and while I was in graduate school. As an undergrad, I taught computer programming and thermodynamics. As a graduate student, I taught programming, and networking (mostly simulation of event-driven network protocols). I think this experience is relevant here, as I had a chance to observe both the ebb & flow of student abilities at a university, but also the chance to teach some pretty challenging subjects (which meant trying to find a way to explain certain topics that were difficult to grasp [based on all of the previous ways they had been attempted to be explained]).

• What's most interesting to me is how much we undersell our kids, in terms of what we assume they are capable of learning. Said another way: traditional schools seem to expect so little of their students (which may explain many kids "checking out"). The most surprising and unexpected thing about homeschool was just how much my student learned in such a short time.
   
  (I do recognize I'm lucky, as my kid is a great learner with an even better attitude)
• The ideal goal for all education to match M students, as closely as is reasonable, with N curriculum. Meaning, everybody learns differently (and that's okay), and we know this at a time when there are custom curricula for nearly every subject. There are specific curricula for kids with dyslexia, dysgraphia, dyscalculia, etc. Ideally, every student would have a learning evaluation done and then a set of curricula selected to optimize their ability to learn.
   
  The problem being: in a traditional classroom setting, this becomes an MxN problem. It's hard enough when it's 1:1, and my guess it's impossible at MxN scale... not theoretically impossible, just "the limits of space and time" impossible.
• The same goes for the "social emotional" side of learning. My student seems to learn best by:
   
        a. learning new material
        b. go back to basics
        c. go back to the new material
        d. then go further
        e. then back to basics
   
  So we're continually going back to the beginning and re-learning stuff she forgot, and practicing the skills she retained to reinforce them, and then forging ahead with new challenges. While this works for my student, it's unlikely to work for others (mainly: those students who want to focus on one topic at a time, practice it until they "get it", and then move on).
• The two ways to lose a student are (1) make it too easy and (2) make it too difficult. Walking the middle line there is tricky, and sometimes I feel like we're toggling back and forth between those two, I think it's worth keeping this in mind at all times, as it's a foundational dynamic.
• Confidence is key. If your student isn't confident, they're going to struggle. Ideally, if you can get them comfortable with making mistakes, this is key, as learning inherently involves making mistakes. The worst thing you can do is to shame a student who has made a mistake (we learned this the hard way via a tutor).
• Teaching is hard. I think most people understand this in an abstract way, but it gives an entirely different perspective when you try it full-time (and I only have one student!). A couple of things are the same whether it's 1:1 vs 1:N (you need to prepare a lesson plan, teach it, and answer questions). The big differences when teaching 1:N are likely (a) grading N assignments and (b) keeping the class rolling along and focused (minimizing disruptions and managing class dynamics).
• I learned early on that I have limitations and that I've had to adjust how I teach over the months. I think continually reevaluating my approach to teaching (and adjusting as necessary) is just part of the deal. After all, if I'm trying to teach my student that making mistakes is okay, well ...