This is a great story.
Math is hard. I believe the only way to really “get it” is by doing all the steps of many problems. I have had this discussion with Ph.D. physicists and mathematicians with whom I have worked over the years. Some “got it” more quickly than others, but all of them had to work their way through a significant number of problems to get a real understanding of the material. It does not really matter what level of math we are talking about either. From Algebra through Geometry, Calculus, and Real and Complex Analysis, if you have never visited the material before, it is not that easy to get the concepts with out working the problems. Math is one of those subjects where it helps to have read through the material for a given day and try to work a few problems before going to the class. It helps because the material gets presented in both a textbook and a lecture format. You cannot get feedback from a textbook. That is why it is helpful to read the material first, so that when the lecture comes along you can ask the professor better questions about what you do not know. Many believe that day to day usage or teaching of math are what is required to really get it. That was certainly true in my case.
I talked about all that because it feels like we have moved into a new stage in our homeschool. The material we cover in Math, Science, and Worldviews is much more complex than in previous years. It is time to start down the path of study methods that are different in delivery, but redundant in content for math and science. The kids perform their own, relatively ad hoc daily planning, given a set of daily learning objectives. I think it is time to do study some different study methods. How to study was something I had to learn by osmosis. There is a better way to go about it. I will look for a book to help me with this, then dive into it, probably as a read aloud in the next month or so.