Students that learn the MathCart way continually do two things, observe and practice.

We constantly illustrate concepts with sensible mathematical meanings. However, we also believe in practice, lots and lots of practice.

Learning is an active procedure. Forgetting, however, seems to be much more passive. It is rather obvious that practice does lead to improvement. Learning is not a linear progression. It is much more iterative.

Books are laid out in sequential order, from one topic to the next. Content in a book, however, is not the same as mastery of a subject.

Often in school lectures, students understand bits and pieces. Without context, so much useful information is missed, but the student needs to start somewhere. A student can hear a lecture at first, and after investigating the subject further, they start to understand better. Typically if a student hears the lecture a second time after a bit of practice and armed with some familiarity, the key concepts become much clearer.

I have taught learners all the way from pre-K to adult, including lecturing at a university with 10 week quarters. I found it helpful to push through the 10 week material in about 7 weeks, so I could iterate back through, revisit topics, connect the entire class curriculum, and fill in gaps in learning.