My First MOOC, "How to Learn Math"

So, I am starting to engage in a MOOC (Massive Open Online Course) at Stanford Univeristy entitled, "How to Learn Math." Jo Boaler, the professor publishes videos, questions, and interactive platforms about the subject matter. I predict a "butterfly effect" to occur, which is a good thing. Today, I watched a video from the MOOC. From it, I learned about a study conducted where certain habits of learners were identified and examined. When solving problems, many low achieving students used counting all and counting on to solve problems. However, most high achieving sudents were able to use numbers more flexibly and apply a variety of strategies to solve problems accurately and efficiently. The power lies in the reality that even though low achieveing students are able to learn and use strategy and numerical flexibility, their support systems are typically based on procedure. What implications does this make about changes that need to be made with the way we remediate and support our students? This disparity also carries over to algegbra. It is documented that many students struggle in "upper mathematics" such as algebra because of a lack of number sense. I agree. As an adult who used to struggle with mathematics, I remember having the most difficulty when I had to remember lots of steps or procedures and not have the ability to apply them. The video compares this type of math to a "never ending ladder." However, I experienced the most successes when I could make sense of what I was doing. My brain was able to internalize, organize,and apply my understandings to a variety of scenarios. There is power in true numerical understanding and flexibility. As a matter of fact, the video calls this type of thought processes as "compression," which is more like a well-organized math triangle. This is powerful.