I was thinking about manipulatives.
As I was thinking about manipulatives, I began to wonder whether or not they would be helpful for math beyond the elementary and middle school years. Does it not make sense that, even with more advanced math, students would benefit from moving from the concrete, to the pictorial, to the abstract? I decided to Google “using manipulatives in high school math” and found the article, “Manipulatives: The Missing Link in High School Math”, by Marilyn Curtain- Phillips, M. Ed.
Here is another link I found in my Google search. This paper talks about the effectiveness and natural use of manipulatives in elementary school, middle school, high-school and (Yes! Even ADULTS use manipulatives in the "real world"!) beyond.