I came across a nice column by the Hechinger Report group on this topic. They state that according to a report from Organization for Economic Cooperation and Development (OECD) finds that the way applied math is taught in the classroom is not good for the students. It appears that lower socio economic students receive a watered down version of applied math while students from the higher socio economic groups are taught a more pure math.
Apparently, the difference in scores between 15 year old students who were exposed to more pure math tasks and those who were least exposed is about two years of education. When this group looked at the PISA and compared it to the student's background they discovered that students who understand the concepts, they can make the jump and apply it to other situations.
However, if students only learn the tricks, shortcuts, and solving small everyday problems, they are unable to transfer their knowledge. This comment right here may explain why the students I get in high school are not able to transfer their knowledge. Their earlier math teachers teach the shortcuts, tricks and do not teach the concepts or foundations associated with the math. Students need to learn the broad concepts, mathematical notation, and real world applications to fully succeed in math.
This particular report supplies an explanation on why students from wealthier backgrounds tend to do better in Math. It boils down to the math classes and expectations for the higher versus lower economic groups. The students who receive the applied math focus more, are not exposed to the complex multi-step questions that require problem solving and significant thought. Furthermore, they learn to solve problems almost mechanically.
This is one reason Common Core focuses on requiring students to boost conceptual understanding. For instance can a student explain why we when we divide a fraction by a fraction, we change it into a multiplication problem? That is one reason many teachers ask students to illustrate the concept. Aside from meeting the Common Core standard, it also increases student understanding of the concept.
I found this report to be both fascinating and supports something I've always been aware of. I feel as if I spend half my time scaffolding many of my students who are missing chunks of knowledge due to any number of reasons.
I'd love to hear from others on what they think of this topic. Thank you in advance.