Why is it important for students to connect their mathematical learning to themselves, to other mathematics, and to the world?

"Learning is intimately linked to connections we make between our prior knowledge and our new experiences. Prior knowledge or experiences help learners interpret and construct meaning from newly introduced ideas or concepts." (Sammons, Building Mathematical Comprehension, 2013, p. 85)

"Connections build conceptual understanding. The more and the stronger the connections are among related ideas, the deeper and richer the understanding of the concept" (Hyde, 2006)

"One of the gaps in many teachers' mathematical backgrounds is an internal map of the subject. They lack a fundamental understanding of how various mathematical topics interconnect, which topics are more important in the long term than others, and which aspects of those topics are most important. As they teach, many teachers often feel like they are going through a checklist, checking off whether students have learned each new discrete concept or skill listed in the curriculum. This is in stark contrast to what we know from research about how much more effective it is for students to learn when connections are explicitly made between new knowledge and ideas that students already know (Borko and Putman, 1995; Schifter, Bastable, and Russell, 1997; Kennedy, 1997)." (Small, Big Ideas from Dr. Small, 2009, pp. xi, xii)