ABSTRACT

Human-created patterns eventually give way to nature’s mountains and hills and rocks, patterns that look similar at different scales, as do the mingling trickles of water that converge into streams and rivers. As educators learn about patterns in math content and how those ideas interconnect, decisions about curriculum made on autopilot turn into conscious choices based on student understanding. The more educators recognize the patterns in the mathematical landscape, the more responsive they can be to their students, and the more likely their students will encounter rich experiences that otherwise would have been hidden from view. Knowledge packages provide the context and the glue for mathematics standards, bringing ideas together into a more comprehensible whole. It is important for teachers to understand learning pathways for mathematics so they can understand how content builds, respond to common student misconceptions, and offer appropriate challenges to students who need them.