In my previous post, I argued that in addition to teaching mathematics for its own sake, we should also teach mathematics so that students learn to value diversity, see mathematics in their lives and cultural backgrounds, and analyze and critique social issues and injustices. These learn-see-analyze purposes require connecting mathematics to real-world contexts, which is emphasized in the Common Core’s fourth Standard for Mathematical Practice: Model with mathematics. What does it look like to connect mathematics to real-world contexts? I see two general approaches.
NCTM’s Principles to Actions: Ensuring Mathematical Success for All provides an example of using the real world as a stepping-stone for thinking about mathematical concepts. It describes a teacher engaging students with real-world problems involving proportional relationships; see the task below (NCTM 2014, p. 31):