Thinking Upstream with a Quadratics Menu

Much of what appears in mathematics textbooks is what I like to call, downstream thinking. Downstream thinking usually involves two features that set the stage for learners. First, it provides a context (however doctored or engineered–often referred to as “pseudo-context”). Second, the problem provides a pre-packaged algebraic model that is assumed to have arisen from that context.  I am imagining the reasons for this are three-fold: Instructional time. Developing these models is messy and takes time, especially with class sizes in the mid-to-high 30s. Accessibility. Developing these models isn’t always possible (i.e. can’t run trials and collect data on every …

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