Mathematics is Kind

Have we been tricked to think that the study of mathematics is cruel? When you ask most people about mathematics in their life you can get anything from a scowl to a recoil; there are few of us who love mathematics. It is a heavily studied subject these days, not just mathematics, but the teaching mathematics, looking at ways to improve student relationships with math.

David Epstein is popularizing the discussion of kind and wicked learning environments in his most recent book Range. He opens his book with a comparison of Tiger Woods, who practices golf a kind sport with Roger Federer who grew up playing a host of sports ending up in Tennis, which is a wicked sport. Few would argue that these two represent the pinnacle of their respective domains.

What is the difference between kind and wicked learning environments? The research comes from Robin Hogarth and his team who frame it this way. First, you have to look at the interaction of the learner, how information is acquired and next how it is applied.

Kind learning environments involve close matches between the informational elements in the two settings and are a necessary condition for accurate inferences. Wicked learning environments involve mismatches.

Perhaps a better framing, in “kind learning environments, feedback links outcomes directly to the appropriate actions or judgments and is both accurate and plentiful. Wicked domains as situations in which feedback in the form of outcomes of actions or observations is poor, misleading, or even missing.”

Math is a kind learning environment for the most part. Those closed-ended questions that students spend much of their time working on provide direct, accurate feedback. If a student is working on a computer than the feedback is immediate. Working with a solutions manual, the feedback can be near immediate.

Open-ended mathematics questions are on the spectrum from kind to wicked, and they require a presence in math teaching, but we will leave that for another day.

Maybe this resurgence of kind and wicked learning environments could be the catalyst to finally shift the conversation to math teaching. That we still have teachers teaching math who have math phobia is another part of the problem we need to solve. You could have a kind learning environment fraught with panic, which does not create an optimal setting for students.

Changing how we think about math is essential. It is beautiful, it is powerful, and it is much simpler than we make it out to be. Math is kind, so embrace its love, and it will love you back.

Hogarth, R.M., Lejarraga, T., and Soyer, E. (2015). The Two Settings of Kind and Wicked Learning Environments. Current Directions in Psychological Science. 24 (5) 379–385.