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Thinking Skills: Apples

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October 11, 2017

What thinking skills are being built through this problem?

       First, a key critical thinking skill for someone at any age is the ability to make sense of what they’re presented with, and then to persevere when they get stuck. In this problem, solvers must repeatedly evaluate what they know, and how they can use it so that they can continue forward with the problem. The perseverance part comes in if and when they get stuck; when they try again, try another way, or simply work more carefully through a part that might be confusing, they are practicing perseverance.

       In this problem, solvers are also learning to reason in different ways. First, they are learning to reason in context, or according to the story set forth by the problem. This is a part of the ability to contextualize, or think about the problem and the story, and then put their ideas and solutions together with what they already know, to finish the story. In this problem, solvers are also doing the opposite of reasoning in context (amazing!). This problem asks us to use the story, but then to go beyond the story, to a rule that will always work. In doing this, we are stripping away the story and thinking about how to represent ideas and solutions outside of the story, in a way that makes sense.

       A third important thinking skill being addressed in this problem is the ability to model. When someone uses a model in their work, it can be a physical model, like the one suggested in this problem (for example, where paper clips are distributed into cups), but it can also be a drawing, an equation, or a story that gives a problem context. Modeling describes a situation and/or its possible solution, and there are lots of ways to do that.

       There are two other important and related thinking skills present in this problem. This problem asks the solver to look for patterns, and then to see if that pattern works in a new situation. The process of identifying patterns is a skill that helps us every day, in every aspect of life. The other skill is looking for and using things that happen repeatedly, to one’s advantage. In the course of this problem, we see the same pattern being applied, but also see this pattern can be applied to additional situations. Identifying and applying the pattern then helps us to discover where it DOESN’T work, and then eventually to determine a general rule. These skills together are key to math, science, engineering and related fields, but also apply to many other aspects of daily life from cooking, and exercise, to relationships between people and more!

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