For some of us, we equate problem solving to the word problems we did in our math textbooks. Word problem are not truly problem solving. These types of problems are designed to help students practice a particular skill or concept. True math problems are more complex and may involve the use of several different concepts in order to solve. The solution is not immediately obvious and they take time to solve. It is important that we have varied and multiple experiences with both these types of problems. One to practice a new skill or concept and the other to apply our mathematical knowledge beyond the simplistic.
This type of 'problem' has its place in mathematics and it is important for children to engage in this type of work. However, it does not engage all aspects of problem solving that are necessary to be mathematical.
A rich, complex problem will ask us to think deeply about a situation and how we might make sense of it mathematically. It calls upon more than one aspect of our mathematical knowledge to solve. It asks us to communicate our understanding in different ways and allows us to make decisions about how to proceed. It is important that we experience both types of problems in math: one to hone our skills and the other to hone our critical and creative thinking skills and our ability to apply our mathematical knowledge. *adapted from Smith, Huinker and Bill, 2017, Taking Action: implementing Effective Mathematica Teaching Practices, NCTM.
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