This is an issue I deal with often in my fundamental math classroom. For example, a student may come in to the program not knowing how to divide using fractions. Once the student learns the skill, they might do really well on the “Dividing by Fractions” test, a test which will ask them to divide using fractions. However, a few weeks later, when trying to do a word problem which they could solve by dividing by fractions on a test, the student can’t even set up the question, let alone get the correct answer. This, I think, is because there is a whole process of critical thinking that the student needs to apply that hasn’t been taught. To solve the problem on the first test, the student just needs to be able to solve the equation by dividing by fractions. To solve the problem on the second test, the student needs to be able to read the problem, identify the problem type so they could translate the words in to an equation and then solve the equation. Just like the dividing by fractions skill, all of these other skills need to be taught and practiced. When I was in school, we learned to solve problems by doing so many of them we could recognize a particular type in our sleep, and that’s certainly one way of learning. However, developing critical thinking skills is both more efficient and a more transferable skill.

To learn more about critical thinking, here’s a good place to start.

- To solve problems, students need to be able to employ critical thinking. Mere knowledge is not enough – you have to be able to apply it. In this article, Snyder and Snyder discuss critical thinking, pointing out that critical thinking is a learned skill that requires both instruction and practice and discussing some instructional strategies for integrating critical thinking skills in to your lessons.Gueldenzoph Snyder, L., & Snyder, M. J. (2008, Spring/Summer). Teaching Critical Thinking and Problem Solving Skills.
*The Delta Pi Epsilon Journal*.

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