When I experienced formal education as a student, I was taught primarily in a procedural way. Rote memorization seemed to be the norm. Understanding the concepts was not necessary as long as the knowledge was present. Through many years of teaching, I now understand that best practice for learning needs to incorporate both procedural knowledge (the how) and conceptual understanding (the why).
Students in Precalculus recently began a focus on trigonometry, a study of the relationship between triangle side lengths and angle measurements. At first glance, their work on paper seems very procedural and surface level. However, most students will agree that the amount of conceptual understanding required to answer those questions is highly complex.
The unit circle is a good starting point to get to the heart of trigonometry. Students created their own unit circle using a paper plate to help visualize the connection between the degree and radian measures of an angle. They also got to see the connection between one radian and the radius of a circle. Once the concepts became more apparent, students worked with procedural fluency. Several ways fluency was addressed with students was through an online flashcard site called Quizlet, online interactive games with the whole class and individually through Quizizz, a card game of war with degrees and radians, an open-middle problem, a relay game, an online matching activity, and “I Have, Who Has” with the unit circle. Giving students opportunities in multiple ways to build conceptual and procedural fluency helps students not only understand but also retain new learning.
