A Reflection on the Process and Value of Studying Our Own Professional Growth Step 2: Decide on the Objectives for My Lesson and Formulate a Research Question When choosing objectives for my lesson, I kept in mind our standardized curriculum as well as the objectives of the inverse function lesson to be taught in my students' college algebra class the hour prior to my co-requisite class. I also needed to make sure my students would be successful in completing their homework assignment, which is regulated. My objectives for my students were the following. Students will be able to: * algebraically determine the inverse function when given a function in algebraic form, * graph an inverse function by reflecting over the line y = x, * state the relationship between the domain and range of a function and its inverse, * describe in words the relationship between a function and its inverse, and * explain in words why we switch the variables when finding the inverse function. My research question was: How do students' understandings of inverse functions change after participating in my lesson on inverse functions? Step 3: Develop the Lesson My third step was to design my lesson plan based on my literature review and chosen objectives. I focused my lesson on the real-world function I re-discovered as part of my literature review-Dolbear's Law-which is the relationship between temperature and cricket chirps. I would introduce the lesson with a short video about Dolbear's Law and have students work in groups on an activity I created. Dolbear's Law states that T= _c4 + 40 where T is estimated temperature in degrees Farenheit and C is the number of cricket chirps per minute (WTHI-TV, 2016). In part one of the activity, students would identify the independent and dependent variable in Dolbear's Law, state the domain and range, and graph the function. In part two of the activity, students would investigate the inverse of Dolbear's Law as they solve algebraically for C, identify the independent and dependent variables, determine the domain and range, and graph the inverse (see Figure 1). Finally, I would give each group a sheet of patty paper, or tracing paper, pre-printed with horizontal and vertical axes and a graph of y = x (or T = C in our case) as a dotted line. Students would graph both T = _c4 + 40 and its inverse on patty paper to see that an inverse function is the reflection over the line y = x. Figure 1: A Student's Work on Part Two of the Groupwork Activity After completing the groupwork, we would discuss our findings and bridge the gap to connect our findings to what our book includes about switching the variables to find inverses algebraically. Next, student-volunteers would come to the board to work on finding the inverse of a function algebraically. We would then discuss how we could know if two functions were inverses. Using this information we would work on an activity which invovles matching various algebraic representations of functions and their inverses to their graphs. For closure, I planned to use a think-pair-share activity with the following questions: What are the main ideas for inverse functions? What are the properties of inverses? "One student brought up opposites, another said they undo each other, and the third mentioned switching the domain and range." 8 | Fall/Winter 2020 Texas Mathematics Teacher

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