What problems are worth the commitment necessary to solve them? (Michael Tilson Thomas)
Students will examine, interpret, and apply the concepts of exponential functions and logarithms through Socratic questioning and real world modeling.
Show 5:36–6:36 (Ch. 3) of the Thomas video. When conducting, Michael Tilson Thomas asks himself the following questions: “What is happening? Why is it happening? What does all of this mean to me? What am I going to do about it?” Upon completion of a unit on exponential functions and logarithms, lead your class in a Socratic Seminar in which students ask themselves the same four questions regarding the topic just learned.
• “What is happening?” = What did we learn to do during this unit?
• “Why is it happening?” = Why do exponential functions have horizontal asymptotes? Why can certain real-world situations be modeled with exponential functions? Why can logarithms be used to solve exponential equations?
• “What does all of this mean to me?” = What are the benefits of expressing ex- ponential equations as logarithms and how does this help me mathematically?
• “What am I going to do about it?” = When and how will I use these concepts again in future math courses and in everyday life?
• Does the study of mathematics involve perseverance?
Ask students to create a real-world problem that models exponential growth or decay and requires the use of logarithms to solve the question they’ve created. What makes this problem worth the commitment necessary to solve it?