Teach 180: Think Like a Mathematician (Day 96)

Today we began a unit on exponential functions in PreCalculus.  Each group of students was given a function and asked to do the following: create a table of values, graph the function, find any asymptotes, determine the domain and range and find any intercepts.  Then, they put their work on large sheets of chart paper, which we posted in the back of the classroom.  You can see two samples of student work here.

Once they were posted I invited students to stand in front of the posted graphs and I asked them the following questions.  How do they compare?  How are they alike?  How are they different?  These are the types of questions we need to ask our students.  Answering these questions help students see connections between ideas and it allows them to reconstruct their understanding of a concept long after the exam is over.  The more we ask these questions of our students, the more comfortable they get with making observations for themselves and the fact that in math there can be more than one approach or one right answer to a question.  Slowly, I am getting my students to think like mathematicians.