As an introduction to exponential functions and equations, instead of jumping right to the algebraic form, I used an "alternative" activity based on population growth. I will e-mail the document to Pam Rawson and ask her to

post it here for those interested. As I expected, students struggled with setting up the graph (units, scale) and reading large numbers expressed as scientific notation on their calculators. These students are college prep juniors and have done lots of graphing and calculator work, but still without specific detailed step-by-step instructions they flounder. I was surprised however by their extreme reluctance to estimate, from the given data, future population. A few even refused to answer the question until I told them how to do it. Over and over I emphasized that there was no right or wrong answer, that there was not an equation or formula, that their answer depended on how they interpreted the data, and that whatever their estimate they needed to have some explanation of their reasoning. I tried to relate the situation to a job -- that the boss has asked for a prediction and their job depends on a well thought out response. Reluctantly they did find a way through to an answer. Interesting class experience for me and the students both.

I was also surprised that there were so very many questions -- I thought I had written instructions with such clarity there could be no confusion, and I had my ed tech complete the activity before class to double check. She agreed that the activity was quite clear, but still students did not understand many of the questions. For example when asked to find the average growth -- and even with a hint to divide by the number of years -- students needed more direction.

I'm not sure yet if the activity will have any carry-over as we proceed with the more abstract content of exponential functions and logarithms, but hopefully it will at least have provided a concrete point of reference.