Passive and Active Activities in the Flipped Classroom (Part 2)


I originally planned this post to be about the Verizon Activity I talked about at MAA Mathfest. However, I decided to write about an activity I came up with on my way back from the Mathfest.

I guess all of you are also finishing off your first week or two of classes. Over the years I have spent less and less time going over the course policies on the first day. For me, the first day used to be an anomaly. I talked all of the hour and fifteen minutes and they sat. None of the subsequent classes would be like this. Yet this first day often turns students off and gives them the impression that my class is a one way communication channel. Many students may drop the class purely on the basis of that first day.

Instead of spending the entire class on the syllabus, I do fifteen minutes on how their grade is determined and then move on to an activity. They take a syllabus quiz over everything and that seems to be a better way to get them to review what they will be held responsible for. For my college algebra class this semester, this activity had a secret motive. I decided to add to the group activities I do in class and make the projects in the class a collaborative effort. To make these groups effective, I need to get a feel for the students and how they work together. I wanted the activity to give me a feel for their personality…leader or follower. Two weeks ago I was in Northern California on my way back from MAA Mathfest in Portland. I decided to drive through the scenic redwood country along the coast. It was not my first trip there, but I was still awed by the size and majesty of the trees along the Avenue of the Giants. I had hoped to take some great pictures and use the trees as some sort of metaphor about learning mathematics. Something like, “You need a good base for your knowledge to soar!”


I don’t think I could have said that with a serious look on my face.

Instead I became fascinated with the dimensions on the trees.

The question that came to mind was, “How heavy is this tree?” During the 17 hours of driving back to Prescott I formulated the activity below for my students.


For my face to face class, I assigned five person groups based purely on alphabetical order. My online class also tackled the question by commenting on the post. Only a few of them actually left comments…but what they did was great. As they worked on the activity, I circulated around the class asking about their strategy and suggesting possibilities. I also made it a point to ask them their names as I conversed with them…this also helped me to make notes on the students actively participating and those standing in the background. I am using those notes to formulate permanent groups for the rest of the semester.

I also made a post about one possible solution later in the week.

This morning I linked my blog to a post on Wired Magazine’s Blog about Google’s open ended problems.

How timely! This post talks about a Google interview question, “How heavy is the Empire State Building?” This is the same sort of question as I asked and a basis for another first day activity.

I like these types of questions in College Algebra and above because it gets them away from thinking that math always has “a correct answer”. This perception comes from students emerging from beginning and intermediate algebra. In fact, I included a survey in College Algebra that asked them to give me their most positive math learning experience. Several students gave answers like, “Passing intermediate algebra