Experience-First Mathematics (EFM) is a term we adopted to describe all approaches of instruction that encourage students to take ownership of their learning. This includes problem-based learning, inquiry-based learning, and project-based learning. All of these instructional techniques require the teacher to carefully design an experience for students.
The physical setup of my room consists of students arranged around tables in groups of four to better accommodate conversation. There are multiple whiteboards around the room for students to work on together and present solutions. The room also has a LCD projector and interactive whiteboard.
The execution of EFM will vary in every classroom and certainly varies in my classroom from day to day. The members of The Blake School mathematics department each implement their own version of the approach, but what is evident in each case is a student-centered approach where students are doing mathematics in all its forms: conjecturing, testing, justifying and applying.
In my Honors Algebra II classroom the inquiry takes the form of students working on sets of problems that are designed to help them develop algebraic techniques or observe properties of functions. When discussing our approach with with Barb Everhart at Minneapolis Public Schools, I realized that a great deal of what I do in the classroom is really just the classic Think-Pair-Share. Students work on problems individually, then discuss in small groups and then we discuss major themes as a class.
To know what the classroom experience feels like for a student, it may be easiest to start at home. A typical night of homework involves two types of problems: practice problems on nearly mastered techniques and topics and motivational problems that are meant to guide students to new conclusions. Whenever possible, I try to give immediate feedback on practice problems, whether it is an online HW using our Hawkes book or just a matter of providing the key on our class website.
The Motivational Problems are the heart of our problem-based experience. Students work on these problems to the best of their ability at home, and come to school with them attempted or sometimes even fully-completed.
At the beginning of class we might answer a few questions about last night’s practice problems, but quickly transition to the motivational problem discussions. Most of the independent thinking occurred at home, and so we can jump straight into the pairing and sharing. Sometimes I will give students a fresh motivational problem, in that case I ask students to work individually for a few minutes before discussing with their table-mates. This brainstorming is important so that the discussions at the tables can have many starting points.
During these Pair discussions I circulate looking to correct groups that are coming to wrong conclusions by asking clarifying and redirecting questions. In addition I am gathering information about which students or groups have come up with efficient, novel, or standard algorithmic approaches. I then make sure that the full group discussions (Share) do not pass without hearing from those students.
It is paramount that students feel comfortable speaking to each other and sharing thoughts to the whole class. In my next post I will discuss how we establish a cooperative classroom environment.
Written by Chris Robinson