Mathematics, Paideia, & Seminar

Mathematics requires higher order conceptual and analytical skills, therefore, it is often difficult to completely forego direct instruction or essential skills practice. For this reason, I developed three strategies to assist students in acquiring rigorous mathematical content at the expense of an instructor as an explicit pedagogue, in favor of the instructor as a nurturer, or participant in the process of paideia. In order the three strategies are:

1) Teacher-Presenter-Scribe
2) Classic Mathematics
3) Practice-Create-Reflect

In order, let me address the methodology of each one. First of all, Teacher-Presenter-Scribe is a two or possibly three day lesson in the “we do” segment of a lesson plan, i.e., within what is called “structured practice.” In short, the students have already received some form of introductory direct instruction and are now ready to practice with the aid of the teacher. Thus, I assign the students to cooperative groupings, which I call PODs, and then assign each of these PODs a problem. The problems vary in difficulty and my choice in assigning problems varies with the blend of the group. Furthermore, I reserve the right to create homogenous, heterogenous, and random groups as needed for student learning. The students partake in the design of this strategy with me and lay out the ground rules. Once the ground rules are decided upon, the students begin the formal stage of cooperative practice on the assigned problem. As I circulate, the students begin to formulate their answers. After the remaining part of one period and possibly the beginning of another, the students begin to “own” the assigned problem and start to debate how they will present it to the other students. I continue to circulate and assist in designing this presentation. Once the students finish, they are graded upon how effectively they introduce the material to their peers. In short, I assign or allow students to pick groups, I circulate and help them problem solve, and then the “presenter” uses the SMART board and other technology I have access to, in order to present the problem to his or her peers. It requires so much work and encourages so much higher order understanding, that I weight this assignment as a test, or a performance assessment.