A Math Lesson (with minimal) Teacher Talk
What is needed to learn mathematics? I don’t know. When students struggle with math, learning occurs? How does math students struggle productively? Here is my problem. I witnessed two students in a 11th-grade course preparing for the end o the year leaving examination. The teacher decided to make the students use their English for my benefit. One student agreed to go to the board to find the difference in area between an inscribed circle and a circumscribed circle with a radius of 5 cm. The student went to the board, in English, (he was Hungarian speaking using English to practice his English in a math class) walked the entire class through his thinking. There was a lot of trust in that classroom. Maybe he was one of the best students. I don’t know, but his struggle showed me that creating a classroom atmosphere of trust one another and make mistakes together is a sign that this is a community of learners ready for anything.
Many years ago I studied social science education at Syracuse University with Dr. Jack Mallan. I had no idea what he was talking about, but now I do. His book, titled “No GODs-No Givers of Directions in the classroom” makes sense now, after 37 years. Dr. Mallan wanted his teacher candidates to perceive ourselves as facilitators of learning. My interpretation of Mallan’s work is that teachers can serve as facilitators of learning if we think about how to help students construct knowledge. If we give students a chance to work, they can demonstrate their learning. With our guidance, then learning will occur. Some teacher talk or some direct instruction is required, but the real learning happens when students are demonstrating, creatively how they understand what we want them to learn. The reformed teacher practice process requires that the teachers provide a safe environment for learning that is interactive, sustainable, and measurable. This National Science Foundation-funded project created a reformed teacher observation protocol (Piburn, 2000) for documenting reformed math teacher behaviors and student learning. The lesson I witnessed, did not conform to a typical teacher lesson with lots of teacher talk, but using the “reformed teacher protocol” the outcomes were met.
Teachers need to talk, but often, teacher talk (add a reference here later) interferes with student learning. Dr. Mallan had a mantra for convincing pre-service teachers to understand their role as facilitators of learning. Creating a space for students to demonstrate their learning is a complicated process. I witnessed the creativity of the students and the patience of the teacher during the lesson. For patience, teachers need time to prepare excellent lessons, so that students can experience the creativity that mathematics has to offer. It was an honor to have witnessed this lesson.
Mallan, J. T., & Hersh, R. H. (1972). No Gods in the Classroom: Inquiry and elementary social studies (Vol. 2). Saunders.
Piburn, M., Sawada, D., & Arizona State Univ., T. T. (2000). Reformed Teaching Observation Protocol (RTOP) Reference Manual. Technical Report.