Teaching and learning mathematics with Math Fair, Lesson Study and Classroom Mentorship

Abstract

IntroductionInitially encouraged by the findings of the Third International Mathematics and Science Study (Institute of Education Sciences, 1995), we started our first Lesson Study. We sought and acquired external funding. We invited mathematicians from the Pacific Institute for the Mathematical Sciences (PIMS) to join our efforts. We extended an invitation to teachers from the schools in which Galileo professional developers were working. Monthly sessions with teachers, mathematicians, mathematics educators and researchers all focused on improving mathematics learning and teaching were followed by job-embedded professional development for teachers. We worked with teachers in the context of their own classrooms providing them with support by teaching alongside them, videotaping their instruction for later examination and discussion and providing them timely, effective feedback on their instruction.Initially, we began with only the findings from Institute of Education Sciences (1995), knowing that something needed to change in order to bring about the stronger mathematical reasoning. Through personal communications in 1999 with James Hiebert, researcher from Institute of Education Sciences (1995) videotape study, we were encouraged to contact Clea Fernandez who was forming a Lesson Study group in the United States. While we built on many of the ideas and approaches from Fernandez and Yoshida (2004), we also modified our approach to Lesson Study to adapt to the needs of our teachers. Like Fernandez and Yoshida, teachers met to collaboratively plan lessons; however, knowing that the majority of our teachers did not have enough mathematical knowledge for teaching we always included at least one, and frequently more than one, PhD mathematician, mathematics educators and researchers in our endeavours to ensure our planning was rooted deeply in the discipline of mathematics. Although our funding allowed us to provide teachers with monies with release time to meet during class hours, we were unable to also fund teachers to obtain teaching release time to observe lessons being taught. That said, we were able to provide teachers with a combination of mathematicians, mathematics educators and/or professional developers to work alongside them in their own classrooms as they tried out new instructional strategies. To provide teachers the opportunity to learn from other teacher's lessons we videotaped the teachers. Videotapes were viewed and discussed during a portion of our group meetings.Our Lesson Study has never been devoted entirely to lesson planning. We always split our time between planning and learning mathematics for teaching as many teachers in Alberta (and Canada) lack sufficient background and understanding of mathematics (Friesen, 2005). In this way, the teachers in Alberta are not unlike many teachers in the United States.In Liping Ma's (1999) groundbreaking study she identified a discrepancy in the mathematical knowledge between teachers in the US and China. Teachers from China have less education than their U.S. counterparts, yet they have a better understanding of mathematics for teaching. Unsurprisingly, the quality of mathematics teaching was dependent on the teachers' mathematical understanding. Ma called for a more connected longitudinal concept development form of teaching mathematics.Ball et al, (2005) observed that of mathematical understanding of many U.S. teachers is dismally thin (p. 14). They argue that rather than more advanced undergraduate mathematics classes, teachers would benefit from knowing more mathematics for teaching. Yes teachers need to know the concepts and procedures they teach: fractions, functions, factoring, symmetry, etc. But to extend this knowledge into their classrooms, teachers need a different type of mathematical knowledge for teaching for planning, implementing, evaluating, and assessing student work. Beyond recognizing student errors, teachers need to be able to pin point the misconception that resulted in the misunderstanding. …