Excellent Teaching: A Collective Case Study of Outstanding Elementary Mathematics Teachers\u27 Teaching of Mathematics

This qualitative collective case study explored the mathematical teaching of three excellent elementary teachers who were nominated by experts in mathematics and mathematics educational organizations, agencies and universities. I examined what excellent elementary mathematics teachers know and do in their practice of teaching. The study depicts detailed verbatim interactions between the teachers and students during actual teaching episodes to give the reader naturalistic examples of the explanation patterns and questioning strategies that these excellent teachers used to further students’ understandings of mathematical concepts and procedures. Analyses of the pedagogical strategies, including the interactive exploratory problem solving format these teachers used, and explanations for those decisions from the teacher and the researcher are included. The teachers were studied individually and collectively in an exploration of what excellent elementary mathematics teaching is through the lens of excellent teachers’ teaching practices in their classrooms and then compared with research literature. The findings show examples of how these teachers enhanced their students’ experiences with mathematics and identified six dimensions of excellent teaching. These teachers enabled students to become active agents of their own learning and showed how to allow students to construct their own understandings without telling them what to think or do. They empowered students by accepting them as capable thinkers who can reason and provide proof for that reasoning in early schooling experiences. These teachers encouraged students to develop and showcase their own thinking and non-routine algorithm discoveries to their peers showing multiple pathways to problem solutions and how they relate to mathematical ideas. Student Understanding of mathematics was described in examples of classroom episodes. The complexity of the teaching and learning of mathematics is explored finding unique interdependent and interwoven relationships between mathematical concepts and procedures. It was found that these teachers used cognitive approaches to mathematics teaching and taught their students based on what the students currently understood