Deepening Teacher Understanding of Fundamental Concepts in Mathematics

Abstract

A growing concern among educators is not just what instructional method to utilize but the actual depth of fundamental mathematical knowledge in today’s educational work force. This project does not ask if discovery is needed or if this is a concern, but declares that the problem of a conceptual understanding deficit exists. The research project, through the development of a professional workshop, addresses both the recognition and improvement of the mathematical content knowledge of teachers. It observes professional development opportunities that focus on fundamental mathematical concepts, deepened understanding, and improved instructional methods. Throughout the project “deep understanding of fundamental mathematics” is defined utilizing Liping Ma’s explanation from Profound Understanding of Fundamental Mathematics (PUFM). This study pragmatically discusses and proposes solutions to this concern through the use of research data that includes: professional workshop materials, pre and post assessment tests of the teacher participants, survey questions, and observations from professional workshops. A professional workshop was offered over five sessions, 75 minutes in length. The workshop explored four major content areas – subtraction, multiplication, division by fractions, and the connection between area and perimeter. The sixteen workshop participants were educators in a large suburban school district and represented grade levels from elementary through high school. Their experience in the field of teaching ranged from less than six years to more than 20. Conclusions drawn from the research data analysis confirm the growing need for professional development that focuses on building fundamental mathematics knowledge for the educators of the day and encourages continued growth for tomorrow.