Procedural fluency in mathematics: exploring elementary teachers’ knowledge, understanding, and application in classroom practices

Abstract

Throughout the history of public education in the United States of America, the teaching of mathematics and its focus have been topics of reform and calls for change. Students need a balanced and intentional approach to learning mathematics, which supports each student in understanding and applying mathematical concepts. The purpose of this study was to determine the level of knowledge and understanding of teachers related to procedural fluency and how components of procedural fluency are applied in classroom practices. In addition, it is important to understand that computational fluency and basic fact fluency are embedded in the larger proficiency strand of procedural fluency. The study employed a multiple case study format as well as multiple data sources to answer the research questions. The overarching research was: How does what a teacher knows and understands about procedural fluency translate into classroom practices during core instruction? The study also included the following subquestions: (1) What does a teacher know and understand about computational fluency in mathematics? (2) In what ways does a teacher plan for computational fluency development? (3) In what ways does a teacher explicitly connect conceptual understanding to computational fluency? (4) What does a teacher do to ensure the development of procedural fluency in the classroom? (5) What does fluency practice look like in the classroom? (6) What components of fluency do the practices present in the classroom address? The research design was qualitative in nature and included six cases with each participant representing one case. The researcher collected data related to teachers’ knowledge and understanding of fluency using a survey, an interview, and a follow-up interview. The researcher then completed three classroom observations for core math instructional block and three debriefs sessions with each participant to determine the level of application of classroom practices that supported the development of fluency. The data was organized in a codebook composed of a priori codes and was analyzed for themes within each case and across all the cases for themes. The study looked to place each participant in one of four categories based on their knowledge and application level: unconsciously unaligned, consciously unaligned, unconsciously aligned, and consciously aligned. The researcher found that five cases were unconsciously unaligned in terms of practices that support fluency, and one case was consciously aligned. Most teachers did not have a strong knowledge base or understanding of procedural fluency. As a result, purposeful instruction needed to support the development of procedural fluency through quality practice and assessment aligned with fluency components and actions did not appear to be occurring based on the data collected. The results suggest that additional professional development, especially in quality fluency practice, is needed to strengthen the knowledge and understanding of the teacher before application can happen in the classroom.