Noticing mathematical fluency in the primary classroom: Attending to and interpreting students’ characteristics of mathematical fluency

Abstract

Problem-solving, reasoning, understanding, and fluency are core proficiencies of the mathematics curriculum. Yet fluency, frequently interpreted as procedural fluency, tends to be misconstrued as a separate skill concerning ‘basic facts.’ This thesis investigated mathematical fluency beyond the constraints of a procedural focus to generate evidence in support of a more expansive view of fluency.

The aim of the research was to investigate mathematical fluency characteristics students displayed and explore what teachers noticed and how they interpreted what they noticed. Qualitative research methods were undertaken through student observations and interviews, analysis of student work samples, and teacher group discussions. A framework was employed as an observational and analysis tool. The research involved two studies. In Study One, data from 160 students from seven K-6 classes were analysed and informed refinements to the characteristics of fluency framework. The importance of students’ representation modes emerged; these became important vantage points from which to view mathematical fluency. Study Two extended the investigation to encompass teachers in the role of researchers participating in the collection and analysis of student data. Nine primary teachers (K-6) and students from six classes (n= 66) participated. Teachers identified that responses beyond numerical representations were important indicators of mathematical fluency. Variations in the degree of mathematical fluency development were detected. Students perceived as possessing well-developed levels of mathematical fluency often focused on sharing ‘what they found out’ rather than ‘how they worked out the problem’.

Based on these findings, practices for nurturing well-developed levels of fluency are identified. The collection of students’ written, oral and drawn responses for noticing mathematical fluency, and the use of an analytical framework to guide teacher observations are recommended.