Calculation fluency: A mixed methods study in English Y6 primary classrooms

Emma-Louise Lord Title of study: Calculation fluency: A mixed methods study in English primary classrooms The teaching and learning of written calculation strategies remains a high priority in many national curricula. However, the available literature was dominated by quantitative studies which explored a restricted range of arithmetic operations, paying limited attention to the role of confidence or the reasons behind the selection of their calculation strategies with the learners themselves. The literature revealed that calculation fluency was generally accepted to require flexibility, efficiency, accuracy, and conceptual understanding, yet recent curriculum reforms in English schools prioritised formal algorithms and thus appeared to restrict calculation fluency in the classroom. This study explored calculation fluency among the first cohort of Year 6 learners (10- to 11-year-olds) studying under the reforms by asking: To what extent does calculation fluency among Year 6 learners vary by gender, confidence level and prior attainment? Phase 1 of this sequential mixed methods explanatory study involved a large-scale survey (N = 590) where each participant was presented with a ten-question, Likert-style mathematics confidence questionnaire followed by a workbook specifically developed for this study containing 16 age-related, context-free multi-digit calculations covering addition, subtraction, multiplication and division. The participants’ answers were compared by gender, mathematical confidence and previous attainment using regression analysis. Phase 2 consisted of a purposeful sample of learners drawn from Phase 1 (n = 23) who attended individual semi-structured interviews exploring their workbook responses in more depth. Their comments were examined using framework analysis, then the findings from both phases were integrated together to address the research question. The findings indicated that too many learners failed to satisfy the stated criteria for calculation fluency. Many learners worked inaccurately, inflexibly and inefficiently by prioritising formal algorithms irrespective of the merits of individual calculations. They either failed to recognise situations where other strategies might have been more efficient and less likely to lead to error, or they were unwilling to deviate from using formal algorithms. The findings indicated that confidence, rather than gender or prior attainment, had the greatest effect of the three predictor variables on use of the formal algorithm; confident learners were less likely to deviate from using formal algorithms than other learners. The findings also revealed that girls were significantly less likely to deviate from using formal algorithms than boys. However, most of the variance in calculation fluency was determined by factors other than gender, prior attainment or confidence. Calculation fluency was also affected by practice, knowledge of testing procedures and an individual’s checking procedures. Hence, it is recommended that future researchers consider adopting a mixed methods research design due to the insights gained in this thesis. Moreover, by addressing all four operations, I was able to identify patterns in my findings across the operations. Regarding policymakers, my findings indicated that the decision to prioritise formal algorithms in the primary curriculum may need further consideration. Schools should consider encouraging their learners to calculate more flexibly to increase their accuracy rates, calculation efficiency and conceptual understanding. Further research should be undertaken to ascertain the longer-term effects on both genders and differing mathematical confidence levels of limiting calculation flexibility at primary level when those learners will experience a curriculum dominated by problem-solving, rather than calculation, later in their education