A profile of reform practices: Enhancing student numeracy achievement for part-whole thinkers

Abstract

National and international studies suggest that many students experience difficulty in developing part-whole mental computation strategies. The purpose of this mixed-methods study in a Decile 2 school was to identify factors contributing to some students' difficulties with part-whole thinking, and to suggest ways of accelerating student progress in this area, within the context of The Numeracy Development Project initiative. System-level, teacher-level and student-level factors were considered in this study. The New Zealand Curriculum and Mathematics Standards together specify mathematics content that students are generally expected to master at particular year levels. However, in the context of group teaching, a child's exposure to the national curriculum hinges on the teacher's identification of the child's learning needs, using a diagnostic interview tool. This tool represents a system-level influence on student opportunity to learn. Quantitative analysis of longitudinal school data was used to describe a student 'plateau' in learning. A complex pattern of summer holiday gains and losses in numeracy stages across six year Levels suggested that student assessments were influenced by a factor in addition to 'actual' student numeracy levels. Further, student diagnostic interview data suggested that teacher assessments might underestimate student capability for part-whole thinking. Additional teacher-level factors were explored using data from semi-structured interviews with two teachers, self-reported teaching strategies, and a teacher questionnaire. Numeracy interviews with four early part-whole students sought to identify specific knowledge gaps limiting further progress. The children used a variety of mental computation strategies to solve problems involving 2-digit and 3-digit numbers, and overall they demonstrated fluent recall of basic addition facts. However two aspects of place-value knowledge appeared to limit student achievement, and to be related to the role of materials in classroom teaching.