Structuring numbers 1 to 20: developing facile addition and subtraction

The Numeracy Intervention Research Project (NIRP) aims to develop assessment and instructional tools for use with low-attaining 3rd- and 4th-graders. The NIRP approach to instruction in addition and subtraction in the range 1 to 20 is described. The approach is based on a notion of structuring numbers, which draws on the work of Freudenthal and the Realistic Mathematics Education program. NIRP involved 25 teachers and 300 students, 200 of whom participated in an intervention program of approximately thirty 25-minute lessons over 10 weeks. Data is drawn from case studies of two intervention students who made significant progress toward facile addition and subtraction. Pre- and post-assessment interviews and five lesson episodes are described, and data drawn from the activity of the students during the episodes are analysed. The discussion develops a detailed account of the progression of students’ learning of structuring numbers, and how this can result in significant level-raising of students’ arithmetical knowledge as it becomes more formalised and less context-dependent.