Documenting the knowledge of low-attaining third-and fourth-graders: Robyn's and Bel's sequential structure and multidigit additon and subtraction

Aspects of students’ arithmetic knowledge are described via two case studies of responses to tasks during a videotaped assessment interview. Tasks include reading numerals, locating numbers, saying number word sequences by ones and tens, number word after or before a given number, incrementing and decrementing by ten, addition in the context of dot strips of tens and ones, and addition and subtraction involving bare numbers. On many tasks the students had significant difficulties and responded differently from each other. The paper demonstrates the idiosyncratic nature of arithmetical knowledge, and the significance of context in students’ multidigit thinking.