Fourth Graders' Gradual Construction of Decimal Fractions during Instruction Using Different Physical Representations

1 classroom of 25 low-achieving fourth graders was introduced to decimal fractions during an 11-day unit that emphasized conceptual features of decimals. Students' understandings were assessed 4 times during instruction by individually interviewing 8 students and providing written tests for 21 students. Changes in students' responses indicated that (1) their thinking was influenced by the types of concrete materials they used to represent decimals; (2) low achievers increased their understanding of some important properties of decimals; and (3) understanding grew gradually through a complex, chaotic looking process rather than through straightforward across-the-board insights. Group test data (N = 21) and 3 interview case studies are presented that elaborate these observations. Implications are discussed regarding teaching for understanding and engaging low-achieving students in learning with understanding.