Curricular Treatments of Length Measurement in the United States: Do They Address Known Learning Challenges? (original) (raw)

2013, Cognition and Instruction

Extensive research has shown that elementary students struggle to learn the basic principles of length measurement. However, where patterns of errors have been documented, the origins of students' difficulties have not been identified. This study investigated the hypothesis that written elementary mathematics curricula contribute to the problem of learning length measurement. We analyzed all instances of length measurement in three mathematics curricula (grades K-3) and found a shared focus on procedures. Attention to conceptual principles was limited overall and particularly for central ideas; conceptual principles were often presented after students were asked to use procedures that depended on them; and students often did not have direct access to conceptual principles. We also report five groupings of procedures that appeared sequentially in all three curricula, the conceptual principles that underlie those procedures, and the conventional knowledge that receives substantial attention by grade 3. From the primary grades forward, many students in the United States, as well as in other countries (Bragg & Outhred, 2001; Hart, 1981; Nunes & Bryant, 1996), struggle to learn measurement. More than 30 years of empirical research, both large-scale studies and smaller more focused studies targeting student reasoning, have shown substantial weaknesses in students' understanding of measurement. In the United States and other countries, children work in the elementary grades to measure many quantities, including time, weight/mass, capacity/volume, and temperature. But more attention is devoted to measuring space-length, area, and volume-than other quantities, starting in the first year of formal schooling. 1 Despite frequent everyday experiences with spatial quantities, many students do not understand units of measure, how the iteration of units produces spatial measures, or how commonly used tools (rulers and computational formulas) generate mea