Abstract: This study investigated elementary teacher education students’ content knowledge and pedagogical content knowledge of decimal numeration. Students completed a decimal comparison test, marked items they thought would be difficult for children, and explained why. Only about 80 percent of the sample tested as experts, indicating that a significant proportion of students have inadequate content knowledge of decimals. Confusion about the size of decimals in relation to zero was a significant (and unexpected) difficulty, raising concerns about the fragmentary nature of these students’ knowledge. Most students were aware of longer-is-larger misconceptions in children but there was little awareness of shorter-is-larger misconceptions. Students’ explanations for the reasons children might have difficulty demonstrated that many are good at identifying features that make comparisons difficult but less able to explain why these cause trouble. Results point to the need for teacher education to emphasise content knowledge that integrates different aspects of number knowledge, and pedagogical content knowledge that includes a thorough understanding of common difficulties.
Stacey, K., Helme, S., Steinle, V., Baturo, A., Irwin, K., & Bana, J. (2001). Preservice Teachers' Knowledge of Difficulties in Decimal Numeration. Journal of Mathematics Teacher Education, 4 (3), 205-225.