Preservice teachers' knowledge of difficulties in decimal numeration

This study investigated preservice elementary school teachers' content knowledge and pedagogical content knowledge of decimal numeration. The preservice teachers completed a decimal comparison test, marked items they thought would be difficult for students, and explained why. Only about 80 percent of the sample tested as experts, indicating that a significant proportion of preservice teachers have inadequate content knowledge of decimals. Confusion about the size of decimals in relation to zero was a significant and unexpected difficulty, leading to concerns about the fragmentary nature of the preservice teachers' knowledge. Most preservice teachers were aware of longer-is- larger misconceptions in students, but had little awareness of shorter-is-larger misconceptions. Preservice teachers' explanations for the reasons students 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. [Author abstract]