EARLI SIG on Conceptual Change edition:8 location:Universität Trier date:1-4 September 2012
For most primary and secondary students the transition from natural to rational numbers is problematic: They incorrectly ascribe characteristics of natural numbers to rational numbers, a phenomenon known in the research literature as the “natural number bias”. To properly address this conceptual gap between the natural and the rational number domain (prospective) teachers need relevant content knowledge (CK) (i.e., Do they have profound conceptual and procedural knowledge in the rational number domain?), and pedagogical content knowledge (PCK) (i.e., Can they anticipate which misconceptions students will have and do they have appropriate representations at their disposal to prevent and remedy these misconceptions?). There is, however, evidence that the CK and PCK of elementary preservice teachers in mathematics, and especially in the domain of rational numbers, is limited. This paper documents on a new paper-and-pencil test that is especially designed to investigate preservice teachers’ CK and PCK in the rational number domain. The test consists of 48 items belonging to the following subcategories: (1) the concept of fraction (8 items), (2) the concept of decimals (8 items), (3) operations (i.e., addition, subtraction, multiplication, and division) with fractions (16 items), and (4) operations with decimals (16 items). Half of the items in each subcategory are devoted to the measurement of teachers’ CK and half to the measurement of teachers’ PCK, including two aspects: (1) teachers’ knowledge of students’ (mis)conceptions regarding fractions and decimals, and (2) teachers’ knowledge of representations that can be used to teach fractions and decimals. We already conduct a pilot study in which the CK and PCK of 30 preservice elementary teachers is measured using this test. In May 2012, a large-scale study on (the relation between) preservice elementary teachers’ CK and PCK is planned. During the SIG meeting, we will present the results of the pilot study and discuss the results from the large-scale study.