Author:

Keywords:

national numbers, rational numbers

Abstract:

For most elementary and secondary students the transition from natural to rational numbers is far from evident: They often incorrectly ascribe characteristics of natural numbers to rational numbers, a phenomenon known in the research literature as the ‘natural number bias’. To properly address students’ conceptual difficulties about rational numbers, (pre-service) teachers need appropriate content knowledge (CK, i.e., a profound knowledge of rational numbers) and pedagogical content knowledge (PCK, i.e., knowledge of instructional strategies to present rational numbers taking into account students’(mis)conceptions). There is evidence that the CK and PCK of pre-service teachers in mathematics is limited, although systematic and large-scale studies in the rational number domain are missing. This study aims to meet this gap by systematically investigating (1) pre-service teachers’ CK and PCK about rational numbers, (2) the relation between CK and PCK, and (3) the difference between pre-service elementary and lower secondary teachers’CK and PCK. We administered a new paper - and - pencil test that was especially designed to investigate teachers’ CK and PCK about rational numbers to 158 pre-service elementary teachers of three teacher training institutes and to 34 pre-service lower secondary teachers of two teacher training institutes. The results reveal, first, gaps in elementary and lower secondary pre-service teachers’ CK and PCK. Second, it was found that pre-service teachers’ CK is a necessary but not a sufficient condition for pre-service teachers’ PCK. Third, whereas pre-service elementary teachers performed significantly worse on the CK-items than pre-service lower secondary teachers, no significant differences were observed on the PCK-items.