EVA KELLNER, ANNICA GULLBERG, IIRIS ATTORPS, INGVAR THORÉN and ROY TÄRNEBERG PROSPECTIVE TEACHERS’ INITIAL CONCEPTIONS ABOUT PUPILS’ DIFFICULTIES IN SCIENCE AND MATHEMATICS: A POTENTIAL RESOURCE IN TEACHER EDUCATION Received: 23 March 2009; Accepted: 14 July 2010 ABSTRACT. A crucial issue for prospective teachers (PTs) in their education is to develop pedagogical content knowledge (PCK; i.e. how to make a topic comprehensible to pupils). However, research has shown that PTs may have tacit ideas about teaching that act as filters preventing consideration of unfamiliar and discrepant ideas. These ideas must be elicited and taken into consideration in order to be modified. Therefore, PTs’ explicit conceptions may constitute a valuable resource in teacher education. The aim of this study was to investigate PTs’ ideas about pupils’ difficulties, at a topic-specific level, upon beginning the teacher education programme. The “Lesson Preparation Method” was used in four case studies to elicit the conceptions of 32 PTs regarding pupils’ difficulties in four specific science and mathematics topics: plant growth, gases, equations and heat and temperature. In all four topic groups (n =5 – 11), there was a variety of initial conceptions about pupils’ difficulties, which were categorised into two to five topic-specific categories. Although, initially, PTs may not have expressed any notions about pupils’ difficulties, conceptions were elicited by using the Lesson Preparation Method. Furthermore, we found that the initial ideas corresponded with earlier research on pupils’ difficulties, which could provide a potential resource when creating a scaffolding context in teacher education programmes where PCK development is stimulated. KEY WORDS: initial conceptions, mathematics, pedagogical content knowledge (PCK), science, teacher education One of the main purposes of compulsory education is to equip all pupils with tools to better understand their world. Understanding science and mathematics plays a central role in achieving this goal; the pupils’ understandings can range from basic everyday phenomena, like cooking and cleaning, to complex issues such as the changing conditions for life on earth. Teachers have an active role in promoting pupils’ conceptual development by setting the context and providing scaffolding for such learning. Teaching in mathematics and science is about transforming relevant subject matter content into a form that is comprehensible to pupils. This International Journal of Science and Mathematics Education (2011) 9: 843Y866 # National Science Council, Taiwan (2010)