Two negatives don't always make a positive: Exploring how limitations in teacher knowledge and the curriculum contribute to instructional quality

Abstract

Abstract This paper examines the contribution of mathematical knowledge for teaching (MKT) and curriculum materials to the implementation of lessons on integer subtraction. In particular, it investigates the instruction of three teachers with differing MKT levels using two editions of the same set of curriculum materials that provided different levels of support. This variation in MKT level and curriculum support facilitated exploring the distinct and joint contribution of MKT and the curriculum materials to instructional quality. The analyses suggest that MKT relates positively to teachers' use of representations, provision of explanations, precision in language and notation, and ability to capitalize on student contributions and move the mathematics along in a goal-directed manner. Curriculum materials set the stage for attending to the meaning of integer subtraction and appeared to support teachers' use of representations, provision of explanations, and precision in language and notation. More critically, the findings suggest that less educative curriculum materials, coupled with low levels of MKT, can lead to problematic instruction. In contrast, educative materials can help low-MKT teachers provide adequate instruction, while higher MKT levels seem to enable teachers to compensate for curriculum limitations. Keywords: curriculum materialsintegersmathematicsteacher knowledgeteaching quality Acknowledgements The research reported in this paper was supported by NSF grants REC-0207649, EHR-0233456, and EHR-0335411. The authors would like to thank the teachers who participated in this study as well as Merrie Blunk, Samuel Eskelson, Jennifer Lewis, Laurie Sleep, and Janine Remillard for their comments on earlier versions of this paper. Notes 1. All the teacher and student names used in this paper are pseudonyms. 2. Rebecca uses plastic tiles shaped as 'pluses' and 'minuses' instead of black and red chips.