ORIGINAL ARTICLE Saying versus doing: teachers’ conceptions of creativity in elementary mathematics teaching Hana Lev-Zamir • Roza Leikin Accepted: 18 September 2012 / Published online: 29 November 2012 Ó FIZ Karlsruhe 2012 Abstract The purpose of our study was to analyze teachers’ conceptions of creativity in mathematics teaching (CIMT). We differentiated between declarative concep- tions that are expressed in teachers’ discourse about CIMT and conceptions-in-action that are expressed in teachers’ lessons. Elementary and middle school mathematics teachers (grades 4–8) were individually interviewed and then welcomed/allowed the first author of this paper to observe their lessons which in their view exemplified CIMT. In this paper we focus on two study participants, named Healy and Debby, in order to demonstrate that while teachers’ declarative conceptions seem to be very similar, their conceptions-in-action may differ dramati- cally. To explain this phenomenon we use a model of teachers’ conceptions of creativity devised earlier in this study (Lev-Zamir and Leikin, Res Math Educ 13:17–32, 2011). The distribution of teachers’ declarative concep- tions, between those of a pedagogical and mathematical nature and those of a teacher-directed and student-directed nature, appears to be central when explaining the gap between declarative conceptions and conceptions-in- action. Additionally, we demonstrate that the model has not only descriptive but also explanatory and predictive power. Keywords Creativity in mathematics teaching (CIMT)  Teachers’ conceptions  Declarative conceptions  Conceptions-in-action  Student-directed conceptions  Teacher-directed conceptions 1 Introduction The research presented in this paper is motivated by two main observations. The first is related to the importance of studying the relationship between teachers’ conceptions and their practice. The second is related to the lack of systematic research devoted to creativity in mathematics teaching (CIMT). During the last three decades, the ques- tion of the relationship between teachers’ conceptions and their teaching practice has remained the focus of attention of many researchers in mathematics education (e.g., Cooney 1985; Ernest 1989; Wilkins 2008). However, during the three decades since Haylock (1987) argued for the necessity of studying mathematical creativity in the mathematics classroom, CIMT has hardly been studied systematically insofar as it relates to teachers’ conceptions and their practice (Leikin 2009, 2011). This study explores the relationships between teachers’ declarative conceptions and their conceptions-in-action with special attention devoted to CIMT. In this paper we focus on two math teachers—Healy and Debby—whose declarative concep- tions are very similar whereas their conceptions-in-action are radically different. Analysis of their discourse on CIMT may explain the reasons for the differences that are so obviously revealed in these teachers’ lessons. 2 Theoretical background 2.1 Creativity as related to teaching mathematics Analysis of the literature devoted to the study of mathe- matical creativity pointed out the lack of an operative definition of mathematical creativity (Haylock 1987; Leikin 2009; Mann 2006). While ‘‘teaching has often been H. Lev-Zamir  R. Leikin (&) University of Haifa, Haifa, Israel e-mail: rozal@construct.haifa.ac.il H. Lev-Zamir Oranim College of Education, Tivon, Israel 123 ZDM Mathematics Education (2013) 45:295–308 DOI 10.1007/s11858-012-0464-4