1 Teachers’ Reflections on Nonstandard Students’ Work* Arne Jakobsen 1 & C. Miguel Ribeiro 2 1 Department of Education, University of Stavanger, Norway 2 Research Centre for Spatial and Organizational Dynamics (CIEO), University of Algarve, Portugal 1 arne.jakobsen@uis.no ; 2 cmribeiro@ualg.pt One of the tasks of teaching (Ball, Thames, & Phelps, 2008) concerns the work of interpreting student error and evaluating alternative algorithms used by students. Teachers’ abilities to understand nonstandard student work affects their instructional decisions, the explanations they provide in the classroom, the way they guide their students, and how they conduct mathematical discussions. However, their knowledge or their perceptions of the knowledge may not correspond to the actual level of knowledge that will support flexibility and fluency in a mathematics classroom. In this paper, we focus on Norwegian and Portuguese teachers’ reflections when trying to give sense to students’ use of nonstandard subtraction algorithms and of the mathematics imbedded in such. By discussing teachers’ mathematical knowledge associated with these situations and revealed in their reflections, we can perceive the difficulties teachers have in making sense of students’ solutions that differ from those most commonly reached. Introduction Inspired by Shulman’s (1987) ideas about subject matter knowledge and pedagogical content knowledge, Ball and colleagues at the University of Michigan have developed a conceptualization of math teachers’ knowledge called Mathematical Knowledge for Teaching (MKT). They describe MKT as the “mathematical knowledge, skills, habits of mind, and insight” used to carry out the work of teaching mathematics (Ball, et al., 2008). In part of their work, they focus on the development of an instrument i intended to measure teachers’ MKT (Ball et al., 2008; Hill, Sleep, Lewis, & Ball, 2007). Scholars around the world have shown interest in the MKT conceptualization and in the MKT measurement instrument, and MKT measures have been adapted and used in several countries (e.g. Indonesia: Ng, 2012; Ireland: Delaney, Ball, Hill, Schilling, & Zopf, 2008; and Norway: Fauskanger, Jakobsen, Mosvold, & Bjuland, 2012). In Norway, a complete form ii with thirty items from the Learning Mathematics for Teaching (LMT) project (e.g. Learning Mathematics for Teaching, 2011) at the University of Michigan were translated and adapted for use among Norwegian teachers (Mosvold, Fauskanger, Jakobsen, & Melhus, 2009). The primary purpose of such a study was to see if the MKT measure could give valuable information about Norwegian teachers’ knowledge, which might then contribute to the design/conceptualization of suitable professional development (PD) * Jakobsen, A. & Ribeiro, C. M. (2013). Teachers’ reflections on non-standard students work. In M. Ogunniyi, O. Amosun, K. Langenhoven, S. Kwofie & S. Dinie (Eds.), Proceeding of the 21 st Annual meeting of the Southern African Association for Research in Mathematics, Science and Technology Education International Congress on Mathematics Education, (pp. 44-54), Cape Town, South Africa. i This is composed by a set of items (questions) in which the teachers have to select the correct answer for each situation proposed from a set of given answers. For more information on these items see Hill, Schilling, and Ball (2004), and Learning Mathematics for Teaching, (2011). ii Elementary form A, MSP_A04.