Error uses in teaching mathematics

Learning errors arise when teachers make decisions in their teaching. Nevertheless, research on error use in teacher education is scarce, even if some of that research shows that educating teachers on this topic help their students become more conscious of their learning and improves their performance. In this paper, we identify and describe the uses of error that 26 secondary mathematics teachers (organized in groups) revealed in a two years long teacher education program. For that purpose, we developed a conceptual framework on teachers' decision making when they plan lessons on mathematical topics. This framework is based on the ideas of purpose, action and result. We used this framework for constructing an initial set of categories with which we codified the final reports that the groups of teachers produced in the program. We looked for the decisions made by the groups in their lesson planning and the justifications that they gave for those decisions. We refined the categories in a cyclic process of coding and revision of the categories. This process enabled us to establish a hierarchy of purposes, actions and results. We found that the uses of error can be organized according to three general teachers' purposes: overcoming the error, assessing students' cognitive state, and producing information that can be useful in other aspects of lesson planning. For each of these general purposes, we identified the specific purposes, actions and results that configure each error use that we found in the groups of teachers written productions. We consider that knowledge about these uses is useful for the design and development of teacher education programs.