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This paper presents the partial results of a research on the professional knowledge of mathematics olympiad evaluators teachers put into action when analyzing errors relating to algebra. By means of two tests on errors interpretation and by using analysis inspired by the grounded theory, we obtained dimensions for the characterization of knowledge in understanding about errors. In the results section, we describe a teacher's knowledge related to practice and knowledge about students' learning. [ABSTRACT FROM AUTHOR]

We present a research methodology used in a classroom study in which two different learning methods of additive problems with negative numbers are compared. With the "writing method" students write the problems, learn their structures and solve problems that have been written by their partners. With the "solving method" students practice additive problems in a given sequence, according to the problems level of difficulty. The knowledge acquired was compared with the one obtained by other students who solved additive problems from the textbook, as application of operational rules. We have used a mixed methodology: A statistical treatment to contrast the effectiveness of the methods for solving problems and a qualitative study of certain aspects of the "writing method". [ABSTRACT FROM AUTHOR]

We present a study with secondary students about three specific processes of algebraic language: Formal substitution, generalization, and modelling. Using a test, we develop a students' errors classifications, and we analyze its possible origins. Finally we present some didactical conclusions from the results. [ABSTRACT FROM AUTHOR]