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This paper reflects on the importance that the dialectic of hypothesis - conjectures can have, not only for the development of demonstrative thinking in students, but also for the development of stochastic thinking. It argues for curricular reasons, for an approach to teaching based on problem solving, for a way of solving problems that considers simulation as a method of resolution with heuristic content and, finally, for new proposals on mathematics that the citizen of the XXI century will require and that includes the analysis of data in contexts of uncertainty. Consequently, a proposal is presented for the training of pre-service teachers to enable them to deal with such challenges. [ABSTRACT FROM AUTHOR]

This paper presents the results of a research study aimed to explore the main beliefs and conceptions that have teachers who teach mathematics at the secondary level in Honduras (students 13 to 18 years), in relation to the teaching /learning and assessment of mathematics. The results show, among other elements, that for Honduran teachers the learning of mathematics is achieved by the active participation of the students. This belief is highlighted by teachers with a bachelor in Mathematics; and that the evaluation is a process that improves teaching and learning, providing useful results but, they must be taken with special scrutiny due to mistakes and inaccuracies that always exist. As conclusions highlight the need to improve initial training and continuous training of teachers so that use resources that promotes active student participation and improve the evaluation processes. [ABSTRACT FROM AUTHOR]

In this paper we analyze the graphs produced by 207 preservice primary school teachers when solving an open-ended task in which they should compare three pairs of distributions. The graphs produced are classified according whether they are correct or not, and according to the kind of error in case of an incorrect graph. The analysis allows us to explain some of these errors in terms of semiotic conflicts. Results suggest the semiotic conflicts are related to knowledge of conventions in building the graphs, selecting the graphs, number sense and conceptual misunderstanding. The influence of using computers on the errors produced is also analyzed. [ABSTRACT FROM AUTHOR]

In this paper we assess pre-service primary school teachers' knowledge in relation to fair games. Common knowledge of content is assessed through the responses given by 167 pre- service primary school teachers to two open-problems. In addition, two components of didactic knowledge are inferred trough the participants analyses, when working in small groups: (a) Specialized knowledge of content is assessed from their analyses of the tasks' mathematical content; and (b) knowledge of content and students is assessed from their assessment of responses provided by primary school students. Results suggest the need to reinforce the training of pre-service teachers both in the mathematical and the didactic knowledge. [ABSTRACT FROM AUTHOR]

In this paper, we apply some theoretical notions of the onto-semiotic approach to mathematical cognition and instruction to analyse a lesson on addition and subtraction taken from a Spanish textbook directed to the fifth grade in primary education. Our aims are: (1) to illustrate a technique for analysing mathematics textbooks based on the ontosemiotic approach, and (2) to identify suitability criteria for developing didactical units to study the additive structures in primary education. The results obtained might be useful in the training of prospective mathematics teachers. [ABSTRACT FROM AUTHOR]