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The aim of this investigation is to explore the preservice teachers' reasoning about variation (variability or spread) when they analyze data in situations that involve risk. In particular, in this communication the responses to two problems of a questionnaire administered to 96 preservice teachers are reported. The problems are of comparing groups of data in situations of risk: stakes in games and the life expected after medical treatments. The questionnaire was applied before the preservice teachers began a course of statistical information processing and the results showed the difficulty found by students to interpret variation in this type of contexts. For these results it is necessary to reflect on the instruction of future teachers about the meanings of measures of center dispersion and dispersion to contribute to an improvement in their academic training. [This paper is written in both Spanish and English. For complete proceedings, see ED581294.]

In this research, quotient strategies and their influence on decision-making in situations that involve the comparison of probabilities are analyzed. In order to achieve this, classical probability situations modeled with urns were designed. In each situation, two urns with simple extraction, involving or not proportional relationships, were proposed to third grade secondary school students. The analysis was carried out through the categorization of the results based on the relationships established between the components of the urns (favorable, unfavorable and possible cases). The study concluded that when comparing probabilities, students not only resort to the quotient (ratio): favorable case numbers among the number of possible cases to make their choice, but to others where they also include unfavorable cases. [For the complete proceedings, see ED629884.]

Researchers, who have studied the understanding of the density property in the set of decimal numbers, have shown that the student uses the property of the discrete of natural numbers to solve tasks related to density. So, a restructuring of concepts is necessary, that is, a conceptual change from "the discrete" to "the dense". This report presents evidence from ten pre-service teachers from Mexico City that this change can initiate through the implementation of a didactic sequence. The pre-service teachers managed to visualize that a decimal number can be found in an interval. Consequently, they were able to conceive an infinity. However, several of them persisted with the idea of the existence of a successor in the set of decimal numbers. [For the complete proceedings, see ED629884.]

The document presents a set of categories for the analysis of the conceptualization of the congruence of polygons--a central theme in school mathematics--and details the application of the analytical tools used, derived from Grounded Theory, in this construction. This set of categories is called 'Interpretive Model of the Conceptualization of Polygon Congruence' (MICP). This model emerged from the interpretive analysis of empirical data recollected during the investigation. The MICP categories can be used by teachers or researchers to cover different didactic objectives (e.g., interpret the resolution of tasks with congruence content; prepare student profiles or identify their difficulties. See Peña, 2019) and it is relevant because it does not seem to exist in the literature a similar model that covers the previously stated objectives. [For the complete proceedings, see ED629884.]