This paper is devoted to examining the validity of a hierarchical competency model of statistical... more This paper is devoted to examining the validity of a hierarchical competency model of statistical literacy by assessing the corresponding competency levels of primary and secondary students from Colombia and Germany. The results replicate prior findings and confirm the hierarchical competency model. The study has two novel components with respect to previous work on competency levels in statistical literacy: it examines elementary school performance and it includes an intercultural comparison. The competency scores reached by the students, however, suggest specific profiles of sub-groups of learners included in the study. The intercultural study is clearly exploratory since the samples both in Colombia and in Germany were not representative. The results point to interesting new questions and motivate further intercultural research.
INTERNATIONAL ELECTRONIC JOURNAL OF MATHEMATICS EDUCATION, 2019
The article reports an empirical study on the introduction of elementary probabilistic concepts i... more The article reports an empirical study on the introduction of elementary probabilistic concepts in school, focusing on tasks related to the psychological tradition of heuristics and biases. The concepts involved were studied using an extensional natural frequencies approach. We describe the school intervention conducted in an interaction across different school levels (5th and 9th grades) with the aim of promoting motivation and cooperation thereby strengthening learning. The different tests were assessed both qualitatively (based on argumentation analyses) and quantitatively. The results provide further evidence on the diversity of obstacles tied to probabilistic notions. More importantly, they exhibit an overall improvement in performance of students at both levels. This work confirms the efficacy of natural frequencies in eliciting the intended interpretation of probabilistic tasks and suggests that an appropriate interaction between different scholastic levels can be implemented as a fruitful learning arrangement.
Capítulo de "Rondas en Sais, ensayos sobre matemáticas y cultura contemporánea", editado por Fern... more Capítulo de "Rondas en Sais, ensayos sobre matemáticas y cultura contemporánea", editado por Fernando Zalamea.
INTERNATIONAL ELECTRONIC JOURNAL OF MATHEMATICS EDUCATION, 2020
We report on a study conceived with the idea that the use of logic in regard to mathematical reas... more We report on a study conceived with the idea that the use of logic in regard to mathematical reasoning as it actually occurs in practice is not limited to its prominent role in formal deductions and proofs. Interpretation of different mathematical situations elicits in fact the use of mostly unconscious forms of reasoning, close to those of narrative processing, which do not coincide with the expectations of traditional logic. This is pervasive, in particular, in educational situations at different levels, as we illustrate with interpretations which can emerge alongside an apparently obvious mathematical statement, namely, Pythagoras Theorem. We defend the position that analyses of "errors", should start by understanding their prevalence and non arbitrariness. Accordingly, we use a nonclassical logics whose features may give new insights to the kind of learning obstacles often found in the literature, as well as in our results.
This paper is devoted to examining the validity of a hierarchical competency model of statistical... more This paper is devoted to examining the validity of a hierarchical competency model of statistical literacy by assessing the corresponding competency levels of primary and secondary students from Colombia and Germany. The results replicate prior findings and confirm the hierarchical competency model. The study has two novel components with respect to previous work on competency levels in statistical literacy: it examines elementary school performance and it includes an intercultural comparison. The competency scores reached by the students, however, suggest specific profiles of sub-groups of learners included in the study. The intercultural study is clearly exploratory since the samples both in Colombia and in Germany were not representative. The results point to interesting new questions and motivate further intercultural research.
INTERNATIONAL ELECTRONIC JOURNAL OF MATHEMATICS EDUCATION, 2019
The article reports an empirical study on the introduction of elementary probabilistic concepts i... more The article reports an empirical study on the introduction of elementary probabilistic concepts in school, focusing on tasks related to the psychological tradition of heuristics and biases. The concepts involved were studied using an extensional natural frequencies approach. We describe the school intervention conducted in an interaction across different school levels (5th and 9th grades) with the aim of promoting motivation and cooperation thereby strengthening learning. The different tests were assessed both qualitatively (based on argumentation analyses) and quantitatively. The results provide further evidence on the diversity of obstacles tied to probabilistic notions. More importantly, they exhibit an overall improvement in performance of students at both levels. This work confirms the efficacy of natural frequencies in eliciting the intended interpretation of probabilistic tasks and suggests that an appropriate interaction between different scholastic levels can be implemented as a fruitful learning arrangement.
Capítulo de "Rondas en Sais, ensayos sobre matemáticas y cultura contemporánea", editado por Fern... more Capítulo de "Rondas en Sais, ensayos sobre matemáticas y cultura contemporánea", editado por Fernando Zalamea.
INTERNATIONAL ELECTRONIC JOURNAL OF MATHEMATICS EDUCATION, 2020
We report on a study conceived with the idea that the use of logic in regard to mathematical reas... more We report on a study conceived with the idea that the use of logic in regard to mathematical reasoning as it actually occurs in practice is not limited to its prominent role in formal deductions and proofs. Interpretation of different mathematical situations elicits in fact the use of mostly unconscious forms of reasoning, close to those of narrative processing, which do not coincide with the expectations of traditional logic. This is pervasive, in particular, in educational situations at different levels, as we illustrate with interpretations which can emerge alongside an apparently obvious mathematical statement, namely, Pythagoras Theorem. We defend the position that analyses of "errors", should start by understanding their prevalence and non arbitrariness. Accordingly, we use a nonclassical logics whose features may give new insights to the kind of learning obstacles often found in the literature, as well as in our results.
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