Ensino e aprendizagem de estatística com ênfase na variabilidade: um estudo com alunos de um curso de licenciatura em matemática - Moreno, Marcelo Marcos Bueno (2010)
Considering that statistics has been newly included in the curriculum of primary and secondary education, the scarcity of research studies about variability described by various authors, and students‟ difficulties in understanding standard deviations and in articulating mathematical and statistical knowledge to apply them in new situations, the objective was to study the characteristics of teaching activities that promote the comprehension of variability in a set of values for students in a Mathematics teaching degree program. A Didactic Sequence was elaborated according to the proposal of constructing learning scenarios that were based on the articulation of the various theories of learning. The sequence was divided into three parts: introduction and construction of the concept of arithmetic mean, construction of the concept of variability through the use of dispersion measures, and application of the concept of variation for decision-making. Of the applied tasks, we chose three that were representative for theoretical analysis and analysis of the participants‟ work, according to the assumptions of Didactic Engineering, which was the methodology used in this study. The result of other research studies related to this subject, regarding the interpretation of variation, was confirmed. The variation was considered, only between the data, and not in relation to a measure of the central tendency. This occurrence consisted of a difficulty factor for interpreting the variability measures. The interval approach based on k standard deviations from the mean helped the participants give meaning to this measure of dispersion, and the comparison between distributions with the same mean and different dispersions helped them to perceive the insufficiency of the mean as a summary measure and the importance of measures of variation. The use of situations in which the knowledge sought is the most appropriate solution to the problem and the strategy for organizing tasks in which the students could mobilize prior knowledge to construct new knowledge were shown to be useful in constructing the concepts. At the end of the course, the students (future teachers) displayed a broader vision for performing an Exploratory Data Analysis and were concerned with considering variability