Prospective high school mathematics teachers'didactic-mathematical knowledge about the sampling distribution of the mean Conhecimento didatico-matematico sobre a distribuicao da media amostral de professores bachareis estagiarios

[Objective] The aim of this study is to evaluate the didactic-mathematical knowledge of prospective Spanish teachers about the sampling distribution of the mean - specifically, basic knowledge about content, as well as epistemic and cognitive aspects of didactic knowledge. [Methodology] A sample of prospective teachers were asked to solve a problem presented to students in the university's entrance exams, to identify the concepts, properties and procedures required for its solution, and to describe the foreseeable errors of the students in this process. [Results] The results obtained showed very good levels of common mathematical knowledge, although some errors were observed, such as confusing population distributions with sampling distributions. The participants were reasonably competent in analyzing the mathematical objects (concepts, procedures and properties) required to solve the proposed task, but the level of competence in identifying possible student errors in solving the task was lower. [Conclusions] The study identifies areas for improvement in the training of prospective teachers about the sampling distribution of the mean, which should be well understood when making inferences. Such training should emphasize the difference between the three probability sampling distributions and the difference between statistics and parameters, since prospective teachers do not recognize the possibility of this type of error by their students.