Juan Jesús Ortiz

Models for Statistical Pedagogical Knowledge

The education of statistics teachers should be based on adequate models for pedagogical knowledge that guide the teachers’ educators in implementing and assessing the training of teachers. In this chapter, some models that are relevant for mathematics and statistics are analysed, and a new framework that complements the previously described models is proposed. The different facets and levels that should be taken into account when educating mathematics and statistics teachers are highlighted. Some implications for the training of teachers are presented and a formative cycle directed to increase the teachers’ statistical and pedagogical knowledge simultaneously is briefly described.

Prospective Teachers’ Probabilistic Reasoning in the Context of Sampling

In this paper, we analyse the knowledge of sampling in 157 prospective primary school teachers in Spain. Using two different tasks, and taking into account common and horizon content knowledge (described in the model proposed by Ball et al. in J Teacher Educ 59:389–407, 2008), we assess the teachers’ understanding of the following concepts: population and sample, frequency, proportion, estimation, variability of estimates, and the effect of sample size on this variability. Our results suggest that these prospective teachers have correct intuitions when estimating the sample proportion when the population proportion is known. However, they tend to confuse samples and populations, sometimes fail to apply proportional reasoning, misinterpret unpredictability, and show the representativeness heuristic and the equiprobability bias.