The ability to reason inferentially is increasingly important in today's society. It is hypothesized here that engaging primary school students in informal statistical reasoning (ISI), defined as making generalizations without the use of formal statistical tests, will help them acquire the foundations for inferential and statistical thinking. Teachers who engage students in ISI need to have good content knowledge of ISI (ISI-CK). However, little is known about the ISI-CK of primary education pre-service teachers. Therefore, the aim of this paper is to describe this knowledge by surveying 722 first-year pre-service teachers from seven teacher colleges across the Netherlands. The survey consisted of five tasks using open-ended questions and true/false statements. The descriptive analysis showed that most respondents understood that descriptive statistics that take the global shape of the distribution into account can be used as arguments within ISI. Although a majority agreed that random sampling is a valid sampling method, distributed sampling was the preferred strategy for selecting a sample. Moreover, when asked to make a generalization beyond the data, most pre-service teachers only described the data and did not appear to understand that a representative sample can be used to make inferences about a population. These findings suggest that it may be useful if statistics education for pre-service teachers places more emphasis on sampling and inference, thereby prompting pre-service teachers to engage in ISI.

Teachers who engage primary school students in informal statistical inference (ISI) must themselves have good content knowledge of ISI (ISI-CK). However, little is known about how college education for pre-service teachers can contribute to the development of their ISI-CK. To address this shortcoming, we used a case study to investigate ISI-CK development in a class of 21 pre-service primary school teachers who participated in a short intervention (180 min). Based on qualitative and quantitative analyses of the pretest, posttest and intervention data, the results suggest that most participants acknowledged it is possible to make uncertain inferences. An assignment to search the media for inferential claims seemed to create awareness regarding inference and the need to distinguish between a sample and a population. A simulation involving random sampling and varied sample size probably increased the participants' knowledge of sampling variability and random sampling. No development was seen in the participants' knowledge about sufficient sample sizes. The statistical investigation conducted by the participants during a model lesson may have strengthened their awareness of ISI, but it also revealed that many participants continued to favour distributed sampling over random sampling. Further research on belief formation with regard to data as evidence, sampling methods and the expression of uncertainty in the context of ISI is needed.Educ Stud Math (2018) 99:217-234 https://doi

and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights.• Users may download and print one copy of any publication from the public portal for the purpose of private study or research. • You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal ? Take down policyIf you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim.