This study aimed to gain knowledge of students' beliefs and difficulties in understanding p-values, and to use this knowledge to develop improved teaching programs. This study took place over four consecutive teaching semesters of a one-semester tertiary statistics unit. The study was cyclical, in that the results of each semester were used…

This study is an exploration of teachers' engagement with concepts embedded in the normal distribution. The participants were a group of 290 in-service teachers enrolled in a teacher development program. The research instrument was an assessment task that can be described as an "unknown percentage" problem, which required the…

This paper presents discussions on stochastic education in early childhood, based on two doctoral research projects carried out with groups of preschool teachers from public schools in the Brazilian cities of Suzano and São Paulo who were participating in a continuing education program. The objective is to reflect on the analysis of two didactic…

The inclusion of statistics and probability in the mathematics curriculum has always generated challenges to mathematics teachers of elementary schools. This article discusses activities that promote the professional development of such teachers. We present part of a doctoral research study of 16 teachers in which we discuss two case studies of…

The objective of this paper is to discuss aspects of high school students' learning of probability in a context where they are supported by the statistical software R. We report on the application of a teaching experiment, constructed using the perspective of Gal's probabilistic literacy and Papert's constructionism. The results…

The objective of this paper is to discuss how blind students learn basic concepts of probability using the tactile model proposed by Vita (2012). Among the activities were part of the teaching sequence "Jefferson's Random Walk", in which students built a tree diagram (using plastic trays, foam cards, and toys), and pictograms in 3D…

Although we use statistical notions daily in making decisions, research in statistics education has focused mostly on formal statistics. Further, everyday culture may influence informal ideas of statistics. Yet, there appears to be minimal literature that deals with the educational implications of the role of culture. This paper will discuss the…

This paper is based on research that investigated the development of probabilistic language and thinking by students 10-12 years old. The focus was on the adequate use of probabilistic terms in social practice. A series of tasks was developed for the investigation and completed by the students working in groups. The discussions were video recorded…

This study investigates the relationship between deterministic and probabilistic reasoning when students experiment on a real-world situation involving uncertainty. Twelve students, aged eight to nine years, participated in an outdoor teaching activity that called for reflection on the growth of sunflowers within the frame of a sunflower lottery,…

This study examined how preservice elementary teachers think about situations involving probability. Twenty-four preservice elementary teachers who had not yet studied probability as part of their preservice elementary mathematics coursework were interviewed using a task-based interview. The participants' responses showed a wide variety of…

We examined how middle school students reason about results from a computer-simulated die-tossing experiment, including various representations of data, to support or refute an assumption that the outcomes on a die are equiprobable. We used students' actions with the software and their social interactions to infer their expectations and whether or…

This paper identifies key concepts and issues associated with the reasoning of informal statistical inference. I focus on key ideas of inference that I think all students should learn, including at secondary level as well as tertiary. I argue that a fundamental component of inference is to go beyond the data at hand, and I propose that statistical…

We investigate the use of external visual representations in probability problem solving. Twenty-six students enrolled in an introductory statistics course for social sciences graduate students (post-baccalaureate) solved eight probability problems in a structured interview format. Results show that students spontaneously use self-generated…

We analyze probability content within middle grades (6, 7, and 8) mathematics textbooks from a historical perspective. Two series, one popular and the other alternative, from four recent eras of mathematics education (New Math, Back to Basics, Problem Solving, and Standards) were analyzed using the Mathematical Tasks Framework (Stein, Smith,…

What people mean by randomness should be taken into account when teaching statistical inference. This experiment explored subjective beliefs about randomness and probability through two successive tasks. Subjects were asked to categorize 16 familiar items: 8 real items from everyday life experiences, and 8 stochastic items involving a repeatable…