Probability signifies a mainstream strand in mathematics curricula. Nonetheless, many curricular documents prepared for teachers might not offer enough support. In such a situation, a further reflection on teachers' professional knowledge for teaching probability is demanded; especially, from the perspective of probabilistic reasoning (PoPR) that…

Informal inference is a critical practice for students to engage in if they are to understand formal statistical methods. However, during informal inference students often utilize complex ideas that many in-service teachers are not prepared for as they have not had the opportunity to think deeply about statistics and develop statistical knowledge…

Modeling using mathematics and making inferences about mathematical situations are becoming more prevalent in most fields of study. Descriptive statistics cannot be used to generalize about a population or make predictions of what can occur. Instead, inference must be used. Simulation and sampling are essential in building a foundation for…

Randomized experiments are often seen as the "gold standard" for causal research. Despite the fact that experiments use random assignment to treatment conditions, units are seldom selected into the experiment using probability sampling. Very little research on experimental design has focused on how to make generalizations to well-defined…

The purpose of this study is to define teacher views about the difficulties in learning and teaching middle school statistics subjects. To serve this aim, a number of interviews were conducted with 10 middle school maths teachers in 2011-2012 school year in the province of Trabzon. Of the qualitative descriptive research methods, the…

The effect of simulation-based probability teaching on the prospective teachers' inference skills has been examined with this research. In line with this purpose, it has been aimed to examine the design, implementation and efficiency of a learning environment for experimental probability. Activities were built on modeling, simulation and the…

The game of Plinko offers students an exciting real-world example of the applications of probability and data analysis. The Common Core State Standards for Mathematics (CCSSI 2010) and the Guidelines for Assessment in Statistics Education (GAISE) (Franklin et al. 2007) suggest that students in grades 6-8 be given ample opportunities to engage in…

Although Bayesian methodology has become a powerful approach for describing uncertainty, it has largely been avoided in undergraduate statistics education. Here we demonstrate that one can present Bayes' Rule in the classroom through a hypothetical, yet realistic, legal scenario designed to spur the interests of students in introductory- and…

Sampling tasks and sampling distributions provide a fertile realm for investigating students' conceptions of variability. A project-designed teaching episode on samples and sampling distributions was team-taught in 6 research classrooms (2 middle school and 4 high school) by the investigators and regular classroom mathematics teachers. Data…

Some intensive quantities, such as slope, velocity, or likelihood, are perceptually privileged in the sense that they are experienced as holistic, irreducible sensations. However, the formal expression of these quantities uses "a/b" analytic metrics; for example, the slope of a line is the quotient of its rise and run. Thus, whereas students'…

This article offers suggestions for teaching confidence intervals, a fundamental statistical tool often misinterpreted by beginning students. A historical perspective presenting the interpretation given by their inventor is supported with examples and the use of technology. A method for determining confidence intervals for the seldom-discussed…

This study investigated the comprehension and effectiveness of teaching formal, probabilistic decision-making skills to middle school students. Two specific objectives were to determine (1) if middle school students can comprehend a probabilistic decision-making approach, and (2) if exposure to the modeling approaches improves middle school…

This paper describes an interactive activity that revolves around the dice-based golf game GOLO. The GOLO game can be purchased at various retail locations or online at igolo.com. In addition, the game may be played online free of charge at igolo.com. The activity is completed in four parts. The four parts can be used in a sequence or they can be…

Inference, or decision making, is seen in curriculum documents as the final step in a statistical investigation. For a formal statistical enquiry this may be associated with sophisticated tests involving probability distributions. For young students without the mathematical background to perform such tests, it is still possible to draw informal…

The authors propose a strategy for studying the effects of time-varying instructional treatments on repeatedly observed student achievement. This approach responds to three challenges: (a) The yearly reallocation of students to classrooms and teachers creates a complex structure of dependence among responses; (b) a child's learning outcome under a…