Literature Index

The purpose of this chapter is to examine a "model-eliciting activity", based on a "real-life" problem situation, in which students were provided with an opportunity to construct powerful ideas relating to data analysis and statistics, without explicitly being taught. Student results of this activity will be examined that reveal the somewhat surprising fact that children, even those who traditionally do not perform well in mathematics, can invent more powerful ideas relating to trends, averages, and graphical representations of data than their teacers ever anticipated. The student results shared in this chapter are not unique. In classrooms where we have piloted and refined problems (including the ones presented), one common observation is that many of the children who emerge as "most productive" are often those whose mathematical abilities had not been recognized or rewarded by their teachers in the past.

This article describes the evaluation of the teaching of statistical inference in a first statistics class. A sample survey project is described as a means of assessing the effectiveness of a Bayesian approach in communicating the basis tenets of inference. There are several advantages of the Bayes viewpoint in performing this survey project, including the explicit modeling of one's prior opinion by means of a probability distribution and the relative ease in reporting statistical conclusions. Some evidence is presented to show that students with sufficient knowledge can accurately specify probability distributions. The success of the survey project is evaluated, and changes to the structure of the project are described that facilitate the interaction of the instructor with the students.

Many adults who need an understanding of statistical concepts have limited mathematical skills. They need a teaching approach that includes as little mathematical context as possible. Iterative participatory qualitative research (action research) was used to develop a statistical literacy course for adult learners informed by teaching in traditional first year university courses, workplace based training, teacher workshops and Masters of Public Policy courses. The latter learners in particular regularly come across confidence intervals and statistical significance in their everyday reading. The goal is to give them a conceptual rather than theoretical understanding of inferential concepts by developing inferential statistics logic through the introduction of exact probabilities in simple non-parametric tests (two-tailed coin tossing) and then contingency tables and parametric situations. The final course developed for the New Zealand Certificate of Official Statistics uses “hands-on” examples to reinforce concepts before proceeding to computer simulations. It emphasizes evaluation of the strength of statistical significance and its relationship to the possible cost of making an incorrect decision. Case studies that have influenced government policy reinforce inferential concepts and demonstrate the importance of statistics in complex real problems.

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 application of properties of the standard normal distribution curve. Responses to the task were analyzed using the Action, Process, Object, Schema (APOS) framework that specified a standardization and a probability layer of understanding. The success rates were 27% and 14% in the two questions, with most teachers experiencing problems in the probability layer because of a failure to link the probability values with the area covered by the curve.