Maxine Pfannkuch

The Language of Shape

Students often struggle with describing the shape of different data distributions as they are distracted by the noise and do not ‘see’ the signal. Their attention is drawn to the actual outline of the distribution rather than an inferred distributional shape. In this chapter, we describe part of an instructional sequence for learning about shape starting with large data distributions. The instruction was trialled in a year 10 class (age 14) and included a focus on developing the language of shape for describing distributions and identifying key features for description. Responses from pre- and post-tests are briefly discussed and a proposed framework for describing distributions is presented.

Developing Teachers’ Statistical Thinking

In this chapter learning experiences that teachers need in order to develop their ability to think and reason statistically are described. It is argued that teacher courses should be designed around five major themes: developing understanding of key statistical concepts; developing the ability to explore and learn from data; developing statistical argumentation; using formative assessment; and learning to understand students’ reasoning.

Conceptual Challenges in Coordinating Theoretical and Data-Centered Estimates of Probability.

A core component of informal statistical inference is the recognition that judgments based on sample data are inherently uncertain. This implies that instruction aimed at developing informal inference needs to foster basic probabilistic reasoning. In this article, we analyze and critique the now-common practice of introducing students to both “theoretical” and “experimental” probability, typically with the hope that students will come to see the latter as converging on the former as the number of observations grows. On the surface of it, this approach would seem to fit well with objectives in teaching informal inference. However, our in-depth analysis of one eighth-graders reasoning about experimental and theoretical probabilities points to various pitfalls in this approach. We offer tentative recommendations about how some of these issues might be addressed.

A Modelling Perspective on Probability

In this chapter, we argue for three interconnected ways of thinking about probability—“true” probability, model probability, and empirical probability—and for attention to notions of “good”, “poor” and “no” model. We illustrate these ways of thinking from the simple situation of throwing a die to the more complex situation of modelling bed numbers in an intensive care unit, which applied probabilists might consider. We then propose a reference framework for the purpose of thinking about the teaching and learning of probability from a modelling perspective and demonstrate with examples the thinking underpinning the framework. Against this framework we analyse a theory-driven and a data-driven learning approach to probability modelling used by two research groups in the probability education field. The implications of our analysis of these research groups’ approach to learning probability and of our framework and ways of thinking about probability for teaching are discussed.

Official Statistics and statistical literacy: They need each other

Statistical literacy involves products that use words, nu mbers and graphs together to communicate messages. It includes skills in making and using these products. The focus for National Statistics Offices (NSOs) is on making data products, in cluding statistical indicators. Such products are becoming more numerous, more detailed, more diverse, and more readily available. Students, in learning to make their own data products, can use Official Statistics as models of good practice, giving them a ready-made and large resource to draw on. Statistics New Zealand, like some other NSOs, has a number of products designed specifically to support school statistic s learning and a larger number designed for public and/or professional audiences. We outline some established and new products of both forms including Synthetic Unit Record Files (SURFs) for schools and the educational use of (free) public releases inclu ding Hot Off The Presses, Infoshare (time-series data sets), Table Builder, and QuickStats about places and subjects. There are fun challenges for both official statistics agencies and statis tical literacy educators here. We discuss how both groups can work together to ensure that the education community knows about these products and knows how to use them effectively. We need to ensure that these data products are accessible, interestin g, valued and engaged with. The Certificate in Official Statistics aims to advance the pra ctice of statistical literacy in the Official Statistics sec tor. We outline our four years of experience with this qualification.

Inference and the introductory statistics course

This article sets out some of the rationale and arguments for making major changes to the teaching and learning of statistical inference in introductory courses at our universities by changing from a norm-based, mathematical approach to more conceptually accessible computer-based approaches. The core problem of the inferential argument with its hypothetical probabilistic reasoning process is examined in some depth. We argue that the revolution in the teaching of inference must begin. We also discuss some perplexing issues, problematic areas and some new insights into language conundrums associated with introducing the logic of inference through randomization methods.

Probability With Less Pain

Summary The teaching of probability theory has been steadily declining in introductory statistics courses as students have difficulty with handling the rules of probability. In this article, we give a data-driven approach, based on two-way tables, which helps students to become familiar with using the usual rules but without the formal structure.

Assessment of school mathematics: Teachers’ perceptions and practices

This is the first report of a proposed ten-year interval longitudinal study about teacher assessment practice in Auckland, New Zealand. Interviews with teachers of Year 3, 6, 8, 10, and 13 students are analysed. These interviews indicate that primary teachers are using a variety of assessment strategies in a mastery-based system. Their judgement of mathematical performance is dominated by the belief that all students must feel that they are achieving. The secondary teacher interviews indicate common use of alternative assessment strategies in non-examination classes. Judgement of student performance is benchmarked against national examinations. It is conjectured that an education system effect determines teachers’ assessment practices.

LAYING FOUNDATIONS FOR STATISTICAL INFERENCE

In this paper we give an overview of a five-year research project on the development of a conceptual pathway across the curriculum for learning inference. The rationale for why statistical inference should be part of students’ learning experiences and some of our long deliberations on explicating the conceptual foundations necessary for a staged introduction to inference are described. Implementing such a pathway in classrooms required the development of new dynamic visualizations, verbalizations, ways of reasoning, learning trajectories and resource material, some of which will be elucidated. The trialing of the learning trajectories in many classrooms with students from age 13 to over 20, including some of the issues that arose, are briefly discussed. Questions arising from our approach to introducing students to inferential ideas are considered.

Students’ difficulties in practicing computer-supported statistical inference: Some hypothetical generalizations from a study

When introducing students to statistical inference using bootstrapping and randomization methods and new infrastructure such as dynamic visualizations, new conceptual development issues may be revealed. From a pilot study and a main study involving over 3000 students from the final year of high school and introductory university statistics, we use preliminary results to conjecture potential conceptual issues and obstacles. In imitation of an insightful paper of Biehler (1997), we identify seven problem areas and difficulties of students related to using bootstrapping and randomization inferential methods from our research. Although dynamic visualizations have the power to reveal chance variation and the depth of the conceptual structure underpinning the methods in ways that were not previously accessible, the identified areas indicate that attention to the necessity of precise verbal descriptions and the nature of the argumentation are important. In accord with Biehler we surmise that we may need to develop a habit of mind in students that is orientated towards a careful interpretation and understanding of graph visualizations.