Journal Article

  • This paper identifies key concepts and issues associated with the reasoning of<br>informal statistical inference. I focus on key ideas of inference that I think all students<br>should learn, including at secondary level as well as tertiary. I argue that a<br>fundamental component of inference is to go beyond the data at hand, and I propose<br>that statistical inference requires basing the inference on a probability model. I<br>present several examples using randomization tests for connecting the randomness<br>used in collecting data to the inference to be drawn. I also mention some related<br>points from psychology and indicate some points of contention among statisticians,<br>which I hope will clarify rather than obscure issues.

  • Practitioners and teachers should be able to justify their chosen techniques by taking<br>into account research results: This is evidence-based practice (EBP). We argue that,<br>specifically, statistical practice and statistics education should be guided by evidence,<br>and we propose statistical cognition (SC) as an integration of theory, research, and<br>application to support EBP. SC is an interdisciplinary research field, and a way of<br>thinking. We identify three facets of SC - normative, descriptive, and prescriptive -<br>and discuss their mutual influences. Unfortunately, the three components are studied<br>by somewhat separate groups of scholars, who publish in different journals. These<br>separations impede the implementation of EBP. SC, however, integrates the facets<br>and provides a basis for EBP in statistical practice and education.

  • Informal inferential reasoning is a relatively recent concept in the research literature.<br>Several research studies have defined this type of cognitive process in slightly<br>different ways. In this paper, a working definition of informal inferential reasoning<br>based on an analysis of the key aspects of statistical inference, and on research from<br>educational psychology, science education, and mathematics education is presented.<br>Based on the literature reviewed and the working definition, suggestions are made for<br>the types of tasks that can be used to study the nature and development of informal<br>inferential reasoning. Suggestions for future research are offered along with<br>implications for teaching.

  • This study documented efforts to facilitate ideas of beginning inference in novice<br>grade 7 students. A design experiment allowed modified teaching opportunities in<br>light of observation of components of a framework adapted from that developed by<br>Pfannkuch for teaching informal inference with box plots. Box plots were replaced by<br>hat plots, a feature available with the software TinkerPlotsTM. Data in TinkerPlots<br>files were analyzed on four occasions and observed responses to tasks were<br>categorized using a hierarchical model. The observed outcomes provided evidence of<br>change in students' appreciation of beginning inference over the four sessions.<br>Suggestions for change are made for the use of the framework in association with the<br>intervention and the software to enhance understanding of beginning inference.

  • This paper focuses on developing students' informal inference skills, reporting on<br>how a group of third grade students formulated and evaluated data-based inferences<br>using the dynamic statistics data-visualization environment TinkerPlotsTM (Konold &amp;<br>Miller, 2005), software specifically designed to meet the learning needs of students in<br>the early grades. Children analyzed collected data using TinkerPlots as an<br>investigation tool, and made a presentation of their findings to the whole school.<br>Findings from the study support the view that statistics instruction can promote the<br>development of learners' inferential reasoning at an early age, through an informal,<br>data-based approach. They also suggest that the use of dynamic statistics software<br>has the potential to enhance statistics instruction by making inferential reasoning<br>accessible to young learners.

  • In this reflective paper, we explore students' local and global thinking about informal<br>statistical inference through our observations of 10- to 11-year-olds, challenged to<br>infer the unknown configuration of a virtual die, but able to use the die to generate as<br>much data as they felt necessary. We report how they tended to focus on local<br>changes in the frequency or relative frequency as the sample size grew larger. They<br>generally failed to recognise that larger samples provided stability in the aggregated<br>proportions, not apparent when the data were viewed from a local perspective. We<br>draw on Mason's theory of the Structure of Attention to illuminate our observations,<br>and attempt to reconcile differing notions of local and global thinking.

  • To characterise statistical inference in the workplace this paper compares a<br>prototypical type of statistical inference at work, statistical process control (SPC),<br>with a type of statistical inference that is better known in educational settings,<br>hypothesis testing. Although there are some similarities between the reasoning<br>structure involved in hypothesis testing and SPC that point to key characteristics of<br>statistical inference in general, there are also crucial differences. These come to the<br>fore when we characterise statistical inference within what we call a "space of<br>reasons" - a conglomerate of reasons and implications, evidence and conclusions,<br>causes and effects.

  • This article considers being inspired by statistics as<br>both a learner and a teacher. It looks particularly<br>at a task involving research of Minard's Map, a<br>statistical representation, to create and present a<br>statistical task for a learner. It describes how the<br>use of imagery, and the enthusiasm that developed<br>as the map and its context were explored by the<br>teacher, were passed on to the learner.

  • A practical hands-on classroom exercise is described and illustrated using the price of an item as dependent variable throughout. The exercise is well-tested and affords the instructor a variety of approaches and levels.

  • This article presents a new approach to generalizing the definition of means. By this approach we easily obtain generalized means which are quite different from standard arithmetic, geometric and harmonic means.

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