Journal Article

  • A well-substantiated, surprising finding is that people judge the occurence of an event of low probability as less likely when its probability is represented by a ratio of small numbers (e.g., 1 in 20) than of larger (e.g., 10 in 200) numbers. The results of three experiments demonstrated that this phenomenon is broadly general and occurs as readily in pre- as in postoutcome judgments. These results support an interpretation in terms of subjective probability, as suggested by the principles of cognitive-experiential self theory, but not as an interpretation in terms of imagining couter-factual alternatives, as proposed by norm theory.

  • This paper provides examples of students' reflections on learning statistics. The Mathematics Learning Centre, where I teach, offers help to students experiencing difficulty with basic mathematics and statistics courses at the university. The excerpts are drawn from surveys or interviews of these and other students studying statistics at the University of Sydney. Activity theory, which is based on the work of Vygotsky, provides a helpful conceptual model for investigating learning at the university level. From the perspective of activity theory, learning is viewed as a mediated activity in a sociohistorical context. In particular, the way a student monitors and controls the ongoing cognitive activity depends on how that individual reflects on his or her efforts and evaluates success. In Semenov's words, " Thought must be seen as a cognitive activity that involves the whole person" (1978, p. 5). Students' interpretations of their learning tasks and the educational goals for their self-development are discussed within this theoretical framework.

  • Statistical education now takes place in a new social context. It is influenced by a movement to reform the teaching of the mathematical sciences in general. At the same time, the changing nature of our discipline demands revised content for introductory instruction, and tehcnology strongly influences both what we teach and how we teach. The case for substantial change in statistics instruction is build on strong synergies between content, pedagogy, and technology. Statisticians who teach beginners should become more familiar with research on teaching and learning and with changes in educational technology. The spirit of contemporary introductions to statistics should be very different from the traditional emphasis on lectures and on probability and inference.

  • A detailed, multisite evaluation of instructional software design to help students conceptualize introductory probability and statistics yielded patterns of error on several assessment items. Whereas two of the patterns appeared to be consistent with misconceptions associated with deterministic reasoning, other patterns indicated that prior knowledge may cause students to misinterpret certain concepts and displays. Misconceptions included interpreting the y-axis on a histogram as if it were a y-axis on a scatter plot and confusing the values a variable might take on by misinterpreting plots of normal probability distributions. These kinds of misconceptions are especially important to consider in light of the increased emphasis on computing and displays in statistics education.

  • This article looks at a process of integrating real-life data investigation in a course on descriptive<br><br>statistics. Referring to constructivist perspectives, this article suggests a look at the potential of<br><br>inculcating alternative teaching methods that encourage students to take a more active role in<br><br>their own learning and participate in the process of assessing what they have learned. The article<br><br>illustrates how this teaching method enabled students to realize that imparting meaning to sets of<br><br>data is a complex activity which involves conceptual flexibility, integration of all the procedures<br><br>that one has learned, and creative reasoning

  • The use of a real data set has the potential to increase engagement and learning in students<br><br>who enrol in a statistics course at university. The present report describes the development of<br><br>an approach that uses a real data set, but one that is collected from the students. The questions<br><br>are designed so that the data set can be used throughout the course to illustrate relevant<br><br>concepts and methods in the application of introductory statistics. An evaluation was<br><br>conducted via individual interviews with a random sample of 38 students. Quantitative and<br><br>qualitative responses indicated that the survey led to in-class participation, was perceived to<br><br>be a different approach, and contributed to an interest in, understanding of, and appreciation<br><br>of the relevance of statistics. The creative use of student data is recommended to facilitate the<br><br>learning of statistics

  • Language and the telling of data stories have fundamental roles in advancing the GAISE <br><br>agenda of shifting the emphasis in statistics education from the operation of sets of <br><br>procedures towards conceptual understanding and communication. In this paper we discuss <br><br>some of the major issues surrounding story telling in statistics, challenge current practices, <br><br>open debates about what constitutes good verbalization of structure in graphical and<br><br>numerical summaries, and attempt to clarify what underlying concepts should be brought to <br><br>students  attention, and how. Narrowing in on the particular problem of comparing groups, <br><br>we propose that instead of simply reading and interpreting coded information from graphs, <br><br>students should engage in understanding and verbalizing the rich conceptual repertoire <br><br>underpinning comparisons using plots. These essential data-dialogues include paying <br><br>attention to language, invoking descriptive and inferential thoughts, and determining <br><br>informally whether claims can be made about the underlying populations from the sample <br><br>data. A detailed teacher guide on comparative reasoning is presented and discussed.

  • This research shows that active learning is not universally effective and, in fact, may<br><br>inhibit learning for certain types of students. The results of this study show that as<br><br>increased levels of active learning are utilized, student test scores decrease for those<br><br>with a high grade point average. In contrast, test scores increase as active learning is<br><br>introduced for students in the lower level grade point average group. Every student<br><br>involved in the experiment is taught three topics, each one by a different teaching<br><br>method. Students take a test following each learning session to assess comprehension.<br><br>The experiment involves more than 300 business statistics students in seven class<br><br>sections. Method topic combinations are randomly assigned to class sections so that<br><br>each student in every class section is exposed to all three experimental teaching<br><br>methods. The effect of method on student score is not consistent across grade point<br><br>average. Performance of students at three different grade point average levels tended to<br>converge around the overall mean when learning was obtained in an active learning<br><br>environment. The effects of the teaching method on score do not depend on other<br><br>student characteristics analyzed (i.e. gender, learning style, or ethnicity). A linear mixed<br><br>model is used in the analysis of results

  • The Wilcoxon statistics are usually taught as nonparametric alternatives for the 1- and 2- sample Student-t statistics in situations where the data appear to arise from non-normal distributions, or where sample sizes are so small that we cannot check whether they do. In the past, critical values, based on exact tail areas, were presented in tables, often laid out in a way that saves space but makes them confusing to look up. Recently, a number of textbooks have bypassed the tables altogether, and suggested using normal approximations to these distributions, but these texts are inconsistent as to the sample size n at which the standard normal distribution becomes more accurate as an approximation. In the context of non-normal data, students can find the use of this approximation confusing. This is unfortunate given that the reasoning behind - and even the derivation of - the exact distributions can be so easy to teach but also help students understand the logic behind rank tests. This note describes a heuristic approach to the Wilcoxon statistics. Going back to first principles, we represent graphically their exact distributions. To our knowledge (and surprise) these pictorial representations have not been shown earlier. These plots illustrate very well the approximate normality of the statistics with increasing sample sizes, and importantly, their remarkably fast convergence.

  • Recognizing and interpreting variability in data lies at the heart of statistical reasoning. Since graphical displays should facilitate communication about data, statistical literacy should include an understanding of how variability in data can be gleaned from a graph. This paper identifies several types of graphs that students typically encounter-histograms, distribution bar graphs, and value bar charts. These graphs all share the superficial similarity of employing bars, and yet the methods to perceive variability in the data differ dramatically. We provide comparisons within each graph type for the purpose of developing insight into what variability means and how it is evident within the data's associated graph. We introduce graphical aids to visualize variability for histograms and value bar charts, which could easily be tied to numerical estimates of variability.

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