Journal Article

  • We report on a study of the relationship between calculator technology and student learning in two introductory statistics class sections taught by the same instructor at the University of Texas at San Antonio. At the introduction of hypothesis testing and confidence intervals, one class section (A) was given graphing calculators capable of inferential statistics to use for a few weeks. At the same time, the other class section (B) was given non-inferential graphing calculators. Data were collected on all test grades and daily quiz grades for both class sections. The students were allowed to use the inferential calculators on only the examination covering hypothesis tests and confidence intervals and on the final examination. Both sections received the same tests. We found that although use of the calculator with inferential capabilities is associated with improved scores on the inferential examination, the improvement is not significant once we adjust for performance on previous tests. Still, we note that on final examination questions specifically utilizing the calculator inference functions, the two classes perform similarly. In fact, both classes had trouble with "calculations" while at the same time answering "concept" questions fairly well. The inferential calculator did not appear to give students any clear advantage or disadvantage in their performance on examinations.

  • Students at the undergraduate level usually tend to view research methods courses negatively. However, an understanding of these attitudes is necessary to help instructors facilitate the learning of research for their students, by enabling them to create more positive attitudes toward such courses. The aim of this study is to describe the development of an "attitudes toward research" scale and verify the dimensions of attitudes toward research among undergraduate students enrolled in introductory research courses. The basic hypothesis of this research study is that the concept of attitudes is multidimensional in nature. The sample of the study consisted of 226 students who had completed a research methods course. Based on a factor analysis, five factors of student attitudes toward research were identified. These were the factors of usefulness of research, anxiety, affect indicating positive feelings about research, life relevancy of research to the students' daily lives, and difficulty of research.

  • Little is known about the way that teachers articulate notions of variation in their own words. The study reported here was conducted with 17 prospective secondary math and science teachers enrolled in a preservice teacher education course which engaged them in statistical inquiry of testing data. This qualitative study examines how these preservice teachers articulated notions of variation as they compared two distributions. Although the teachers made use of standard statistical language, they also expressed rich views of variation through nonstandard terminology. This paper details the statistical language used by the prospective teachers, categorizing both standard and nonstandard expressions. Their nonstandard language revealed strong relationships between expressions of variation and expressions of distribution. Implications and the benefits of nonstandard language in statistics are outlined.

  • This study investigated introductory statistics students' conceptual understanding of the standard deviation. A computer environment was designed to promote students' ability to coordinate characteristics of variation of values about the mean with the size of the standard deviation as a measure of that variation. Twelve students participated in an interview divided into two primary phases, an exploration phase where students rearranged histogram bars to produce the largest and smallest standard deviation, and a testing phase where students compared the sizes of the standard deviation of two distributions. Analysis of data revealed conceptions and strategies that students used to construct their arrangements and make comparisons. In general, students moved from simple, one-dimensional understandings of the standard deviation that did not consider<br>variation about the mean to more mean-centered conceptualizations that coordinated the effects of frequency (density) and deviation from the mean. Discussions of the results and implications for instruction and further research are presented.

  • This article discusses five papers focused on "Research on Reasoning about Variation and Variability", by Hammerman and Rubin, Ben-Zvi, Bakker, Reading, and Gould, which appeared in a special issue of the Statistics Education Research Journal (No. 3(2) November 2004). Three issues emerged from these papers. First, there is a link between the types of tools that students use and the type of reasoning about variation that is observed. Second, students' reasoning about variation is interconnected to all parts of the statistical investigation cycle. Third, learning to reason about variation with tools and to understand phenomena are two elements that should be reflected in teaching. The discussion points to the need to expand instruction to include both exploratory data analysis and classical inference approaches and points to directions for future research.

  • This article is a discussion of and reaction to two collections of papers on research on Reasoning about Variation: Five papers appeared in November 2004 in a Special Issue 3(2) of the Statistics Education Research Journal (by Hammerman and Rubin, Ben-Zvi, Bakker, Reading, and Gould), and three papers appear in a Special Section on the same topic in the present issue (by Makar and Confrey, delMas and Liu, and Pfannkuch). These papers show that understanding of variability is much more complex and difficult to achieve than prior literature has led us to believe. Based on these papers and other pertinent literature, the present paper, written by the Guest Editors, outlines seven components that are part of a comprehensive epistemological model of the ideas that comprise a deep understanding of variability: Developing intuitive ideas of variability, describing and representing variability, using variability to make comparisons,<br>recognizing variability in special types of distributions, identifying patterns of variability in fitting models, using variability to predict random samples or outcomes, and considering variability as part of statistical thinking. With regard to each component, possible instructional goals as well as types of assessment tasks that can be used in research and teaching contexts are illustrated. The conceptual model presented can inform the design and alignment of teaching and assessment, as well as help in planning research and in organizing results from prior and future research on reasoning about variability.

  • Evaluating the statistical process is considered a higher order skill and has received little emphasis in instruction. This study analyses thirty 15-year-old students' responses to two statistics assessment tasks, which required evaluation of a statistical investigation. The SOLO taxonomy is used as a framework to develop a hierarchy of responses. Focusing on the quality of response allowed insight into and suggestions for how instruction might be improved. The implications for teaching, assessment, and the curriculum are discussed.

  • The study describes the nature of pre-service teachers' idiosyncratic metaphors for the concept of statistical sample. These metaphors were investigated because of their potential to provide insight about individuals' content knowledge and how that content knowledge is enacted during teaching. Personal metaphors were elicited from 54 pre-service teachers through writing prompts. The writing prompt responses revealed seven different categories of thinking. In some instances, pre-service teachers struggled to construct a metaphor for the concept of sample. In the majority of cases, they constructed a metaphor for sample and discussed its relationship to their knowledge of the concept. The categories of thinking highlight some of the aspects of the concept of sample that teacher educators need to attend to over the course of instruction, and they also point out directions for further research related to metaphorical thinking about statistical content and its interaction with teaching practice.

  • A postal survey was conducted regarding statistical techniques, research methods and software used in the workplace by 913 graduates with PhD and Masters degrees in the biological sciences, psychology, business, economics, and statistics. The study identified gaps between topics and techniques learned at university and those used in the workplace, and points to deficiencies in statistical preparation for employment. Courses requested include multivariate statistics, generalized linear models, research design and power analysis taught with minimal emphasis on probability and mathematics. Recommendations are presented, such as expanding statistical service courses to eliminate gaps, the development of intensive workshops for postgraduate students and for workplace retraining, or involving staff from other departments to provide context for statistics teaching.

  • In this work we first reinterpret, using the idea of (epistemological, cognitive and didactical) obstacle some biases, heuristics, fallacies and paradoxes that arise in assigning probabilities to random phenomena, and have been described in previous research. We then reflect on the way obstacles should be taken into account in the process of teaching and learning probability. Thirdly, we analyse some didactic units related to "Dealing with chance" in a sample of Compulsory Secondary Education Spanish's textbooks (12 to 16 year-old students) to show some possible obstacles that might be induced by the presentation of this knowledge in the books. The final aim is providing some criteria to elaborate new textbooks that take into account research on probability education. Note: An extended summary in English is provided at the beginning of this paper, which is written in Spanish.

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