Journal Article

  • nformal statistical inference (ISI) has been a frequent focus of recent research in statistics education. Considering the role that context plays in developing ISI calls into question the need to be more explicit about the reasoning that underpins ISI. This paper uses educational literature on informal statistical inference and philosophical literature on inference to argue that in order for students to generate informal statistical inferences, there are a number of interrelated key elements that are needed to support their informal inferential reasoning. In particular, we claim that ISI is nurtured by statistical knowledge, knowledge about the problem context, and useful norms and habits developed over time, and is supported by an inquiry-based environment (tasks, tools, scaffolds). We adopt Peirce's and Dewey's view that inquiry is a sense-making process driven by doubt and belief, leading to inferences and explanations. To illustrate the roles that these elements play in supporting students to generate informal statistical inferences, we provide an analysis of three sixth-graders' (aged 12) informal inferential reasoning - the reasoning processes leading to their informal statistical inferences.

  • The increased importance of developing statistical understanding in school education is recognised in curriculum documents across the world. The role of technology in enhancing the teaching of statistics is emphasised in these documents and the emergence of quality computer software and websites provides teachers with access to unprecedented resources for teaching statistics to young students. Assessment processes, however, have not kept pace with the advances in technology. This paper highlights some emerging and existing issues in the assessment of statistical understanding at the school level, and includes discussion of the implications for teachers and researchers

  • This paper is a comprehensive attempt to compile and classify<br>mnemonics (memory aids) that can be used in statistics education

  • This research compares a student-centered, proficiency-based assessment and reassessment of learning outcomes (PARLO) system to traditional assessment in a college-level introductory statistics class. The PARLO class was assessed on learning outcomes using a three-tiered proficiency scale and given the opportunity to resubmit assignments to increase their rating. Students' attitudes towards statistics improved more in the PARLO group, but no differences between groups were found on the CAOS test or on a common final exam. Within the PARLO group, students with a higher resubmission rate scored better on the final exam and those who resubmitted and achieved proficiency performed similarly to those achieving proficiency with the first submission. Assessing proficiency on specific learning outcomes allowed both students and the instructor to better evaluate learning.

  • Although a number of instruments for assessing attitudes toward statistics have been developed, several questions with regard to the structure and item functioning remain unresolved. In this study, the structure of the Survey of Attitudes Toward Statistics (SATS-36), a widely used questionnaire to measure six aspects of students' attitudes toward statistics, is investigated. This study addresses the previously unexplored issue of individual item functioning. Based on confirmatory factor analysis using individual items, the results suggest that the SATS-36 can be improved by removing some poorly functioning items and that depending on the goals of a specific study either six subscales could be used or three of them (Affect, Cognitive Competence, and Difficulty) can be combined into one subscale without losing much information.

  • Results of analysis of responses to a first-year undergraduate engineering activity are presented. Teams of students were asked to develop a procedure for quantifying the roughness of a surface at the nanoscale, which is typical of problems in Materials Engineering where qualities of a material need to be quantified. Thirty-five teams were selected from a large engineering course for analysis of their responses. The results indicate that engagement in the task naturally led teams to design a sampling plan, use or design measures of center and variability, and integrate those measures into a model to solve the stated problem. Team responses revealed misunderstandings that students have about measures of center and variability. Implications for instruction and future research are discussed.

  • This paper presents a framework that captures the complexity of reasoning about variation in ways that are indicative of robust understanding and describes reasoning as a blend of design, data-centric, and modeling perspectives. Robust understanding is indicated by integrated reasoning about variation within each perspective and across perspectives for four elements: variational disposition, variability in data for contextual variables, variability in relationships among data and variables, and effects of sample size on variability. This holistic image of robust understanding of variation arises from existing expository and empirical literature, and additional empirical study.

  • This article describes an investigation of Buffon's coin problem and related problems with the aid of an applet. The problems are accessible at a variety of grade levels and facilitate making connections between geometry and probability.

  • This note shows how some density functions for continuous probability distributions can be constructed in a transparent manner to help students appreciate their development.

  • This paper shows how the variance and standard deviation can be represented graphically by looking at each squared deviation as a graphical object - in particular, as a square. A series of displays show how the standard deviation is the size of the average square.

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