Conference Paper

  • Statistics is viewed as having no true connection with real-life activities. Even the typical components of an introductory statistics course (descriptive statistics, probability, and inferenctial statisticsP are seen as being unrelated to each other. Often descriptive statistics, being less mathematically sophisticated, is rushed through, then lase of probability and combinatorics are inroduced via formulas, and finally inferential statistics is presented. The link between inferential statistics and probability is often completely lost upon the student (Hawkins, Jolliffe, & Glickman, 1992). Most research in statisitcs education has been focused upon what the instructor can do to imrpove the cognitive side of instruction (Gal & Ginsberg, 1992); Fordon, 1999). RElatively less research has focused upon the statistics student (some examples are Gal & Ginsberg, 1994; Garfield, 1995; Gordon, 1995a, 1995b, 1999). In particular, little work has been done in exploring the approach to learning used by statistics students; one such work, that classified students as using either a deep or surface approach to learning, is by Gordon (1999).

  • We distinguish two conceptions of sample and sampling that emerged in the context of a teaching experiment conducted in a high school statistics class. In one conception "sample as a quasi-proportional, small-scale version of the population" is the encompassing image. This conception entails images of repeating the sampling process and an image of variability among its outcomes that supports reasoning<br>about distributions. In contrast, a sample may be viewed simply as "a subset of a population"- an encompassing image devoid of repeated sampling, and of ideas of variability that extend to distribution. We argue that the former conception is a powerful one to target for instruction.

  • In order to investigate the impact of simulation software on students' understanding of sampling distributions, the Sampling Sim program (delMas, 2001) was developed. The use of this software with students has been the subject of several classroom research studies conducted in a variety of settings (see Chance, delMas, and Garfield, in press). This paper examines the effect of several versions of a structured activity on students' understanding of sampling distributions. The first version of the activity was created to guide the students' interaction with the simulation software based on ideas from previous studies as well as the research literature. Two subsequent versions introduced a sticker and scrapbook activity that allowed students to keep a visual record of the effects of change in population shape and sample size on the resulting distributions of sample means. Four questions guided the studies reported in this paper: how can the simulations be utilized most effectively, how can we best integrate the technology into instruction, which particular techniques appear to be most effective, and how is student reasoning of sampling distributions impacted by use of the program and activities. A variety of assessment tasks were used to determine the extent of students' conceptual understanding of sampling distributions. As classroom researchers, a main goal was to document student learning while providing feedback for further development and improvement of the software and the learning activity. Ongoing collection and analysis of assessment data indicated that despite students' engagement in the activity and apparent understanding of sampling distributions and the Central Limit Theorem,<br>they were unable to apply this knowledge to solve novel problems. In particular, they had<br>difficulty solving graphical items that resembled tasks in the activity as well as well as applying the Central Limit Theorem to different situations. We comment on the lessons we have learned from this research, our explanations for why so many students continue to have difficulties, and our plans for revising the activity.

  • To support the development of statistical inquiry, teachers must know more than statistical procedures; they must learn to investigate, reason, and argue with statistical concepts and techniques. For mathematics teachers, this is often unfamiliar territory. This study investigates the process of teachers' statistical inquiry and documents its development during a 6-month professional development sequence that immerses teachers in learning statistics while analyzing their students' high-stakes state assessment results. We will report, based on empirical research, how an immersion model in statistics can influence that development.

  • This study developed a graphicacy assessment instrument which can (a) assess and measure pupils' progress in graphical understanding for the National Curriculum, (b) identify significant errors and misconceptions in graphing held by Year 10 Mathematics pupils and so (c) help raise teachers' awareness of their pupils' mathematical thinking.<br>A carefully constructed set of graphical problems related to the research literature and located in the National Curriculum was administered to a pilot group of pupils. The problems were deliberately posed in such a way as to encourage relevant isconceptions to come to the surface. The test was 'scaled' using Rasch methodology and a graphicacy measure results, with the main misconceptions plotted with the items on the same scale. The pupils producing the most common errors in the test were selected to take part in some group interviews to get an insight into their way of thinking and to collect evidence for discussion with teachers. Data from teachers' interviews and questionnaires were also collected to ascertain the curriculum validity of the ssessment and to probe their knowledge of their pupils' understanding.

  • The development of a Revised National Curriculum Statement is seen as a key project in the transformation of South African Society. The thrust of the project is towards achieving "a prosperous, truly united, democratic and internationally competitive country with literate, creative and critical citizens leading productive, self-fulfilled lives in a country free of violence, discrimination and prejudice." (Curriculum 2005, Learning for the 21st Century 1997, Department of Education, Pretoria.)<br><br>Curriculum reform in South Africa thus faces a two-fold challenge. The first is the post-apartheid challenge which requires developing the knowledge, values and skills base for South Africa's citizens necessary for greater social justice and development. Secondly, there is the challenge of participating in a global economy. This raises questions about the knowledge, values, skills and competencies for innovation and economic growth for the 21st Century.<br><br>The view taken by the curriculum designers is that the best route to greater social justice and development is through a high-knowledge and high skills curriculum.<br><br>This paper will explore the meaning and importance of numeracy and in particular of statistical literacy, within this context. The paper will focus largely on the relationship between values and mathematical/statistical literacy within the South African context.

  • The authors prepared a paper that described an example of a second course in applied regression analysis as part of the ASA Undergraduate Statistics Education Initiative (USEI) Symposium. They recommended that such a course include many practices that are not commonly integrated in a typical applied statistics course. Here the authors will give examples of such practices that they have used successfully (and can be effectively used in any introductory applied statistics course). Because data analysis must be the central theme of the course, examples of how the instructor and students can obtain interesting, real-world data will be given. These include novel activities to collect data in class, as well as web and text resources for data. The USEI paper strongly recommended that students should experience the entire data collection and analysis process. The USEI paper emphasized that active learning must be included in any such course. Activities that promote active learning such as the use of short talks to introduce concepts followed by class discussion and student presentations of examples will be given. Appropriate technology is an indispensable part of such a course. At a minimum this means that the course has suitable computational and conceptual software.

  • Students in the first statistics course generally have trouble reasoning about statistics and the concept of probability. The reform movement tin teaching statistics suggests a variety of good practices. In an attempt to increase student learning, we have researched the use of active learning, cooperative groups, and authentic assessment. In this study we have added web-based instructional materials and on-line small group discussion activities. This classroom-based research looks at an aspect of learning we have not studied previously, reasoning about probability. Due to the large size of this section of sophomore level statistics (N=126), student interaction in thinking g through activities was captured electronically through the use of WebCT on-line group discussion. The on-line discussion format had both strengths and weaknesses, which will be discusses. The WebCT content of the group discussions on-line was captured and analyzed to determine how students reasoned through the activity. The purpose of this study was to explore students' reasoning in completing group-based activities on probability.

  • This paper presents a summary of action research I am doing investigating statistics students' understandings of the sampling distribution of the mean. With 4 sections of an introductory Statistics in Education course (n=98 students), I have implemented and evaluated a computer simulation activity (delMas, Garfield, &amp; Chance, 1999) to show students the sampling distribution "in action," as recommended by many authors and statistics professors. Assessments after the activity point to clear deficiencies in student understanding, such as not understanding how sample size affects the shape and variability of sampling distributions. With the addition of the computer simulation, students' understandings are still incomplete. This is most evident as I move forward in class and introduce inferential statistics. My results discuss some of the deficiencies I have identified in student understandings. Also included is a discussion of how the action research cycle will continue to work on these deficiencies.

  • Statistical communication has become a larger part of statistics pedagogy during the previous decade, particularly for those students who are majoring in the discipline. Students in servicing courses may have less opportunity to develop statistical communication skills, as they usually take only a small number of statistics subjects: it is this group that forms the basis of our present study. Based on analysis of the discourse in interview transcripts, we highlight an interesting disjunction: many students seem to be able to communicate their understanding of statistics to the interviewer, but their statements about their statistical communication imply that they are unaware that they are communicating statistically during this process. We briefly explore the pedagogical implications of our findings.

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