Research

  • Recent research into students' reasoning about variation refers specifically to notions of distribution that emerge. This paper reports on research where written responses, from tertiary introductory statistics students, were coded according to the level of consideration of variation. A hierarchy of reasoning about distribution is proposed, based on the notions of distribution that were evident in these responses. The hierarchy reflects students' progression from describing key elements of distribution to linking them for comparison and inference. The proposed hierarchy provides researchers with an emerging framework of students' reasoning about distribution. The research also highlights that educators need to be aware that, without a well developed consideration of variation, students' ability to reason about distribution will be hampered.

  • Our primary goal is to design a microworld which aspires to research thinking-in-change about distribution. Our premise, in line with a constructivist approach and our prior research, is that thinking about distribution must develop from causal meanings already established. This study reports on a design research study of how students appear to exploit their appreciation of causal control to construct new situated meanings for the distribution of throws and success rates. We provided on-screen control mechanisms for average and spread that could be deterministic or subject to stochastic error. The students used these controls to recognize the limitations of causality in the short term but its power in making sense of the emergence of distributional patterns. We suggest that the concept of distribution lies in co-ordinating emergent data-centric and modeling perspectives for distribution and that causality may play a central role in supporting that co-ordination process.

  • This exploratory study, a one group pretest-posttest design, investigated the development of elementary preservice teachers' understandings of distribution as expressed in the measures and representations used to compare data distributions. During a semester-long mathematics methods course, participants worked in small groups on two statistical inquiry projects requiring the collection, representation, analysis and reporting of data with the ultimate goal of comparing distributions of data. Many participants shifted from reporting descriptive exclusively to the combined use of graphical representations and descriptive statistics which supported a focus on distributional shape and coordinated variability and center. Others gained skills and understandings related to statistical measures and representations yet failed to utilize these when comparing distributions. Gaps and misconceptions in statistical understanding are discussed. Recommendations for supporting the development of conceptual understanding relating to distribution are outlined.

  • We applied a classroom research model to investigate student understanding of sampling distributions of sample means and the Central Limit Theorem in post-calculus introductory probability and statistics courses. Using a quantitative assessment tool developed by previous researchers and a qualitative assessment tool developed by the authors, we embarked on data exploration of our students' responses on these assessments. We observed various trends regarding their understanding of the concepts including results that were consistent with research completed previously (by other authors) for algebra-based introductory level statistics students. We also used the information obtained from our data exploration and our experiences in the classroom to examine and conjecture about possible reasons for our results.

  • This study uses the Attitudes Toward Statistics (ATS) scale (Wise 1985) to investigate the attitudes toward statistics and the relationship of those attitudes with short- and long-term statistics exam results for university students taking statistics courses in a five year Educational Sciences curriculum. Compared to the findings from previous studies, the results indicate that the sample of undergraduate students have relatively negative attitudes toward the use of statistics in their field of study but relatively positive attitudes toward the course of statistics in which they are enrolled. Similar to other studies, we find a relationship between the attitudes toward the course and the results on the first year statistics exam. Additionally, we investigate the relationship between the attitudes and the long-term exam results. A positive relationship is found between students' attitudes toward the use of statistics in their field of study and the dissertation grade. This relationship does not differ systematically from the one between the first year statistics exam results and the dissertation grade in the fifth year. Thus, the affective and cognitive measures at the beginning of the curriculum are equally predictive for long-term exam results. Finally, this study reveals that the relationship between attitudes toward statistics and exam results is content-specific: We do not find a relationship between attitudes and general exam results, only between attitudes and results on statistics exams.

  • Despite considerable research having been done in the area of sex differences in mathematical ability, statistical ability has rarely been the subject of a major research effort. This study focuses on the question of whether there are sex differences in statistical reasoning for college students. Participants included 245 college students in Taiwan and 267 American college students. The Statistical Reasoning Assessment (SRA) was used in this cross-cultural study to assess students' statistical reasoning ability. While the original version of the test was administered to students in the United States, a Chinese version of the instrument was administered to participants in Taiwan. Statistical methods were used to ascertain whether there were mean differences between males and females and whether there was equality between the correlation matrices for males and females. All the analysis were based on both the correct reasoning scores and the misconception scores obtained from the SRA instrument. Results tend to support the general research findings that when sex differences appear, they are in the direction favoring males, particularly in higher cognitive task such as mathematical reasoning. Analysis of the correlation matrices suggests that there are no differences in statistical reasoning between males and females for both countries. However, it should be noted that the results may be due to low item intercorrelations.

  • The teaching and learning of statistics has impacted the curriculum in elementary, secondary, and post-secondary education. Because of this growing movement to expand and include statistics into all levels of education, there is also a considerable interest in how to teach statistics. For statistics concepts that tend to be very difficult or abstract, many researchers have recommended using computer simulation methods (CSMs), but there have been very few empirically and theoretically based studies related to student achievement using these methods. The purpose of this study was to determine whether using CSMs enhanced student understanding of abstract statistics concepts for students enrolled in an introductory course. Based on a theoretical framework of how students learn statistics, the preliminary results of this study indicate some evidence that these methods may improve student understanding of abstract statistics concepts.

  • The emergence of a reform movement in statistics education has influenced the teaching and learning of statistics over the past few decades. The teaching of statistics concepts and courses in elementary and secondary education as well as the implementation of technology into the statistics classroom are important changes involved in this movement. Considering the changes in instruction and learning over the past few years, the purpose of this paper was to describe the attitudes of students enrolled in a reformed course. Although previous research has suggested that student attitudes toward statistics have been negative, the overall results suggested that students in introductory statistics courses today have more positive attitudes toward statistics than negative. Important variables related to statistics achievement such as mathematics ability, statistics experience, student confidence, and gender continue to influence student attitudes. Implications from the findings of this study might suggest that the collaborative effort from researchers and teachers to improve the teaching and learning of statistics over the past few years reveals optimistic results.

  • Although there has been a considerable amount of work evaluating the effects of different (non-traditional) instructional styles, inquiries into students?preferences of instructional style have been few. From 1998-2001, we surveyed introductory statistics students regarding various aspects of their class preferences, especially the teaching style they prefer. We analyzed the data for the purpose of seeing if there has been an increasing trend in preference towards non-traditional methods. Our results are inconclusive (p = 0.35) about the presence of such a trend. However, the overall proportion of students preferring non-traditional classes is higher than students preferring traditional classes (p < 0.001). We also used the survey data to investigate the possible attributes that relate to preference. Using Stepwise Logistic regression (with alpha = 0.10) we find that the students?ideal class-size, the number of years since they graduated from high school, the perceived learning styles of the students, and the attitudes of students towards the use of visual aids and hands-on activities are all significantly related to the teaching style preferences of students.

  • What do statistics teachers believe makes a good student of statistics? What part does the ability to communicate statistical results and ideas playing this judgment? IN this paper, we investigate these questions and suggest answers based on a recent empirical study carried out by e-mail interview with IASE members from around the world. The responses alert us to the diversity of views on the relative courses. Some teachers propose that communication skills are essential to learning statistics at university, others do not mention communication. In any discussion on statistical communication, we should be aware of the range of views held by statistics educators themselves, and the range of views that they communicate to students through their teaching.

Pages