Journal Article

  • Words that are part of colloquial English but used differently in a technical domain may possess lexical ambiguity. The use of such words by instructors may inhibit student learning if incorrect connections are made by students between the technical and colloquial meanings. One fundamental word in statistics that has lexical ambiguity for students is “random.” A suggestion in the literature to counteract the effects of lexical ambiguity and help students learn vocabulary is to exploit the lexical ambiguity of the words. This paper describes a teaching experiment designed to exploit the lexical ambiguities of random in the statistics classroom and provides preliminary results that indicate that such classroom interventions can be successful at helping students make sense of ambiguous words.

  • This study investigates the relationship between deterministic and probabilistic reasoning when students experiment on a real-world situation involving uncertainty. Twelve students, aged eight to nine years, participated in an outdoor teaching activity that called for reflection on the growth of sunflowers within the frame of a sunflower lottery, where students were involved in the process of creating their own empirical data of the growth. However, the study shows not only that the students do not make use of data for predicting the outcome of an uncertain event, but also how this can be explained by students’ attention to deterministic features of the situation, brought to the fore within an ecology context and connected to a conceptual principle of ‘sharing’.

  • Many teachers of statistics recommend using real-life data during class lessons. However, there has been little systematic study of what effect this teaching method has on student engagement and learning. The resent study examined this question in a first-year university statistics course. Students (n=38) were interviewed and their reflections on the use of real-life data during the classes were coded into themes. Resulting themes were (a) relevant perspective in learning, (b) interest, (c) learn/remember material, (d) motivation, (e) involvement/engagement, and (f) understanding of statistics. The results indicate both cognitive and affective/motivational factors are associated with using real-life data to teach statistics. The results also suggest the features in data sets statistics teachers should look for when designing their lessons.

  • Context provides meaning for data analysis and the evaluation of evidence but may be distracting to students. This research explores the role of context in students’ reasoning about sampling: specifically, the relationship between the strength of students’ opinions about a topic, which provides the context for a study, and their ability to judge the quality of the sampling method and the scope of the conclusions in the study. Data were collected at four diverse institutions in both a testing environment and through individual interviews. Student responses were analyzed using a grounded theory approach. Testing environment results showed little evidence of the use of context whereas interview results shows more evidence of reliance on context-bases opinions rather than statistical principles.

  • The framework of linguistic register and case study research on Spanish-speaking English language learners (ELLs) learning statistics informed the construction of a quantitative instrument, the Communication, Language, and Statistics Survey (CLASS). CLASS aims to assess whether ELLs and non-ELLs approach the learning of statistics differently with respect to the distinctive linguistic features of the field of statistics and with respect to language resources they bring to the class. The CLASS was administered to all (n=137) students in an introductory statistics literacy course at a university with majority Mexican-American student body. Findings suggest ELLs often have distinctive patterns in how they experience aspects of statistics instruction (e.g., wait time) as well as movement between mathematics/statistics and everyday registers.

  • Statistics anxiety is a problem for most graduate students. This study investigates the relationship between intolerance of uncertainty, worry, and statistics anxiety. Intolerance of uncertainty was significantly related to worry, and worry was significantly related to three types of statistics anxiety. Six types of statistics anxiety were significantly lower by the end of the semester.

  • The mixed-methods study reports psychometric properties of the 34-item Reasoning about P-values and Statistical Significance (RPASS) scale. RPASS is being designed as research tool to assess effects of teaching methods on students’ inferential reasoning. During development (Phase I), two graphical scenarios and 12 items were added to the scale, field tested, and eventually by three content raters. During Phase II, reliability and validity evidence were gathered in three college statistics courses. Score reliability was sufficient to conduct group research (ɑ=0.76, n= 105). RPASS scores were correlated with college entrance scores and GPAs as evidence of construct-related validity. Further validity evidence was obtained by analyzing consistency between students’ reasoning and answers for eight items. Future development and research are discussed.

  • Data distributions can be represented using different external representations, such as histograms and boxplots. Although the role of external representations has been extensively studied in mathematics, this is less the case in statistics. This study helps to fill this gap by systematically varying the representation that accompanies a task between participants, and assessing how university students use such representations in comparing aspects of data distributions. Following a cognitive fit approach, we searched for matches between items and representations. Depending on the item, some representations led to better achievement than other representations. However, due to the low overall accuracy rates and various difficulties that students displayed in interpreting these representations, we cannot make strong claims regarding matches between items and representations.

  • Students with positive attitudes toward statistics are likely to show strong academic performance in statistics courses. Multiple surveys measuring students’ attitudes toward statistics exist; however, a comparison of the validity and reliability of interpretations based on their scores is needed. A systematic review of relevant electronic databases yielded 532 citations, 78 of which were reviewed, and 35 included in a final analysis. Fifteen instruments were identified; however, evidence of validity and reliability has only accumulated for the Statistics Attitude Scale, Attitudes Toward Statistics Scale, and Survey of Attitudes Toward Statistics (two versions). In conclusion, a number of surveys exist, but there is a paucity of peer-reviewed validity and reliability evidence.

  • This study examined the relationships among statistics achievement and four components of attitudes toward statistics (Cognitive Competence, Affect, Value, and Difficulty) as assessed by the SATS. Meta-analysis results revealed that the size of relationships differed by the geographical region in which the studies were conducted as well as by the component of statistics attitudes being examined. Medium effect sizes were found between statistics achievement and scores on the Affect and Cognitive Competence components for studies conducted in the United States whereas those conducted in other countries yielded small effect sizes. The Value and Difficulty components exhibited small effect sizes for both regions. In every case, the U.S. effect sizes were about double in size in comparison to those from non-U.S. countries.