This article describes an activity that helps students understand data analysis concepts while learning how to take control of their learning.
This article describes an activity that helps students understand data analysis concepts while learning how to take control of their learning.
Since the introduction of the first iPod portable music player (MP3 player) by Apple, Inc., users have questioned the randomness of the shuffle feature. Most evidence cited by users claiming to show nonrandom behavior in the shuffle feature is anecdotal in nature and not based on any systematic analysis of its randomness. This article reports on our attempt to investigate the shuffle feature on the iPod and to test its randomness through the use of probability and statistical modeling. We begin by reviewing the research on people's inability to perceive and understand both random and nonrandom behavior. Probability models are then developed, under the assumption of a random shuffle, for several of the most common types of events cited as evidence of a nonrandom shuffle. Under this null hypothesis of a random shuffle, several goodness-of-fit tests of one of the probability models are conducted using data collected from real iPods. No evidence to support user claims of a nonrandom shuffle was found. Finally, we conclude with some reflections on and ideas for incorporating these examples into undergraduate probability and statistics courses.
In an ongoing debate between two visions of statistical reasoning competency, ecological rationality proponents claim that pictorial representations help tap into the frequency coding mechanisms of the mind, whereas nested sets proponents argue that pictorial representations simply help one to appreciate general subset relationships. Advancing this knowledge into applied areas is hampered by this present disagreement. A series of experiments used Bayesian reasoning problems with different pictorial representations (Venn circles, iconic symbols and Venn circles with dots) to better understand influences on performance across these representation types. Results with various static and interactive presentations of pictures all indicate a consistent advantage for iconic representations. These results are more consistent with an ecological rationality view of how these pictorial representations achieve facilitation in statistical task performance and provide more specific guidance for applied uses.
In this study directive tutor guidance in problem-based learning (PBL) of statistics is investigated. In a quasi experiment in an educational setting, directive guiding tutors were compared with tutors in a more traditional role. Results showed that the subjective perceptions of the students with regard to the course, the tutor, and the discussions in the tutorial meetings were more positive in the guided condition. The quality of the problems used in the meetings and general tutor functioning were evaluated as equal in both conditions. Achievement was marginally higher in the guided condition. It can be concluded that directive tutor guidance is an effective addition to PBL of statistics.
In three studies we looked at two typical misconceptions of probability: the representativeness heuristic, and the equiprobability bias. The literature on statistics education predicts that some typical errors and biases (e.g., the equiprobability bias) increase with education, whereas others decrease. This is in contrast with reasoning theorists' prediction who propose that education reduces misconceptions in general. They also predict that students with higher cognitive ability and higher need for cognition are less susceptible to biases. In Experiments 1 and 2 we found that the equiprobability bias increased with statistics education, and it was negatively correlated with students' cognitive abilities. The representativeness heuristic was mostly unaffected by education, and it was also unrelated to cognitive abilities. In Experiment 3 we demonstrated through an instruction manipulation (by asking participants to think logically vs. rely on their intuitions) that the reason for these differences was that these biases originated in different cognitive processes.
Case discussions have become an integral component of our business statistics courses. We have discovered that case discussion adds enormous benefits to the classroom and learning experience of our students even in a quantitatively based course like statistics. As we read about discussion-based methods, we discovered that the literature is mostly silent about the specific challenges of case teaching in statistics courses. This article is an attempt to fill that void. It provides a "how-to" starter's guide for those interested in incorporating case discussions in statistics courses. It includes resources for background reading, tips on setting up a statistics case discussion course, and examples of four specific case discussions involving statistics topics. An illustrative case and instructor's notes that can be used on the first day of class are provided as well. Because we have had mixed reactions to conducting case discussions online, we believe that the use of case discussion in distance education statistics courses is a fruitful area for experimentation and research. Although our experience is in the business statistics classroom, this article is also applicable to statistics courses in other disciplines.
The study analyzed a conversation among a group of teachers responsible for teaching the concepts of mean, median, and mode. After reading an article describing some specific student difficulties in learning the concepts, teachers were asked to discuss how the teaching of the concepts could be improved. Several claims pertinent to improving teaching practice were offered. Claims focused on the appropriate age at which to introduce statistical concepts, the influence of the state-prescribed curriculum on teaching practice, content-specific teaching strategies, and content-independent teaching strategies. Teachers' claims were discussed in terms of points of departure and agreement with existing empirical research.
The purpose of this study was to explore the effect of providing preservice teachers the opportunity to collect real data in a science methods inquiry investigation and using the data, design data displays in their mathematics methods course. The research questions focused on how preservice teachers' understandings of data displays, research design, and the specific content addressed improved when they used these displays to attempt to communicate the data they had collected themselves in their inquiry investigations. The 46 preservice teachers were given questionnaires at the beginning and end of the courses, twelve were interviewed both pre and post, all written work pertaining to data displays and the inquiry investigations was collected, methods class sessions were audio and videotaped, and the final data display and science investigation projects were photocopied. The findings show that by creating and scrutinizing their data displays, the preservice teachers were able to recognize the limitations of their inquiry investigation design. Through working with data in the context of inquiry projects of their own design, the preservice teachers realized meaningful connections and commonalities that exist in mathematics and science while strengthening their knowledge and skills in both disciplines.
In current curriculum materials for middle school students in the US, data and chance are considered as separate topics. They are then ideally brought together in the minds of high school or university students when they learn about statistical inference. In recent studies we have been attempting to build connections between data and chance in the middle school by using a modeling approach made possible by new software capabilities that will be part of TinkerPlots 2.0 (TinkerPlots is published by Key Curriculum Press and has been developed with grants from the National Science Foundation (ESI-9818946, REC-0337675, ESI-0454754). Opinions expressed here are our own and not necessarily those of the Foundation.). Using a new Sampler object, students build "factories" to model not only prototypical chance events, but also distributions of measurement errors and of heights of people. We provide the rationale for having students model a wide range of phenomena using a single software tool and describe how we are using this capability to help young students develop a robust, statistical perspective.
A simple question about average class size yields a surprisingly rich classroom-tested exploration of conceptual and procedural knowledge about measures of central tendency