An International Journal on the Teaching and Learning of
JSE Volume 22, Number
Undergraduate students who have just completed an introductory statistics course often lack deep understanding of variability and enthusiasm for the field of statistics. This paper argues that by introducing the commonly underemphasized concept of measurement error, students will have a better chance of attaining both. We further present lecture materials and activities that introduce metrology, the science of measurement, which were developed and tested in a pilot study at Iowa State University. These materials explain how to characterize sources of variability in a dataset, in a way that is natural and accessible because the sources of variability are observable. Everyday examples of measurements, such as the amount of gasoline pumped into a car, are presented, and the consequences of variability within those measurements are discussed. To gauge the success of the material, students’ initial and subsequent understanding of variability and their attitude toward the usefulness of statistics were analyzed in a comparative study. Questions from the CAOS and ARTIST assessments that pertain to using variability to make comparisons, understanding the standard deviation, and using graphical representations of variability were included in the assessment. The results of the comparative study indicate that most students who were exposed to the material improved their understanding of variability and had a greater appreciation of the value of statistics.
Key Words:Variability; Statistics curriculum; Undergraduate statistics; Deep understanding; Data collection.
Many adults who need an understanding of statistical concepts have limited mathematical skills. They need a teaching approach that includes as little mathematical context as possible. Iterative participatory qualitative research (action research) was used to develop a statistical literacy course for adult learners informed by teaching in traditional first year university courses, workplace based training, teacher workshops and Masters of Public Policy courses. The latter learners in particular regularly come across confidence intervals and statistical significance in their everyday reading. The goal is to give them a conceptual rather than theoretical understanding of inferential concepts by developing inferential statistics logic through the introduction of exact probabilities in simple non-parametric tests (two-tailed coin tossing) and then contingency tables and parametric situations. The final course developed for the New Zealand Certificate of Official Statistics uses “hands-on” examples to reinforce concepts before proceeding to computer simulations. It emphasizes evaluation of the strength of statistical significance and its relationship to the possible cost of making an incorrect decision. Case studies that have influenced government policy reinforce inferential concepts and demonstrate the importance of statistics in complex real problems.
Key Words: Statistics education; Inferential statistics concepts; Hands on data and real world case studies; Use of exact probabilities; Action research.
Statistics courses for prospective teachers are being developed in response to recent K-12 curriculum recommendations. As these courses are developed, it is important to design accompanying assessments. This manuscript describes a strategy for assessing aspects of statistical knowledge for teaching. The strategy involves analyzing and responding to children’s work samples from the National Assessment of Educational Progress. An example is provided to illustrate how such an assessment task can serve to reveal different aspects of respondents’ subject matter knowledge as well as their pedagogical content knowledge. Thoughts are provided on how to use the assessment tasks to identify levels of statistical knowledge for teaching.
Key Words: Teacher preparation; Pedagogical content knowledge; Subject matter knowledge; Classroom example.
We analyzed the statistical content within mathematics textbooks used in courses for preparing elementary teachers. Six textbooks commonly used in the United States comprised our sample. Each task in statistical sections was analyzed using both the levels of the GAISE framework (Franklin et al. 2007) and phases of the statistical problem solving process (Formulate Questions, Collect Data, Analyze Data, and Interpret Results). Tasks within the Analyze Data phase were also classified as creating or reading a display, performing a mathematical computation, or using statistical reasoning beyond mathematical computations. The majority of statistical tasks in each book required data analysis. Two textbooks primarily consisted of tasks addressing statistical concepts beyond computations, while three series focused on graphical displays and computational procedures.
Key Words: Statistics education; Mathematics textbooks; Elementary teacher preparation; Content analysis.
This paper explores the use of a lesser-known dynamic model for the median, a foundational topic that starts in the middle school curriculum and is associated with student misconceptions and knowledge gaps. This model appears to offer a rich vehicle to explore the median interactively in greater conceptual depth that includes some of its more subtle associated ideas. An exploratory study to assess performance of this model in a class for pre-service middle school teachers yielded evidence that students who completed the dataset sequence associated with the model gained further insight about the median, especially concerning how the mean and median are affected differently by outliers. Analyses of open ended questions as well as empirical results of multiple-choice questions are used to assess the overall learning outcomes gained by students. A one-minute video is offered to illustrate key points of the model.
Key Words: Mean; Median; Measures of Center; Misconception; Representation.
The statistical preparation of in-service teachers, particularly middle school teachers, has been an area of concern for several years. This paper discusses the creation and delivery of an introductory statistics course as part of a master’s degree program for in-service mathematics teachers. The initial course development took place before the advent of the Common Core State Standards for Mathematics (CCSSM) and the Mathematics Education of Teachers (MET II) Reports, and even before the GAISE Pre-K-12 Report. Since then, even with the recommendations of MET II and the wide-spread implementation of the CCSSM, the guidance available to faculty wishing to develop a statistics course for professional development of in-service teachers remains scarce. We give an overview of the master’s degree program and discuss aspects of the course, including the goals for the course, course planning and development, the instructional team, course delivery and modifications, and lessons learned through five offerings. With this paper, we share our experiences developing such a course, the evolution of the course over multiple iterations, and what we have learned about its value to the middle-level teachers who have participated. As more and more universities are being asked to develop courses specifically for in-service teachers, we wrote this article in the hopes of providing guidance to others, and to share our lessons learned.
Key Words: Statistics education research; Middle-level mathematics in-service.
Although the use of simulation to teach the sampling distribution of the mean is meant to provide students with sound conceptual understanding, it may lead them astray. We discuss a misunderstanding that can be introduced or reinforced when students who intuitively understand that “bigger samples are better” conduct a simulation to explore the effect of sample size on the properties of the sampling distribution of the mean. From observing the patterns in a typical series of simulated sampling distributions constructed with increasing sample sizes, students reasonably—but incorrectly—conclude that, as the sample size, n, increases, the mean of the (exact) sampling distribution tends to get closer to the population mean and its variance tends to get closer to the population variance divided by the square root of sample size. We show that the patterns students observe are a consequence of the fact that both the variability in the mean and the variability in the variance of simulated sampling distributions constructed from the means of N random samples are inversely related, not only to N, but also to the size of each sample, n. Further, asking students to increase the number of repetitions, N, in the simulation does not change the patterns.
Key Words: Simulated sampling distribution; Sampling variability; Variance of means; Variance of variances; Central Limit Theorem.
Jennifer R. Winquist and Kieth A. Carlson
In this paper, we compare an introductory statistics course taught using a flipped classroom approach to the same course taught using a traditional lecture based approach. In the lecture course, students listened to lecture, took notes, and completed homework assignments. In the flipped course, students read relatively simple chapters and answered reading quiz questions prior to class and completed workbook activities in class. The workbook activities consisted of questions (multiple choice, short answer, computation) designed to help students understand more complex material. Over one year after taking the course (median = 20 months), students took a standardized test of their knowledge of statistics as well as nine other content areas in psychology. Students in the flipped course outperformed the students in the lecture course on the statistics portion of the test (d =.43), but not on non-statistics portions of the test.
Key Words: Flipped class; Active learning; Flip teaching; Reverse teaching; Inverted class.
with Statistics Educators
Josh Tabor teaches at Canyon del Oro High School in Oro Valley, Arizona. He has served on the Test Development Committee for the Advanced Placement program in Statistics and was one of five finalists for Arizona Teacher of the Year in 2011. This interview took place via email on October 5 – November 8, 2014.
I located 15 articles and one set of conference proceedings that have been published from July through October 2014 that pertained to statistics education. In this column, I highlight a few of these articles that represent a variety of different journals that include statistics education in their focus. I also provide information about the journals and book and a link to their websites so that abstracts of additional articles may be accessed and viewed.
The aim of this short column is to provide an overview of resources and events from CAUSEweb (www.causeweb.org) and MERLOT (www.merlot.org) to help you stay connected with the Statistical Education community.