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An International Journal on the Teaching and Learning of
Statistics
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JSE Volume 23, Number
3 Abstracts
Most homework sets in statistics courses are constructed so that students concentrate or “mass” their practice on a certain topic in one problem set. Distributed practice homework sets include review problems in each set so that practice on a topic is distributed across problem sets. There is a body of research that points to the efficacy of distributed practice for developing a variety of skills from word recall to surgical techniques. A trial was conducted in several sections of a business statistics course where students were randomly assigned to either have massed practice homework sets or distributed practice homework sets. The two groups were then compared on the course assessments. The results show some evidence for the efficacy of distributed practice homework sets, although this effect may be modified significantly by the instructor or by a Hawthorne effect.
Key Words: Massed practice; Cognitive theory; Interaction; Hawthorne effect.
The new Australian Senior Secondary Curriculum: Mathematics contains more statistics than the existing Australian Curricula. This case study examines how a group of Queensland mathematics teachers define the word “statistics” and five statistical terms from the new curricula. These definitions are compared to those used in some commonly-used Queensland mathematics textbooks and in the glossaries of new Australian Senior Secondary Curriculum: Mathematics. The findings of this study suggest that many teachers do not have a good understanding of statistical concepts and that they rely on procedural definitions (instrumental understanding). This is reflected in the presentation of statistics in Queensland senior secondary mathematics textbooks. Definitions in the glossaries of the new curricula are generally better but perhaps other simpler concepts could be introduced first to develop relational understanding.
Key Words: Relational Understanding; Mathematics Curriculum; Teacher Development.
Bloom’s taxonomy is proposed as a tool by which to assess the level of complexity of assessment tasks in statistics. Guidelines are provided for how to locate tasks at each level of the taxonomy, along with descriptions and examples of suggested test questions. Through the “Blooming” of an examination – that is, locating its constituent parts on Bloom’s taxonomy - the difficulty level of an examination paper in statistics can be pseudo-objectively assessed, via both its Bloom’s Index and the proportion of marks allocated to higher order cognitive skills. One suggested application of the approach is in assessing the impact on student learning due to course transformations implemented incrementally over time. Assessment tools, in particular examination papers, can be compared for difficulty and student performance. A case study is provided in which examinations from an introductory course are Bloomed post-hoc and compared to student performances.
Key Words: Statistics education; Bloom’s taxonomy; Assessment; Calibrating difficulty.
Blind students are bound to make up a very small part of the population most university lecturers will encounter during their careers. Research to date shows that good communication between staff and student improves the chances of a successful outcome for both parties. The research does show, however, that the exercise seems to be one of re-inventing the wheel, perhaps with a less than fully informed blueprint to work from. The authors use their own experiences as blind students who progressed beyond research methods or first year introductory courses into careers as teachers and researchers of statistical methods to provide guidance for their sighted colleagues. Our principle point of difference to the existing research work is that we rely on the experience of our statistical education for our current livelihoods; we were not one-off students taking a research methodology course or first year introductory course. We benefitted from the successful (and possibly the not so successful) interactions we had with our sighted teachers. It is our hope that by saving staff from wasted effort, we can spare students from unnecessary discomfort in classes that could improve their future employment prospects. Our aim is therefore to provide practical support for our sighted colleagues and blind peers as we work together towards the empowerment of blind students in becoming competent producers of statistical information, not just consumers who interpret that information.
Key Words: Low vision; Tactile images; Braille; Speech output.
The purpose of this article is to sketch a conceptualization of a framework for Advanced Placement (AP) Statistics Teaching Knowledge. Recent research continues to problematize the lack of knowledge and preparation among secondary level statistics teachers. The College Board’s AP Statistics course continues to grow and gain popularity, but is a challenge for most secondary teachers to teach because of the emphasis on conceptual understanding and problem solving. Therefore, examining the components of teaching knowledge required for the course is of high importance. Using existing statistics teaching knowledge guidelines, previous research findings, national standards and College Board content requirements, a teaching knowledge framework for AP Statistics is proposed that will appropriately focus the teaching of AP Statistics courses to better prepare teachers and minimize current deficiencies.
Key Words: Secondary statistics education; Statistics content knowledge; Statistics pedagogical content knowledge; Advanced placement statistics.
This study reports on the statistical content of five U.S. textbook series written for elementary students in grades 1-5. The researchers examined 17,688 pages and coded 7445 statistical tasks to determine (1) the distribution of statistical topics within textbooks, and (2) the relative emphasis on the phases of the statistical problem solving process (Formulate Questions, Collect Data, Analyze Data, and Interpret Results). Different series contained markedly different distributions of statistical content: two series located most statistical content near the end of the text, whereas two other series located statistical tasks more uniformly throughout the textbook. A large majority of statistical tasks required students to Analyze Data, with a heavy emphasis on the activities of reading displays and performing mathematical calculations.
Key Words: Statistics education; Mathematics textbooks; Elementary school; Content analysis; Curriculum.
One econometric rule of thumb is that greater dispersion in observations of the independent variable improves estimates of regression coefficients and therefore produces better results, i.e., lower standard errors of the estimates. Nevertheless, students often seem to mistrust precisely the observations that contribute the most to this greater dispersion. This paper offers an assignment to help students discover for themselves the value of the observations that are farthest from the mean.
Key Words: Active learning; Outlier; Linear regression.
This paper examines the use of a randomization-based activity to introduce the ANOVA F-test to students. The two main goals of this activity are to successfully teach students to comprehend ANOVA F-tests and to increase student comprehension of sampling distributions. Four sections of students in an advanced introductory statistics course participated in this study. When the topic of ANOVA was introduced, two sections were randomly assigned to participate in a traditional approach (one for each instructor), while the other two sections participated in a randomization-based method. Students were administered a pre-test and a post-test that asked them to apply hypothesis testing concepts to a new scenario. Students also responded to some basic conceptual questions. This study showed mixed results related to students’ understanding of the logic of inference, but the activity utilized shows some promising gains in student understanding of sampling distributions.
Key Words: Sampling distributions; ANOVA, F-test, Hypothesis test, Randomization, Statistical inference, P-values.
Interviews
with Statistics Educators
Deborah Nolan is Professor of Statistics and holds the Zaffaroni Family Chair in Undergraduate Education at the University of California – Berkeley, where she has also served as Associate Dean of Mathematical and Physical Sciences. She is a Fellow of the American Statistical Association and the Institute of Mathematical Statistics. This interview took place via email on April 1 – November 3, 2015.
Teaching
Bits
I located 15 total articles and 1 dissertation that have been published from July 15 through November 15, 2015 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 a link to their websites so that abstracts of additional articles may be accessed and viewed.
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