Peer-Reviewed Contributed Posters
(alphabetical order by lead author name)
Beyond the Second Course in Statistics: Applied Survival Analysis
Vittorio Addona, Macalester College
Much energy has gone into redesigning a student's first experience in a college statistics class and, more recently, this effort has shifted toward potential second courses in statistics. Relatively little has been broached beyond the second course, even though more colleges are moving away from the traditional Probability/Mathematical Statistics sequence which often served as the follow-up to a student taking a course in multiple regression (a common second statistics course). In addition to multiple regression, our students at Macalester College cover model diagnostics and selection, and generalized linear models in their second statistics course. We present an applied survival analysis course, offered for the first time in Fall 2010, as an alternative "third course" in statistics. The field of survival analysis evolved from a practical reality of time-to-event data: the exact value of some observations is often unknown (so-called censored data). Survival analysis is typically encountered in graduate school, and is often taught in a theoretical manner. Thus, our course is rather unique, being offered to undergraduates, and focusing on applications. We were successful in allowing the students to gain an understanding of material primarily through data analysis, without delving into too many technical details. In this poster, we will illustrate a variety of classroom activities, computer labs, and datasets that were deemed most effective. We will also share key features of the course structure and syllabus, along with some student comments provided on end-of-term evaluations. In summary, we exposed students to an area of statistical application which is current, and has been gaining in popularity, not only in medicine, but also in fields such as economics, sociology, and political science. At Macalester College, survival analysis was introduced into the curriculum via an applied "topics" course entitled Modern Statistics. Consequently, depending on the particular interests of the professor charged with teaching this course, the material covered might change from year to year. This provides an exportable model for other colleges with the desire to augment their statistics curriculum, but which may have different areas of expertise.
The Chance News Wiki
Jeanne Albert, Middlebury College
Bill Peterson, Middlebury College
Chance News began in the early 1990s as an online newsletter to support the Chance Project, and since 2005 exits in a Wiki format. A central focus of the Chance Project was the development of the Chance quantitative literacy course, designed cooperatively by Laurie Snell and Peter Doyle of Dartmouth College, Joan Garfield of the University of Minnesota, Tom Moore of Grinnell College, Bill Peterson of Middlebury College, and Ngambal Shah of Spelman College, with support from the Pew Foundation and the National Science Foundation's Undergraduate Curriculum Development Program. For over two decades Laurie Snell managed the Chance News website, but after "really" retiring in 2010, the editorial torch was passed to Bill Peterson and Jeanne Albert of Middlebury College, and web hosting moved to CAUSEweb.org.
The Chance Wiki provides reviews of current news stories that are relevant to teaching statistics and probability, along with links to original articles and related resources. We are always interested in receiving your suggestions for stories. But the Wiki format actually allows anyone to post and edit. This poster session will highlight the basics of editing, and even allow for real-time contributions. Please come see how. You might even consider bringing a story!
Clickers: Technological Fad or Effective Tool to Enhance Academic Performance in the Introductory Statistics Classroom
Andrea Allen, Georgia Gwinnett College
Alan Marks, Georgia Gwinnett College
Sarah Marks, Georgia Gwinnett College
Although student response systems (SRS) or clickers have increased in popularity, data on their use in statistics classrooms remain limited. In this study, clickers were introduced to 28 students in two sections of an introductory statistics course for psychology students. Data on clicker use was collected in a mixed model crossover design study with students in one section using clickers for four weeks while covering a section of material while the second section covered the same material without the use of clickers. In the following weeks roles were reversed with students in the second section using clickers while students in the first section did not use clickers. In sections with clickers, students were able to anonymously share answers to questions designed to gauge their understanding of both the conceptual and computational aspects of the material presented throughout lectures via response with handheld clickers. These responses were then collectively displayed in the form of a bar graph for the entire class to view. Thus, students were provided with the opportunity to gauge their own understanding of the presented concepts in comparison to the rest of the class as they progressed through the lecture. In the section without clickers the same material and problems were presented but answers were registered by a show of hands or verbal responses. A mixed model ANOVA found that clickers were not associated with increased student performance. The students using clickers had lower mean scores than the class not using the clickers on identical quizzes. However, this difference was neither significant nor large. A survey completed by fifteen participating students conveyed an overall positive student perception of clickers. Using a Likert scale with one corresponding to strongly disagree and five corresponding to strongly agree students thought that clickers increased their participation (M=4.27) and they enjoyed the use of clickers (M=4.07). This research is ongoing and we are currently using a far more sophisticated system which enables individual tracking of correct responses. We are also conducting longitudinal surveys on student perception to examine if students continue to find clickers engaging throughout the semester since much of the literature reporting increased engagement is based on short term exposure. This presentation will include a demonstration of the clickers or will explore both the potential benefits and the tradeoffs in implementation of clickers in introductory statistics classrooms, including experiences with two different clicker systems and will explore the paradox of students' reported increased engagement, but lack of objective data indicating increased performance.
Elementary School Teachers: Teaching, Understanding and Using Statistics
Anna Bargagliotti, University of Memphis
Derek Webb, Bemidji State University
As the world becomes increasingly interested in data and data driven decision-making, it is crucial for us as educators to consider how we can prepare a statistically literate population. Since teachers are the primary vehicles through which information is transferred to students in the classroom, it is important to identify the type of statistical knowledge teachers much have in order to ensure students embark on the pathway towards statistical literacy. In this poster and demonstration, we present three interweaving factors that must be considered when answering the question: What should elementary teachers know about statistics? We focus on what statistical ideas students need to acquire in elementary school, what guidelines and standards teachers must adhere to, and what type of data teachers are required to analyze and interpret on the job.
We compare the content described in the GAISE framework levels A and B, those that may be pertinent to the elementary grades, to the content put forth in the "Measurement and Data" strand of the Common Core standards, the strand which contains statistical concepts for the elementary grades. The Common Core Standards are a set of national standards that were unveiled in 2010. At this time, they have been adopted by 41 states and thus have the potential to be very influential in effecting mathematics and statistics education in K-12.
To compare GAISE with the Common Core, two tables will be shown on the poster that outline the statistics concepts covered in each document. The table comparison illustrates that in general, the approach presented in the Common Core is fundamentally different than the approach presented in the GAISE guidelines. The Common Core covers a subset of the concepts outlined by GAISE, however, the difference between the two ultimately lies in the manner in which students are supposed to acquire and be guided through statistical learning. GAISE focuses on student's overall statistical literacy - this means growing students to think statistically from the beginning of a problem to the end of a problem. Encompassed in this idea is a student's ability to pose a statistical question and then subsequently investigate the answer using appropriate data collection and data analysis methods. On the other hand, the Common Core focuses on ensuring that students can perform specific tasks related to statistics.
Furthermore, in addition to considering student learning and the standards when making recommendations about elementary teacher statistical knowledge, we examine the type of data teachers are confronted with on the job. Under the No Child Left Behind Act (NCLB), all states have to produce an Annual Yearly Progress (AYP) report. Every state, school system, and school is then issued a Report Card. The Report Card lists the subjects and the assessments that are included in the evaluation of the specific state. For example, in the state of Tennessee, the report card includes the Tennessee Value Added Assessment System (TVAAS). The TVAAS provides each teacher confidential information on each of their student's standardized test scores on the Tennessee Comprehensive Assessment Program (TCAP) exam from grades 3 to 8. Using these performances, a teacher is presented with a predicted score for each student's achievement during the year.
The TVAAS also provides information open to the public. For example, the public can access the System Value Added Report for a school district and school. As part of our demonstration, using the state of Tennessee as an example, we will show how to obtain a sample report card from a sample school district to illustrate the enormous amount of statistical information that teachers must be able to interpret and use to modify and improve their practice. In addition, we will show example state resources that are available to help teachers understand the report cards. Through this demonstration, it will be seen that at first glance, the statistical knowledge needed to understand the report appears limited to being familiar with a few statistical terms. However, when observing the report more closely, one quickly notices the depth of knowledge beyond just statistical terminology a teacher must have in order to adequately understand the report. A teacher receiving these reports must be not only able to interpret them but also be able to use the information to modify and improve their practice.
Based on the GAISE report, the Common Core standards, and the type of data teachers are presented with on the job, we will conclude the poster with suggestions and recommendations of how and when teachers should be taught statistics. Currently, most teacher preparation programs do not require teachers to take a separate statistics course. In most cases, the only exposure pre-service elementary teachers receive in statistics is possibly one unit or chapter in their mathematics content courses. However, even this minimal amount of exposure is not a guaranteed since these courses are already packed with material. In addition, because these courses are typically taught in mathematics departments, they are seldom taught by statisticians or statistics educators. This means that if pre-service elementary teachers are at all exposed to statistics, they are mostly being exposed to statistics through a mathematical point of view and not a statistical one.
Because of the increased push for statistically literacy put forth in policy, it is imperative for teacher preparation programs to "catch up" to this demand. Teachers at all levels must be exposed to statistical thinking and be trained accordingly. If this does not happen, how can we expect teachers to be able to use student data in order to influence their practice? How can we expect to have students become statistically literate? Moreover, science and science classes at the K-12 level and beyond now require students to possess statistical abilities since much of the curriculum introduces science through experiments and testing. This is yet another reason why teachers at all levels must possess knowledge of statistics.
The Clicker Effect: Assessing Introductory Business Statistics Students' Understanding and Attitudes Towards Statistics
Josh Bernhard, Iowa State University
Holding the attention of students during an introductory statistics can be difficult, especially in large lecture classes. The ability to hold students' attention when texting, picture messaging, and the Internet can be easily accessed is an on-going problem. However, through the use of clickers, technology may be the key to actively engaging students in course material and helping motivate students to find the importance of statistics. In this poster, we will present methodology for using clickers in introductory statistics courses. We will also describe the design and results of an experimental study of the effectiveness of clickers in the areas of students understanding and attitudes about statistics using data collected on four sections of the introductory business statistics course at Iowa State University.
More "I", Less "US" in our Datasets
Rob Carver, Stonehill College
USCOTters know that interesting and important real data are important ingredients in a good course. Many of our 'old favorites' are US-centric, focusing on sports, popular culture, environment, demographics and politics. Such examples invariably engage some students and leave others feeling disadvantaged if they don't know much about the substantive area. It's time to step up our use of "I" (for International) data. Given the rapid pace of global trade and intellectual exchange, the huge growth in foreign study for US students and for international students studying in the US (who are not turned on by NFL examples), and easy access to reliable global sources, this poster illustrates a dozen on-line sources for global data in a variety of applied disciplines.
Using foreign data in class can tend to have a leveling effect, in that students often have comparable domain-area knowledge and no one is expected to be an expert. More importantly global data can be eye-opening for undergraduates whose natural orientation is provincial. The poster cites some sources that the author presents to students as well as several that students have used in class projects; some excerpts of such projects are also referenced.
Some sites present hurdles for students or faculty--e.g., finding the "English version" link within a page in another language, spotty or missing data from some governmental agencies, the need to reformat prior to analysis--but these hurdles are relatively easy to clear and afford excellent opportunities for valuable lessons along the way.
An Argument for Teaching Metrology in Introductory Statistics Classes
Emily Casleton, Iowa State University
Amy Borgen, Iowa State University
Ulrike Genschel, Iowa State University
Alyson Wilson, Iowa State University
Undergraduate students in introductory statistics courses often struggle with acknowledging, explaining, and dealing with variability. The aim of this work is to help students develop a deep understanding of the difficult and often underemphasized concept of variability through the presentation of metrology, the science of measurement.
Garfield and Ben-Zvi (2005) details seven components required to develop a comprehensive knowledge of variability. The introduction of metrology into an introductory statistics course most specifically aims to increase students' ability to correctly account for variability when making comparisons. However, measurement quality and the inherent variability resulting from the measurement process are also underemphasized topics in the statistics curriculum. To this end, materials have been developed for use in introductory statistics courses. These materials explain how to characterize sources of variability in a dataset, which is natural and accessible because the sources of variability are observable, i.e. a device or operator. Another issue this work addresses is how statistics translates to the students' lives beyond the classroom. 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.
These materials were implemented into an introductory statistics course at Iowa State University. Student's initial and subsequent understanding of variability and 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. This poster will not include a demonstration.
Garfield, J., & Ben-Zvi, D. (2005). A framework for teaching and assessing reasoning about variability. Statistics Education Research Journal, 4(1), 92-99.
Using Video Games to Introduce Statistical Research in Undergraduate Statistics Courses
Jessica Chapman, St. Lawrence University
Ivan Ramler, St. Lawrence University
Guitar Hero is a series of popular video games that most college students are familiar with. Because of its current popularity, it can be turned into a fun multi-staged project to introduce statistical research techniques to students in upper-level undergraduate courses such as Statistical Computing or Mathematical Statistics. The project consists of multiple stages from developing an estimator to comparing the power of various estimators in different situations. This poster outlines the learning goals and the steps of the project. We'll share our opinions about the success of the project, include some of the student-created methods, and discuss possible extensions or modifications to the project.
Do the Chi-square Test and Fisher's Exact Test Agree in Determining Extreme for 2x2 Tables?
Yung-Pin Chen, Lewis and Clark College
When drawing statistical inference for 2x2 contingency tables, there are two common methods for determining extreme. One is the widely taught Pearson chi-square test, which uses the well-known chi-square statistic. The chi-square test is appropriate for large sample inference, and it is equivalent to the Z-test that uses the difference between the two sample proportions for the 2x2 case. Another method is Fisher's exact test that evaluates the likelihood of each table with the same marginal totals. This note mathematically justifies that these two methods for determining extreme do not completely agree with each other. Our analysis obtains two conditions, one one-sided and another two-sided, under which a disagreement could occur. It also addresses the question whether or not this discrepancy in determining extreme between the two tests would yield different results when testing homogeneity or independence.
The Use of Case Studies in the Teaching of Undergraduate Business Statistics
Alan Chesen, Wright State University
For many years I have utilized case studies of my own construction in the undergraduate inferential statistics course I teach in the Raj Soin College of Business at Wright State University. I believe that requiring students to complete assignments of this type at the sophomore level lends an aura and degree of sophistication to their education. Moreover, case studies have a long history of service in business programs, and this study will help place the study of statistics in that context.
Description of Assignments:
The package of assignments numbers five or six each quarter. A common business-related theme of likely interest to students is used each term. The table below illustrates applicable techniques and past themes.
Actual data sets are used in the assignments when possible, including business data culled from local media. In all cases, the data sets relate to the very real and hopefully interesting situations that I utilize. There is a substantial amount of writing required of students as they complete these assignments, and while this course is not labeled as writing intensive for the purposes of the university, the accomplishment of the assignments does allow students to develop their written communication skills, something I view as very important to their education.
The statistical analysis component of these assignments is required to be completed with the use of PHStat, an add-in to Microsoft Excel that accentuates the statistical processes that are a part of Excel. While not nearly as powerful as a purely statistical program such as Minitab, PHStat is very user friendly, easy to learn and sufficient to accomplish the procedures of the assignments. In the few instances where PHStat is not adequate to accomplish facets of an assignment, excel data analysis techniques are used.
My primary goal is to get students to realize the power of statistical packages for analytical purposes rather than simply to teach students how to use statistical software. A dual goal is to utilize the case study format in order to create for them a business environment of a type in which they might someday find themselves. In addition to requiring students to create and provide statistical output, I require them to explain the meaning of what they have generated in both statistical and business related terms and to answer certain questions about their results. These questions often include, but are not limited to, addressing the reasons for the possible change in results due to changes in inputs for statistical estimates and minimum sample size computations, the effect of a change of a confidence level or significance level on the size of an interval or the statistical decision, and the effects of a possible change in the statistical decision due to the choice of test where it might be possible to justify the use of multiple tests. Also addressed in some cases are the assumptions and preconditions that must be met in order for chosen procedures to be correct for the type of analysis that is to be accomplished. Finally, recommendations within the context of the assignment to a relevant business entity concerning the manner in which the results could be used to dictate organizational policy or impact business decisions are required to be accomplished as an integral part of the assignments. I feel that the ability to relate their results to a business situation will serve students well when they become employed in a business environment.
Reading and Writing in a Theme-Based Introductory Statistics Course
Adam F. Childers, Roanoke College
Jeffery L. Spielman, Roanoke College
A student's perception of an introductory statistics course is often times established before they set foot in a classroom and unfortunately most of their preconceptions are negative. A fear of mathematics or the "I can't do math" mentality runs rampant in an introductory statistics course and can cripple a student's ability to learn the material. While it is impossible to eliminate the mathematical content from an introductory statistics course, it is possible to add content to the course to give these students confidence and assignments in which they are more comfortable. Two ways we have attempted to change the preexisting stereotypes or alleviate mathematical anxiety is by supplementing the statistical content with reading and writing assignments as well as teaching the course relating to a common theme such as sports, weather, gun control, botany, health or social justice. In any introductory statistics course the statistical content is the core of the class but it is possible to ease students into material where they lack confidence.
Through observation we have found students that are terrified of mathematics will often times assert that they are strong readers and writers. One of our goals in adding writing and reading to the coursework is to access the confidence students have in their academic abilities, regardless of where their strengths lie. In our courses we have students read a variety material ranging from magazine articles to popular press books. For example, in one course, students read the book Moneyball by Michael Lewis to gain insight on how baseball teams use statistical techniques to assess the value of baseball players. None of the students were intimidated by the book or material in the book as it is written for a general audience, but they immediately could see where the content of the class could be applied and had examples in which to relate. Reading a statistics text can seem daunting, whereas introducing the ideas outside of the traditional texts allows students to be exposed to the concepts in an environment where they are not intimidated.
As noted by Bradstreet, deciding to teach statistical reasoning, statistical methods or both is a crucial decision when shaping an introductory course (Bradstreet 2006). Statistical reasoning is the most important aspect of our courses and we believe having students write about statistics is paramount to developing their statistical reasoning abilities. The writing assignments come in two forms for our classes. The first is project based where students submit assignments that resemble "papers" discussing statistical content from reading assignments and what the corresponding statistical calculations mean. The other type of writing assignment is short answer questions they are assigned to work on throughout the semester. The short answer questions emphasize what the statistical calculations mean and will often lead to excellent in-class discussions. Simulation naturally lends itself to short answer questions and we have modeled our material after the work Rossman and Chance have done. To write successfully about statistics, one must understand statistics; however, students that feel they are strong writers at least feel confident in one aspect of an assignment.
The goal of this poster is to show how we have successfully implemented reading and writing into theme-based introductory statistics courses. The poster will show summaries of writing assignments and examples of reading assignments and how they each relate to the statistical content of the course. Additionally, we will discuss feedback we have received from students and data pertaining to how shifting the style of instruction from traditional introductory statistics courses has affected students' grades. Finally, we will talk about how the students' perception of the course has changed in regard to in-class discussions, their investment in the course and the amount of work they are willing to do.
Bradstreet, T. E. (1996). Teaching introductory statistics courses so that nonstatisticians experience statistical reasoning. The American Statistician, 50, 69-79.
Beins, B. C. (1993).Writing assignments in statistics classes encourage students to learn interpretation. Teaching of Psychology, 20, 161-164.
Chance, B., and Rossman, A. (2006). Using simulation to teach and learn statistics. Proceedings of the Seventh International Conference on Teaching Statistics. Voorburg, The Netherlands: International Statistical Institute. Retrieved January 25, 2011 from http://www.ime.usp.br/~abe/ICOTS7/Proceedings/PDFs/InvitedPapers/7E1_CHAN.pdf
Rumsey, D.J. (2002, November). Statistical literacy as a goal for introductory statistics courses. Journal of Statistics Education, 10(3). Retrieved January 25, 2011, from http://www.amstat.org/publications/jse/v10n3/rumsey2.html
Russek, B. (1998). Writing to learn mathematics. Plymouth State College Journal on Writing Across the Curriculum, 9, 36-45.
Smith, G. (1998). Learning statistics by doing statistics. Journal for Statistics Education, 6(3). Retrieved January 25, 2011, from http://www.amstat.org/publications/JSE/v6n3/smith.html
Stromberg, A. J., and Ramanathan, S. (1996). Easy Implementation of Writing in Introductory Statistics Courses, The American Statistician, 50, 159-163.
Theoret, J. M., and Luna, A. (2009). Thinking statistically in writing: Journals and discussion boards in an introductory statistics course. International Journal of Teaching and Learning in Higher Education, 21(1), 57-65.
Diversity Content Fosters Deeper Statistical Learning: A Case Study of a "Statistics of Sexual Orientation" Freshman Seminar
Michele DiPietro, Kennesaw State University
This course is the first of its kind. It's the first queer-themed course to be offered out of a statistics department and it has been featured in the Chronicle of Higher education.
I have developed this freshman seminar on the premise that an empirical, data-driven approach combined with the understanding of statistical methodology, would help students develop statistical and critical thinking skills and take informed positions. Rather than following a traditional statistics curriculum, the course is structured around LGBT questions in a Problem-Based Learning approach--we develop the statistics we need to answer those questions, so it covers a little less and a little more than a traditional intro stats course. We start from questions such as "How can we accurately sample LGBT people? How can we reliably count them and control for those who are in the closet? Is the cause of homosexuality biological or environmental? Can sexual orientation be changed through therapy?" Diversity and statistical goals are intertwined and in service of each other. The rich LGBT context motivates deep statistical learning (e.g., since you can never obtain a completely random sample of LGBT people, what other techniques are available to study this population?) and being grounded in research enables students to have more informed views on complex societal issues like gay marriage and ex-gay therapies.
By unpacking the structure behind the design of the course (how statistical objectives and diversity ones were selected, how the assessments were aligned with these objectives, and how the instructional activities were designed to be engaging but meaningful), poster viewers will acquire a rationale for this kind of model.
They will also preview several learning activities that are transferable (and in fact have already been transferred) to traditional intro courses to illustrate certain statistical concepts and techniques.
By examining evidence from student assessments (pre/post concept maps, journal entries, student presentations) Poster viewers will witness the kinds of learning gains students achieved. These include gains in statistical knowledge and skills, gains in critical thinking, and gains in intercultural competency. In particular, poster viewers will gather evidence that a diversity curriculum does not need to water down essential knowledge.
Faculty Perceptions of Statistics
Kirstie Doehler, Elon University
Laura Taylor, Elon University
With a world that is becoming increasingly driven by data analysis skills, it is not uncommon to see applied statistics being used by psychologists, biologists, anthropologists, and individuals in other disciplines. Since students are often exposed to statistics through the professors in their majors, it is important to better understand how faculty view statistics as it could affect the views of students. It seems natural that if faculty value statistics more in their disciplines, students will also. Most of the current literature studies the attitudes, anxiety, and perceptions of students toward mathematics and statistics (Cherney and Cooney, 2005; Roberts and Bilderback, 1980; Wise, 1985; Cruise, Cash, and Bolton, 1985). This poster introduces an inventory to measure faculty perceptions toward statistics and the results of a pilot study at a liberal arts university in North Carolina. The majority of students at this university are required to take an introductory statistics class as part of the general studies curriculum for their first year. The data is collected from faculty members across all disciplines. The four constructs explored are general attitudes toward statistics, the role of statistics in teaching, the role of statistics in research, and the role of statistics in the education and post-graduation plans of students. Our goal in this pilot study is to begin to validate the instrument and better understand how statistics is viewed by faculty members from a variety of disciplines. Faculty perceptions could ultimately impact the views and attitudes that students have toward the discipline of statistics and its usefulness in their own lives and future careers.
Enhansing Statistical Thinking Among Undergraduates
Harshini Fernando, Purdue University North Central
Case studies in statistics can be used to enhance statistical thinking among undergraduate students. The presentation describes in detail what "statistical thinking" is, and definitions and statements related to statistical thinking. This presentation provides details of incorporating a case study course in an undergraduate statistics minor/major as a capstone course. The case study course as the capstone course requires students to utilize key concepts that they have learned in the other statistics courses in their statistics minor/major. Such course will help the students bridge the connection between statistical methods and its potential applications, making them well prepared for their careers, hence improve their statistical thinking skills. Also the presentation describes in detail the methodology used in construction of such course, the value and insights about the statistics minor/major where a case study course as a capstone course is introduced.
Teaching Innovations for QBIC Statistics Courses at Florida International University
Ramon Gomez, Florida International University
A special undergraduate program for selected biology majors was inaugurated at Florida International University in 2007. This undergraduate program identified as QBIC, an acronym for "Quantifying Biology in the Classroom" is rigorous and interdisciplinary. It emphasizes the use of mathematics and statistics for analyses of biological/biomedical data and includes two statistics courses during the sophomore year. This poster describes the present author's experience in teaching these courses with technology resources and real data to improve students' understanding.
The traditional approach to teaching Statistics consists of using a board during lectures, a textbook as a reference, and supplementary material posted on a website. Two technology additions are integrated in our courses: the daily use of PowerPoint for lectures as well as statistical software (SPSS) for data computations and analyses. The classroom setting consists of a fully equipped computer lab including twenty five seats and a projection system. Each student has access to a desktop personal computer and real data from the biological/biomedical field, which is used to illustrate statistical concepts and teach the statistical software. Data generated in the biology and ecology labs by QBIC students are incorporated in numerous examples. The PowerPoint presentations are created by the instructor and include: a) text for definitions, concepts, formulas, examples and exercises, b) tables and graphs, c) SPSS instructions, and d) SPSS output. A course pack equipped with the PowerPoint slides for all lectures and developed by the present author is made available to the students at the beginning of the course.
A typical class session begins with a review of the previous lecture content, from both a conceptual and computational standpoint. Then, new lecture material is introduced, followed by a discussion of the SPSS output for a selected example. Accordingly, the instructions for the related software procedure are displayed as QBIC scholars implement them on a new example, using their personal computers and data previously loaded in their flash memory drives. The instructor supervises this step and provides guidance. When the students complete the SPSS execution of the example, a discussion is conducted concerning the software output. This type of lecture synergistically combines the teacher-centered, student-centered, and interactive styles.
The teaching-learning method used for QBIC statistics courses is illustrated in this poster with two examples involving: a) Predictive values, an application of the Bayes' theorem, using actual data from a clinical study, and b) Two way ANOVA analysis for a repeated measures design with data generated by QBIC scholars in the ecology lab. While using this methodology, QBIC students are able to learn quickly and effectively. This is evidenced by the number of statistical topics covered, the acquired knowledge of statistical software and overall students' performance.
The Next Big Thing: Homework + e-Textbook = Integrated Online Learning
Brenda Gunderson, The University of Michigan
Perry Samson, The University of Michigan
Our educational infrastructure is based largely on the idea that the student will progress far more quickly under the guidance of a skilled instructor - both knowledgeable in the subject matter and competent in instructional methodologies. Technology can be a facilitator on the student side of education, and provide assistance to the instructor during the teaching and learning process - especially in the large introductory statistics courses.
I strive to create a continuous learning experience for my students through the considered implementation of appropriate technological components, both in and out of the classroom. The newest component to be interwoven into my course is an online homework tool which is combined with the e-textbook.
Students need practice and more opportunities for productive struggle outside the classroom - that is especially true in the field of Statistics. Starting this past Spring 2010, I have been piloting and guiding the development of an online tool called LectureBook (www.lecturebook.com), which facilitates the creation and grading of online homework linked to the corresponding e-textbook. The idea is to make the e-textbook a to the homework questions. Doing homework questions on-line makes sense, having access to the book in the same media makes sense. This online homework/e-textbook prototype is currently being used in my statistics course with an enrollment of over 1,500 students per term. This project is work with Perry Samson (Professor of Atmospheric, Oceanic and Space Sciences, University of Michigan Engineering), as a new component of the current LectureTools (www.lecturetools.org) system.
I have created a bank of customized homework questions that can be linked directly to e-textbook content. I have created solutions that go beyond just providing the correct answer. I select problems to assign weekly to match content presented in lectures and lab. Students work through the weekly homework online, with direct links to the e-textbook material if questions or a review is needed. The submission of the paperless homework is automatic and set for one common time for all students (no more 'I lost my homework' or 'I forgot to turn in my homework').
My many Graduate Student Instructors (GSIs) are able to grade the homework and supply feedback within a few days because of the efficient design of the grading system. Students receive the solutions immediately after submission and their scores with tailored feedback a few days later. Students have all homework assignments with their answers and feedback in one place for future reference.
Consider this direct quote regarding this online homework tool from a current student's nomination letter for the University of Michigan Teaching Innovation Prize (TIP) www.crlt.umich.edu/TIP/2011.php:
"At first, I was skeptical about the online homework tool, but within the first week I became greatly appreciative of its features. Notably, the online homework tool allows graduate student instructors to provide feedback on individual responses, meaning that graduate student instructors can comment on what error students made in their logic and how to think about the question in the future. I find this immensely valuable, as it allows students to quickly identify and understand their mistakes. Additionally, the online homework tool publishes the complete set of answers to each homework assignment, meaning that students can work through the problems before the exam. The online homework tool is fundamentally a learning tool and a study tool, which I find very useful."
In the Fall 2009 term, the average grade for the = 1326 students was 3.09. This past Fall 2010, the average grade for the = 1395 students was 3.22. The Online Homework Tool was the only new innovation incorporated in Fall 2010 over the Fall 2009 term. Interestingly, while most e-textbooks obtain less than 5% buy-in when offered as an alternative to hard-copy texts, this model obtained about a 25% buy-in last Fall 2010 and over 50% buy-in this current Winter 2011 - as students appreciate the integration of textbook with homework questions.
A survey was conducted of the Fall 2010 users of this online textbook and homework tool. The graph at the right shows the results regarding students' overall experience rating. Another student wrote this comment in their nomination letter for the TIP award: "The extensive online homework assignments are "convenient to access and require you to both mathematically and visually demonstrate the knowledge we learn in class."
There are future plans (April-May, Spring 2011) to further enhance this online HW/e-textbook tool. I am using Camtasia Relay - a lecture capture software that allows for closed captioning and exporting media in multiple modes to capture all Stats 250 Winter 2011 lectures. The full lectures go up on iTunes U for current students to utilize. The captured lectures will be further used to create small mini video snippets to be tagged to various homework questions in the online homework tool. A student working on homework and needing a hint or guidance could click on the associated mini video of 3-5 minutes of lecture showing an example or the discussion that correlates with the homework problem.
Classroom Strategies for Engaging Nursing Students in a Statistics Class
Matt Hayat, Johns Hopkins University
Statistics education is an essential component of nursing education. This is a result of the focus in the nursing field on the use of evidence-based nursing practice (EBNP). Each undergraduate and graduate nursing program requires successful completion of one or more statistics courses. In addition to formal statistics coursework, each degree program also includes a research course which makes frequent use of statistics in reading and critiquing the literature. Articles in the nursing literature use statistical language, methods, and interpretations. Statistical literacy and knowledge is needed for understanding and use of EBNP.
In this poster I share strategies for engaging nursing students in the statistics classroom. This includes an interactive discussion on the first day with the students about uncertainty, stigma, and fear of statistics. Active learning strategies are described, including the use of EBNP publications for illustrating statistical concepts and methods. Activities and classroom exercises are described that aim to engage the student and relate statistics concepts and methods to everyday nursing practice. A description of a planned study of graduate nursing student knowledge and attitude about statistics is given.
The Research Process: A Statistics Course for Biology Majors
Debra Hydorn, University of Mary Washington
In its 2003 publication "BIO2010: Transforming Undergraduate Education for Future Research Biologists" the National Research Council provides a series of recommendations for a new curriculum in biology to provide a "strong foundation in mathematics, physical and information sciences to prepare students for research that is increasingly interdisciplinary in character." This poster will describe a new interdisciplinary course on the research process based on some of the BIOL2010 recommendations. Co-created and co-taught by a biologist and a statistician, the course prepares students for participating in undergraduate research in biology. With its emphasis on experimental design and data analysis methods, however, the course could be modified to meet the needs of students in many other disciplines. The course focuses on (a) writing a research proposal, (b) data analysis methods, (c) collaborative assignments, and (d) analyzing and describing research outcomes to prepare students for designing and conducting their own research. In-class activities encourage students to consider research-related topics, such as how the design and implementation of an experimental protocol can impact the accuracy and precision of results or how the form in which results are presented can impact how the results are interpreted. The poster will include a course outline, example data analysis assignments and class activities, and a description of how the course has developed through several iterations, based on identifying which concepts and methods students struggle with most.
"Where Do Statistics Come From?" - Setting the Table for Introductory Statistics
Marc Isaacson, Augsburg College
This poster presents the results of 200+ student responses to the big picture first day activity / question "Where do statistics come from?" This initial discussion can set the table for introductory statistics students by providing a framework with which to connect nearly every topic in the first semester course. While most students know that statistics are the result of mathematical calculations, few recognize or understand the multiple processes that result in the birth of those data and their eventual presentation in everyday encounters.
Many introductory statistics textbooks begin with the near-biblical premise "There is data" as if they are pre-existing facts and then concentrate on the language, mechanics and science of statistical calculations. Most of these same textbooks completely ignore the fundamental question about the origin of statistics and the critical yet often subjective decisions (i.e. choices of population, sample, measures, definitions, categories, etc.) that can greatly impact the data and values eventually calculated.
Setting the table for the introductory statistics course by beginning with this central question and presenting a process-oriented structure provides a compelling motivation for students to frame their newly learned statistical knowledge. It also allows them to ask intelligent questions as statistically literate consumers of information, which should be a primary outcome of introductory courses. This poster will include a proposed outline of the necessary chapter to set the table for introductory statistics students.
Student answers to this written activity vary greatly in detail and sophistication but provide valuable insight into student thinking about statistics at the beginning of the course. They also provide a forum for classroom discussion (where there are multiple levels of correct answers) of this vital and yet rarely asked big picture question in the introductory statistics course. Pairing this activity with others such as Roxy Peck's "Seeing Red" activity (http://www.ncssm.edu/courses/math/Stat_Inst/Stats2007/Seeing%20Red/Seeing%20Red%20Overview.pdf), current news article evaluations and course projects provides an opportunity to continually revisit the idea that statistical calculations are not isolated events. Rather, they are an integral part of a much larger endeavor to study a question of interest.
Connecting Statistics with Calculus and Vice Versa
Daniel Kaplan, Macalester College
Introductory statistics courses are sometimes taught with a calculus pre-requisite, but often not. Almost always, the calculus is used as a way of segregating out the "mathematically mature" student from others. The techniques of calculus themselves are hardly ever used in the statistics course.
This is unfortunate. Calculus can provide many insights to the study of statistics, and similarly statistics can provide a powerful motivating setting for teaching concepts of calculus. Of course, the connection between calculus and statistics is not about techniques for integration or the use the word "integral" rather than "area under the curve." Instead, both calculus and statistics can be about modeling and approximation. I'll describe some of the connections we make at Macalester in our integrated calculus/statistics sequence: the importance of partial derivatives in interpreting statistical models, how model fitting is done, how to measure the quality of an approximation, what an interaction term is, etc. A properly taught calculus course can equip students to go further in their statistics course. And using statistics as a motivation for teaching calculus can lead to a calculus syllabus that is much better connected with real-world uses of calculus.
Real exam questions will be used to illustrate the learning gains that can occur in both calculus and statistics from this approach, and enrollment and student survey data will be presented. The poster will also describe some of the obstacles to adapting the integrated approach, the value of having instructors who teach can both calculus and statistics, and the curricular resources -- texts, exercises, activities, software -- that are available to support instructors and departments who want to adopt the approach.
Designing an Undergraduate Statistics Program for the Future
April Kerby, Winona State University
Tisha Hooks, Winona State University
Chris Malone, Winona State University
Brant Deppa, Winona State University
Does our current undergraduate statistics curriculum properly prepare students for their future? Upon graduation undergraduate students either seek employment or pursue an advanced degree in statistics. Ideally, an undergraduate program would provide the skills necessary to be successful in either path. Is this even possible? If so, what does the optimal curriculum include? This poster will present a preliminary review of existing undergraduate programs and their requirements in addition to the current ASA's Curriculum Guidelines for Undergraduate Programs in Statistical Science. Audience members will be asked to actively participate in such discussions. The outcomes from these discussions will be gathered and displayed on this interactive poster. A summary of all discussions will be compiled and distributed via email upon request.
Teaching Undergraduates Categorical Data Analysis Using R: Absorb the Textbook!
Ji Young Kim, Mount Holyoke College
The interest in learning statistical methods for categorical data is growing in the undergraduate institutions, as the number of students who take statistics classes grow. The course of categorical data analysis is more challenging than other courses for continuous data in the sense that it requires more prior knowledge in regression modeling and probability distributions. Conducting all the analysis using R is also one of the valuable challenges in this course. To get this content down to an undergraduate level, the course was designed to have students completely absorb the textbook (Agresti, 2nd). It was taught by going over the book repeatedly in several different formats. As one of the strategies, we employed seemingly elementary techniques such as highlighting the textbook together, to make the course more approachable to undergraduate students. This poster will summarize the strategies we employed as well as the issues and difficulties we faced in this course.
Statistics Without Tables
Larry Knop, Hamilton College
The computer revolutionized statistics but the past lives on, and reliving the past seriously complicates the present. Consider the problem:
In 2002 the NCAA required Division I athletes to score at least 820 on the combined math and verbal parts of the SAT exam in order to compete in their first year of college. That year the scores of students taking the SATs were approximately Normal with mean 1020 and standard deviation 207. What percentage of all students had scores less than 820?
The problem is easy to understand and easy to set up: draw a bell shaped curve with center at 1020 and inflections at 1020 +/- 207. Mark the point 820 on the Xaxis. The percentage sought is the area under the curve to the left of the 820 mark, times 100.
The standard procedure for finding the answer is not so easy. Students start with X < 820 and transform the inequality into standard normal form. The fact that many intro stats students are inequality-challenged is ignored. Also ignored is the fact that the transformation takes the meaning out of the problem. The inequality, Z < -0.9662, is a dimensionless statement with no obvious relationship to the original question. Then, once the number -0.9662 is obtained (if the number -0.9662 is obtained), students must consult the standard normal probability table to get an (approximate) answer to the question.
The computational tail is wagging the dog. The procedure was once necessary but is now a distraction. The computational part of the problem takes three times as long as the setup of the problem - to no good purpose. Students focus on the procedure, because that's where their time is spent and where the majority of their errors occur. And the computational aspect is where the instructional time is spent because that's where the students have questions. Meaning takes a back seat to process, and that doesn't have to be. In SPSS the answer is generated by a single command, CDF.NORMAL(820, 1020, 207). A simple problem stays simple, instructional time can be devoted to meaning rather than computation, and students can focus on explaining instead of calculating.
Hamilton College, where I teach, provides its students with good software access. This past year I decided to take full advantage of this access and use software wherever appropriate on homework and on exams. The example above was one appropriate place; there were many others. My approach had some drawbacks, the main one being that textbooks are mired in the past. My approach had some significant advantages; I find discussions of conclusions to be much more satisfying than discussions of how to read a table.
A Comparison of College Students' Inferential Reasoning Using RPASS-8
Sharon Lane-Getaz, Saint Olaf College
This poster reports results of a quasi-experimental study comparing inferential reasoning outcomes for three college statistics courses at a small liberal arts college in the Midwest. Of the three courses in the study two are at the introductory level (one with a Calculus prerequisite and the other with an Algebra perquisite.) The third course is a second course in statistics emphasizing regression modeling techniques. In spring 2010 a 35-item version of the Reasoning about P-values and Statistical Significance (RPASS) scale was administered as a Pretest and Posttest in each of these courses to assess and compare gains in students' inferential reasoning. RPASS gains were adjusted for prior knowledge using the Pretest scores and mathematics ability using college entrance scores for ACT Mathematics. In addition to reporting the quantitative evidence based on RPASS gains, the study highlights how students' reasoning changes from Pretest to Posttest based on student explanations for their responses on twelve selected RPASS items. The RPASS-8 scores are also shown to be reliable (Cronbach's coefficient alpha = .95) and validity correlations are reported. Implications for research and the teaching of inferential concepts are discussed. The most prevalent correct conceptions and misconceptions exhibited by the respondents are reported.
Using In-test Mnemonic Aid - Getting Statistics Students Engaged!
Karen Larwin, Youngstown State University
Researchers have explored a plethora of pedagogical approaches in an effort to assist students in finding meaning and even comfort in their required statistics courses. The present study is the first attempt to investigate the impact of In-test Mnemonic Aids (IMAs) (a.k.a., cheat sheets) on students' statistics course performance in particular. In addition, the present study explores several hypotheses that have been proposed to explain the potential benefit of using IMAs during examinations. These include the student engagement hypothesis, the perception of control hypothesis, the dependency hypothesis, and a placebo effect hypothesis. The results indicate that student-generated IMAs are clearly superior to the other forms of in-test aids examined, however they were not superior to conditions where IMAs are not allowed. Results are presented in terms of their implications for the four hypotheses regarding the beneficial effects of IMAs, and the implications of different levels of engagement on student success.
Conceptions and Misconceptions in Statistics: The Role of Experience, Gender, and Individual Differences in Statistical Reasoning
Nadia Martin, University of Waterloo
Our information-laden society challenges citizens to be astute consumers of numerical information, which increases our need to understand factors that influence the development of statistical literacy.
In this project, we were primarily interested in examining the interactive effect of gender and experience, as well as the role of individual differences in cognitive ability and thinking dispositions, on statistical reasoning.
To do so, men and women with varying levels of experience in statistics were recruited to complete the Statistical Reasoning Assessment (SRA; Garfield, 2002) along with various measures of individual differences (e.g., Wonderlic Personnel Test, Numeracy Scale, Preference for Numerical Information, Need for Cognition).
A structural equation model, based on Stanovich's dual-process model of reasoning, was used to test the relation between thinking dispositions and cognitive ability in predicting statistical reasoning differences.
Overall, individual differences in cognitive ability and thinking dispositions were insufficient to explain a persistent gender gap in performance across levels of experience. More research is granted due to the negative impact such a resistant gap can have on women's educational and work opportunities.
An Interactive Web-based Tutorial to Teach Correct Interpretations of Confidence Intervals
Justin C. Mary, Claremont Graduate University
Dale E. Berger, Claremont Graduate University
Amanda T. Saw, Claremont Graduate University
Giovanni W. Sosa, Claremont Graduate University
Both students and professionals often misinterpret confidence intervals. A common misinterpretation is that any overlap of two 95% CI denotes a non-significant difference between the means (Belia, Fidler, Williams, & Cummings, 2005). This misinterpretation is called the "overlap fallacy" because, in fact, two 95% CIs can overlap to a considerable degree and still indicate a statistically significant difference between the means. Because CI's are based on normally-distributed sampling distributions, when two CIs overlap, only a small portion of the two sampling distributions may actually overlap because the tails of the distributions are thin. Consequently, two CIs can overlap to a considerable degree before the two sampling distributions overlap to the extent that an independent sample t-test will result in a non-significant p-value.
A web-based tutorial to correct the overlap fallacy was designed and tested on a sample of graduate and undergraduate students from four different colleges in Southern California (N = 55). This tutorial was designed to provide a highly interactive and self-paced learning experience based upon empirically validated principles in statistics education. Accordingly, students actively participated in constructing their own knowledge. Students made predictions, tested them in real time, and were given immediate feedback in this self-paced tutorial. The tutorial was successful in providing students with a deeper understanding of confidence intervals that allowed them to correct misconceptions about the relationship between CI overlap and statistical significance.
The tutorial featured an interactive Java applet that allowed students to visually manipulate the height of one of two bars in a bar chart, along with the corresponding CI, and note the change in the p-value for an independent sample t-test at varying degrees of CI overlap (See Figure 1 below). The cover story was that the Pepsi Corporation wanted to assess whether consumers preferred a reformulated version of their cola to the original version. The applet contained bars representing the mean preference rating for each Pepsi version, along with the corresponding 95% CI. Through the use of an interactive slider, students were able to adjust the mean of the reformulated Pepsi group; the p-value was displayed next to the bar chart so students could note the p-value at varying degrees of overlap between the two CIs.
At the beginning of the experiment, a primer on CIs was provided, where CI calculations and interpretations were given, as well as a comprehensive example of CIs. Students then completed two exercises with the applet. In the first exercise, students were asked to predict how far the means of the two groups needed to differ for an independent sample t-test to be just significant at a = .05. Students were then prompted to use the applet to adjust the mean of the reformulated Pepsi to attain p = .05. This exercise of having students predict and test an outcome required them to confront misconceptions they may have about overlapping CIs. Students were prompted to consider why two means could be significantly different when CIs overlap and they were then given feedback and an explanation.
In the second exercise students used the interactive slider to adjust the reformulated Pepsi mean to four different values that were equally spaced, noting the p-value at each mean value. This exercise aided students in discovering that the p-value did not change uniformly with decreases between the means of two independent samples, but rather changed more slowly when the distributions had only small amounts of overlap. Students were asked to explain why this may be the case, and their findings were then connected back to the shape of the underlying (normal) sampling distributions as shown in the applet (see Figure 1).
To test the efficacy of this tutorial in aiding students' correct interpretation of CIs, pretest and posttest measures of CI estimates were collected. During these assessments, students were asked to adjust the mean and confidence interval for one mean until a two-tailed independent samples t-test conducted on two means was just statistically significant. On pre-test only 18% of students made p-value judgments that were within 10 percentage points of the correct value, while on post-test this proportion increased to 41% (z = 3.02, p = .003). This finding demonstrates that the applet and tutorial helped students to improve the accuracy of their interpretations of confidence intervals.
Several studies have demonstrated the prevalence of the overlap fallacy and its important implications for biological and social research. The results from this experiment show that our tutorial is a useful tool to address this problem and help students and researchers interpret confidence intervals more accurately.
The tutorial and interactive applet, to be freely available on the Internet, will be demonstrated at the conference; attendees will be able to manipulate the applet and examine the tutorial.
Figure 1. Annotated depiction of interactive confidence interval applet. Students manipulated the applet using an interactive slider and noted the change in p-value when the CIs overlapped. The applet is oriented to demonstrate the overlap fallacy.
Using Crossword Puzzles in Introductory Applied Statistics Courses
John McKenzie, Babson College
Arthur Wynne is credited with the creation of the crossword puzzle in 1913. Such puzzles soon became a standard feature of paper newspapers and, more recently, on-line newspapers. With improvements in technology they have begun to be used in a variety of tertiary classrooms such as psychology (Crossman and Crossman (1983)), sociology (Childers (1996)), and microbiology (Miller (2008)) as an educational tool.
This poster explains how crossword puzzles can be used to enhance introductory applied statistics classrooms. It demonstrates how these familiar puzzles have been used as in-class exercises, quizzes, and examination questions at an undergraduate institution with approximately 2000 students. It explains how such puzzles have been most successful as active-learning exercises in classroom. It makes clear how crossword puzzles can assist the students in understanding basic statistical terminology from a first chapter (e.g., interval and ratio levels of measurement), along with often difficult terms found in basic inference (e.g., critical values and p-values) and regression (e.g., response and predictor variables).
The poster presents an assessment of the use of such puzzles to improve the student's knowledge of statistical terms. This evaluation includes analyses of both quantitative and qualitative data from students in an introductory applied statistics for business students. Crossword puzzles can also improve their spelling of such terms.
The poster presents innovative numerical crossword puzzles that can be to ask questions about statistical software output. It explains how the use of such puzzles was impractical due to time it took to construct them. Today that is no longer the case with the availability of a number of Internet sites. The poster illustrates how a 10-term criss-cross quiz can be constructed in less than 15 minutes by using the free software available at www.discoveryeducation.com/free-puzzlemaker. It also explains how easily it is to construct quizzes with same terms but different structures to prevent cheating.
The poster explains other ways that crossword puzzles have been used by others, such as to review for exams (Davis, Shepherd, and Zwiefelhofer (2009)) and to promote group work in the classroom. It also mentions some other puzzles that might be used in introductory applied statistics courses.
Shifting from a Traditional to Project-Based Statistics Course
Susan Perkins, Northwest Nazarene University
Previous educators have identified several benefits of using projects in teaching statistics, including reducing anxiety, retaining student interest, increasing student motivation, and improving student ability to make appropriate decisions about the use of data. Information about the benefits of using projects in statistics courses and descriptions of projects used in teaching statistics are available. However, because instructors may not have experienced project-based statistics learning, adjusting from traditional, lecture-based instructional approaches to more experiential methods of teaching can be a daunting task. Additionally, while authors address statistics courses in isolation, educational programs may have specific requirements which need to be considered by professors in the design of their statistics courses. Therefore, a description of how one instructor considered a project-based design and program-level factors when redesigning a statistics course may be a useful example for educators.
This poster will describe one instructor's process in transforming an introductory, Masters-level statistics course from a didactic, instruction-focused statistics course to a project-based, outcome-focused statistics course. Emphasis will be given to methods used to tailor the course to the needs of the educational program, which required students to complete, write, and present a research project. Adjustments to the syllabus, content, and teaching style will be addressed. Examples of the projects assigned will be provided and examples of student reports will be available. The poster will include an overview of strengths and challenges experienced in both course design options. Finally, a conclusion will include lessons learned and recommendations for creating a project-based statistics course within the context of larger program requirements.
Using a Student Advisory Board to Facilitate and Improve Development of a New Course
Jamis Perrett, Texas A&M University
Developing a new course or making significant revisions to an existing course might be a daunting task for any instructor. However, students could be most helpful in this process. At the invitation of the instructor, three students volunteered to be on an advisory board for the class. They met with the instructor weekly to discuss the delivery of course instruction, use of technology in the classroom, behavior of fellow classmates, and level of difficulty and quantity of assigned classwork.
The student advisory board proved to be an invaluable resource to the instructor because it facilitated development of the course throughout the semester and revealed improvements that could benefit current and future semesters.
Teaching Statistics to Prospective Teachers: Residual Understandings
Susan A. Peters, University of Louisville
Rose Mary Zbiek, The Pennsylvania State University
Expository literature documents a widely held belief that many teachers lack knowledge in and experiences with statistics (e.g., Ben-Zvi & Garfield, 2004; Franklin & Mewborn, 2006), including some that suggest teachers' poor backgrounds in statistics are a critical barrier for improving statistics education (e.g., Shaughnessy, 1992). Discussions surrounding teacher education in statistics focus on providing teachers with opportunities to study statistics in ways similar to how they are expected to teach the content (e.g., Chance & Rossman, 2006; Heaton & Mickelson, 2002). This poster describes an activity that we use with prospective teachers to exemplify an opportunity in the context of bivariate data analysis. The activity, Residual Understandings, actively engages teachers with statistical exploration through a distinctive combination of tasks that capitalize on dynamic features of technology and enable teachers to make connections among statistics concepts and to school mathematics content.
Fathom and Barrett (2000)
Open the Fathom file named Barrett.ftm, which should be on the desktop. Double click on the "Barrett Data" collection box to inspect the collection. Make sure you examine the formulas that are used for the calculation of the different columns in the table. These formulas also can be found in the table on p. 231 of the Barrett (2000) article. (Note: Clipart from Microsoft)
Examining a Univariate Data Distribution
Create a dotplot of the Husband_Age variable by creating a new graph and dragging the Husband_Age variable to the horizontal axis. Use all of the information you have for husband ages to answer the following questions.
- The ages for sixteen husbands are displayed in the dotplot. If the age of a seventeenth husband was collected but not recorded, what age would you guess for the missing age and why did you choose that age?
- How confident are you that the age you guessed matches the actual age of the husband? To what do you attribute your level of confidence?
Examining Bivariate Data Distributions and the Coefficient of Determination,
- Create a scatterplot of the Wifes_Age and Husband_Age variables using Wifes_Age on the horizontal axis and Husband_Age on the vertical axis.
- Plot the function on the scatterplot.
- Describe how well the average husband age predicts the age of a 51 year-old wife's husband.
- Choose the "Show squares" option from the Graph menu.
- Create a second scatterplot of the Wifes_Age and Husband_Age variables using Wifes_Age on the horizontal axis and Husband_Age on the vertical axis.
- Add the least-squares regression line using the Graph menu and again choose the "Show squares" option.
- Using the least squares regression line, describe how well the line predicts the age of a 51 year-old wife's husband.
- Which prediction, the prediction from 3 or from 4, allows you to predict the husband's age with more confidence and why?
- How do the squares in the original graph relate to the formula for calculating R2?
- How do the squares in the second graph relate to the formula for calculating R2?
- Using what you wrote for (6) and (7), describe R2 in a way that someone unfamiliar with statistics could understand.
- Compare and contrast the graphs you created with the graphs displayed in Figure1 and Figure 5 in Barrett (2000) and shown below.
(Barrett, 2000, p. 231) (Barrett, 2000, p. 232)
Examining a Residual Plot
Create a third scatterplot of the Wifes_Age and Residual variables using Wifes_Age on the horizontal axis and Residuals on the vertical axis.
- Describe the positioning of the "dots" on the scatter plot.
- How does this "residual plot" compare with the scatterplot of Husband_Age versus Wifes_Age?
Reflection for Teachers
- What is a residual plot?
- How did the subheadings help you organize your ideas about what mattered in this activity?
- How does the clip art relate to the main statistical ideas in this activity?
Barrett, G. (2000). The coefficient of determination: Understanding and . The Mathematics Teacher, 93(3), pp. 230-234.
Stepping from service-learning to SERVICE-LEARNING Pedagogy: Where Do You Fall on the Continuum and How Do We Move Along the Continuum?
Amy Phelps, Duquesne University
Service learning can mean different things and look quite different in varying statistics curriculum which may include undergraduates, graduates, majors and non-majors across a wide array of higher institutions. The terms community engagement, volunteerism, community-based projects and service learning are tossed around on various institution's website. The purpose of this proposal is two-fold. First to try to unify and define some of the terminology and second to present some examples of how a first and second course in business statistics can step up the rigor of service learning to SERVICE-LEARNING.
Hydorn (2007) draws from a Campus Compact1 publication by Heffernan (2001) to present 6 models for course design:
- "Pure" Service Learning
- Discipline-Based Service Learning
- Problem-Based Service Learning
- Capstone Courses
- Service Internships
- Community-Based Action Research
Service-Learning is presented by our institution as a teaching methodology that combines three key concepts to enhance student learning and social responsibility.
- Academic instruction
- Meaningful service
- Critical reflective thinking
By emphasizing students' civic development; use of ongoing, structured reflection; and sustained, reciprocal partnerships between faculty and community partners, Service-Learning differs significantly from other forms of community engagement such as volunteerism (model 2 described frequently by activities such as tutoring that do not promote reciprocity), consulting (model 3), internships (model 5), or practicum/capstone coursework (models 4 and 6). While these experiences are excellent and support the GAISE guidelines, many are geared toward upper level classes and represent experiences along a continuum of service learning concepts. Consider the service learning typology (Sigmon, 1994):
service-LEARNING: learning goals primary; service outcomes secondary
SERVICE-learning: service outcomes primary; learning goals secondary
service learning: service and learning goals completely separate
SERVICE-LEARNING: service and learning goals of equal weight and each enhances the other
for all participants (reciprocity)
Service-learning has taken on a variety of experiential education forms including (Furco, 2003):
Volunteerism is engagement of student activities where the primary emphasis is on the service provided and the primary intended beneficiary is the community recipient. SERVICE
Community service is the engagement of students in activities that the primary focus is on the service being provided (serving food to the homeless) while the student may receive some benefit by learning how the service may make a difference in someone's life. SERVICE-learning
Internships engage students in service activities primarily for the purpose of providing students with hands-on experience that enhances their learning or understanding of issues related to their discipline of study. service-LEARNING
Field Education provides students with co-curricular service opportunities that are related, but not fully integrated with their classroom instruction. service learning
SERVICE-LEARNING programs are distinguished from the other approaches by their intention to benefit the provider and the recipient of the service equally. SERVICE-LEARNING is an approach that unifies what you learn in the classroom with the service you are doing in the community. Through meaningful reflection, you can solidify the concepts taught in the classroom and develop a sense of responsibility in the community. SERVICE-LEARNING pedagogy structures class activities around the service so the students are learning the statistical concepts while simultaneously performing the data collection, description, analyses and concluding summary reports. Students see immediately the concepts come alive in a real context, provide a meaningful service while learning more about the agency than the agency itself might have predicted through the analysis. Also, when given time to reflect on the process, the repetition provides a deeper understanding of the statistical concepts as well as personal growth (Phelps, 2008).
Service learning in the social sciences has been growing since the early days of the Campus Compact. Examples cited in the statistics education literature began to develop with the statistical reform movement and discussions leading to the GAISE guidelines. Frequently cited statistical education papers describing service learning experiences often are applied in consulting-type classes (Jersky, 2002) or involve more advanced students in the natural sciences (Anderson and Sungur, 1999). Other cited studies focus on anecdotal student self-evaluations without a detailed description of the level of the course. These studies offer supporting evidence that service projects affect social cognitive development (Sperling et al, 2003) and improve students' attitudes toward a course (Evangelopolis et al, 2003 and Gordon, 2004). Thorne and Root (2001 and 2002) provide supporting evidence of ways community-based projects help students learn statistics in an applied class.
Applying service learning in a truly beginner, non-major statistics class is less frequent. Having students at this level physically gather their own data as opposed to it being handed to them is also less frequent. And finally, incorporating critical reflective thinking has not been widely reported in the statistics education literature. The proposed poster will demonstrate the steps taken by a business statistics professor over the last 5 years to fully incorporate the three key concepts to enhance student learning and social responsibility and to ensure that the pedagogy is based soundly on 'reciprocal learning'. Students gain experience from data collection, to data summarization, to statistical analyses and presenting an oral and written report. Community partners not only learn some basic statistical techniques of their own, but gain valuable assessment information from which to reflect and change their own programming and policies.
All projects begin with 2-4 meetings between the instructor and the community partners prior to the start of the semester. The project and community partner are introduced at the beginning of the semester. Once students get HIPAA certified, they can begin to sift through the boxes of paper that most non-profits collect in copious amounts but have little time or expertise to do anything about it. Once the data are entered and cleaned, students can begin the analyses. The proposed poster will include a project proposal agreement, a list of assignments, an example of a critical reflection piece and descriptions of some of the community partners and projects completed. Examples for a one-semester and a two-semester project will be presented which include: a study of insurance coverage and prescription aid support over three time periods, program assessment for a faith-based homeless organization and a teen supervised independent living foster care program, and survey results supporting the viability of a mentor program in homeless shelters. Additionally, preliminary data results will be available comparing learning, civic responsibility and personal growth differences between groups that select a service learning project and those that choose to do a traditional project based on a research question of their own interest.
1 Founded in 1985, Campus Compact is a national coalition of more than 1,100 college and university presidents whose primary focus is dedicated to campus-based civic engagement. Campus Compact promotes public and community service that develops students' citizenship skills, helps campuses forge effective community partnerships, and provides resources and training for faculty seeking to integrate civic and community-based learning into the curriculum. Campus Compact was created to help colleges and universities create such support structures. (http://www.compact.org/about/history-mission-vision/).
Anderson, J.E. and Sungur, E.A. (1999). Community Service Statistics Projects. The American Statistician, May 1999, vol. 53, No. 2.
Evangelopoulos, N, Sidorva, A. and Riolli, L. (2003). Can service-learning help students appreciate an unpopular course?: A theoretical framework. Michigan Journal of Community Service Learning, Winter 2003, pp. 15-24.
Furco, A. (2003). Service-learning: A balanced approach to experiential education. Introduction to Service-Learning Toolkit, 2ed. Campus Compact.
Gordon, S. (2004). Understanding students' experience of statistics in a service course. Statistics Education Research Journal, May 2004, 3(1):40-59.
Hydorn, D.L. (2007). Community Service-Learning in Statistics: Course Design and Assessment. Journal of Statistics Education, Volume 15, Number 2 (2007).
Heffernan, K. (2001). Fundamentals of Service-Learning Course Construction. Providence, RI: Campus Compact, Brown University.
Jersky, B. (2002). Statistical consulting with undergraduates - A community outreach approach. ICOTS6, 2002.
Phelps, A.L. and Dostilio, L. (2008). Studying student benefits of assigning a Service Learning project compared to a traditional final project in a Business Statistics Class. Journal of Statistics Education, 16 (3).
Sigmon, R.L. (1979). Service-Learning: Three principles. Synergist, 8(1):9-11.
Sperling, R., Wang, V., Kelly, J. and Hritsuk, B. (2003). Does one size fit all?: The challenge of Social cognitive development. Michigan Journal of Community Service Learning, Winter 2003, pp. 5-14.
Thorne, T. and Root, R. (2001)"Community-Based Projects in Applied Statistics: Using Service-Learning to Enhance Student Understanding," The American Statistician, Volume 55, Number 4, Nov 2001, pp. 326-331(6).