TOPIC 7: Technology in Statistics education

Modern technology continues to impact all aspects of our lives. This topic explores how various technologies have changed how students learn statistics, and what the educational possibilities might be for new and emerging technologies. These developments include the innovative use of the internet as a means of widespread distribution of software, learning materials, and data, of new devices that blur the distinction between calculators and computers, and of powerful software tools designed specifically for students. Session topics will explore instructional implementations at various scales, with an emphasis on research that explores the extent and impact on student thinking in technology-rich environments.

---

SESSION 7A: Building and using databases for student analysis

7A1: AT THE INTERSECTION OF STATISTICS AND CULTURALLY RELEVANT PEDAGOGY: POTENTIAL AND POTENTIAL CHALLENGES OF LEARNING STATISTICS THROUGH SOCIAL ACTIVISM

Noel Enyedy, Shiuli Mukhopadhyay, Joshua Danish
University of California – Los Angeles, United States

This paper describes data from the Community Mapping Project (CMP), a set of activities within a summer seminar for high school students. CMP was designed based on the principles of culturally relevant pedagogy to create conditions where students themselves would recognize the relevance of statistics in identifying and describing inequities that face their communities. Using mixed methods we analyzed pre- and post assessments, final projects and process data from video case studies to begin to understand how this learning was organized for the 21 twelfth graders participating in this project. Our qualitative analysis revealed several tensions that emerged between the social justice goals and statistical goals and how those tensions mediated learning. The article may help inform both teachers who wish to rethink their statistics pedagogy, and the designers of culturally relevant curricula.

7A2: TOWARDS STATISTICAL THINKING: MAKING REAL DATA REAL

Robert Gould, Frauke Kreuter, Christina Palmer
University of California – Los Angeles, United States

Although the Statistics Education community has advocated using real data to teach introductory statistics for quite some time, often these data sets are not recognizably real to statisticians since the students’ limited experience with “real” statistical software and data management techniques precludes the use of truly messy data. But grappling with messy and complex data sets is important for teaching Statistical Thinking (broadly defined as “thinking like a statistician”) and is appropriate for an introductory statistics course. We describe our experience collecting rich data sets and developing computer lab assignments using STATA to teach statistical thinking to first-year university students using these data sets. Collecting useable, real, data sets turns out to be fairly difficult for several reasons, and teaching data management and analysis without resorting to rote-based rules is quite challenging.

7A3: TEACHING STATISTICS USING A REAL TIME ONLINE DATABASE CREATED BY STUDENTS

Carl Lee, Felix Famoye
Central Michigan University, United States

The advancement of computer technology creates unlimited opportunities for teaching and learning statistical concepts. A significant impact is the paradigm shift from a passive teaching-centered to an active learning-centered environment. Although one should not make a paradigm shift solely for the sake of technology, there is no doubt that technology will play a crucial role in this transformation. Research has suggested that meaningful learning takes place when students are actively involved in constructing knowledge themselves through their own experiences and active participation. This article proposes an active learning environment for introductory statistics courses using an online real-time database created by students. The experience of implementing the active learning activities using the real-time online database will be shared. Some strengths and weaknesses will be discussed.

7A4: USE OF WEB-BASED PUBLIC DATABASES IN STATISTICS COURSES: EXPERIENCES AND CHALLENGES

Lea Bregar, Irena Ograjenzek, Mojca Bavdaz
University of Ljubljana, Slovenia

During the past decade, national and international organisations have been steadily increasing the number of web-based statistical databases available to general public. While often user-unfriendly (mostly due to poor design and organisation as well as lack of navigation options) in their pioneer years, many of these databases have been gradually transformed into well-managed expansive resources that can greatly enhance the teaching and learning of statistics. A number of illustrative examples are presented in this paper along with discussion of our experiences and identification of future challenges pertaining to their use in statistics courses.

---

SESSION 7B: On-line course and web-based instruction

7B1: WEB-BASED INSTRUCTION FOR STATISTICAL POWER ANALYSIS

Ann A. O’Connell
University of Connecticut, United States
Rosemarie L. Ataya
University of South Florida, United States
Jiarong Zhao
University of Connecticut, United States

Use of the internet to support instruction in general and the use of statistical software in particular provides instructors and students with an opportunity to improve learning while maintaining effective use of limited classroom time. We have developed a Web site (http://power.education.uconn.edu/) that encompasses instruction in power analysis issues and teaches students and others how to use the nQuery Advisor© software to establish sample size for research designs ranging from the simple to the complex. The evaluation results of our Power Project Web site and materials are promising, and the purpose of this paper is to share our approach and materials with other instructors of statistics and research design.

7B2: GIVING AN INTERNET COURSE ON STATISTICS TO ENVIRONMENTAL SCIENTISTS IN EIGHT COUNTRIES

Bryan F.J. Manly
University of Sao Paulo, Brazil
Western EcoSystems Technology, United States

In this paper I describe my experiences teaching a four week internet course on environmental statistics over the internet in 2004. The course was run by an organization called Statistics.com, which provides many statistics courses this way on a regular basis. The course was based on my book on environmental statistics, which the participants had to have. I discuss the preparation of the materials, the workload for participants, coursework, and the assessment process. It seems inevitable that online courses will be more common in the future, provided by private companies, universities, and other organizations. There were some minor problems with providing the course described here, but the format is basically sound for situations where a group of professionals want to learn about a particular topic, but do not have the time to take a regular course.

7B3: WEB SITE AND CONCEPT MAPS TO TEACH STATISTICS

Gloria Icaza, Carlos Bravo, Sergio Guiñez, Julio Muñoz
University of Talca, Chile

We constructed a web site to support service statistic courses at the University of Talca (http://dta.utalca.cl/estadistica/). The web site was developed around two fundamental ideas: object learning and concept maps. The statistical content was structured based on object learning organized around the scientific method. The object learning is imbedded in concept maps which highlight the structure and connections in statistics. Each concept map links complementary information in various formats. Students have positively evaluated the web page. This work was founded by the Education Ministry of Chile, MECESUP TAL0103 project: “Diversification of strategies for teaching and learning in basic sciences” (Diversificación de las estrategias de enseñanza-aprendizaje en las Ciencias Básicas).

7B4: DEVELOPING AND PRESENTING CONCEPTUAL MAPS OF COURSE CONTENT

Rodney Carr
Deakin University, Australia

Teaching online involves providing an environment that is interactive and engaging. A large part of this is providing suitable learning resources. In this talk we will demonstrate an efficient method for producing conceptual maps of the actual course content, showing the structure of the subject for students in a visual way. The structures that result allows for learning resources to be linked in as required. The maps are developed using PowerPoint but they can be deployed in a web-friendly format or on CD-ROM.

---

SESSION 7C: General purpose statistical tools for students

7C1: STUDENTS’ PROBABILISTIC SIMULATION AND MODELING COMPETENCE AFTER A COMPUTER-INTENSIVE ELEMENTARY COURSE IN STATISTICS AND PROBABILITY

Carmen Maxara and Rolf Biehler
University of Kassel, Germany

Modeling and simulation with the software Fathom has become an important part of an introductory course on probability and statistics for future mathematics teachers at our institution. We describe our conception of modeling and simulation competence that students are supposed to acquire. We use various means such as modeling guidelines, simulation plan and a guidebook with examples for simulations to support students’ learning processes. We report on results of empirical studies that made us change and extend our initial educational approach.

7C2: DYNAMIC, INTERACTIVE DOCUMENTS FOR TEACHING STATISTICAL PRACTICE

Deborah Nolan
University of California – Berkeley, United States
Duncan Temple Lang
University of California – Davis, United States

Along with many others, we propose that statistical thinking and literacy are the important elements to teach rather than rules and methods. We propose that this is true for all levels of statistics education. We further argue that we must teach our students how statistics can be used to answer scientific questions and how to connect relevant statistical methods to these questions. We outline an approach that allows authors to create documents describing data analyses and tutorials that combine the description of the analysis with the computations performed along with the thought process. These documents can contain the different branches of exploration which the author pursued, along with the more traditional distilled approach. The document can also contain interactive controls that allow the reader to modify the computations. The documents are thus dynamic (outputs can be recalculated), interactive (controlled by reader) and contain the thought process of the author and also methods for reproducing and exploring the results.

7C3: MEANINGS’ CONSTRUCTION ABOUT SAMPLING DISTRIBUTIONS IN A DYNAMIC STATISTICS ENVIRONMENT

Ernesto Sánchez
CINVESTAV-IPN, México
Santiago Inzunza
Autonomous University of Sinaloa, México

This paper presents an analysis of the meanings of sampling distribution as supplied by some undergraduate students in a dynamic statistics environment (Fathom). The paper identifies stages in the simulation process where multiple and dynamic representations were crucial to students’ understanding of the relationships among sample size, the behavior of sampling distributions and the probabilities of some sample results. One of the foremost difficulties observed in the simulation process was linked to the use of symbolic representations in the software, mainly at the formulation of the population model stage.

7C4: HOW REPRESENTATIONAL MEDIUM AFFECTS THE DATA DISPLAYS STUDENTS MAKE

Anthony Harradine
Prince Alfred College, Australia
Clifford Konold
University of Massachusetts – Amherst, United States

We compare two methods of recording data and making graphic displays: a standard paper-and-pencil technique and a “data-cards” approach in which students record case information on individual cards which they then arrange to make displays. Students using the data cards produced displays that tended to be more complex and informative than displays made by those in the paper-and-pencil group. We explore plausible explanations for this difference by examining structural aspects of the two approaches, such as the saliency of the case and the use of space in organizing the information. Our results call into question the wisdom of the current practice of introducing young students to particular graph types and of the idea that they need to master handling of univariate data before they move on to multivariate data.

---

SESSION 7D: Interactive software targeting specific statistical concepts

7D1: INTERACTIVE SIMULATIONS IN THE TEACHING OF STATISTICS: PROMISE AND PITFALLS

David M. Lane
Rice University, United States
S. Camille Peres
University of Houston – Clear Lake, United States

Research on discovery learning and simulation training are reviewed with the focus on principles relevant to the teaching of statistics. Research indicates that even a well-designed simulation is unlikely to be an effective teaching tool unless students' interaction with it is carefully structured. Asking students to anticipate the results of a simulation before interacting with it appears to be an effective instructional technique. Examples of simulations using this technique from the project Online Statistics Education: An Interactive Multimedia Course of Study (http://psych.rice.edu/online_stat/) are presented.

7D2: INTERACTIVE 3-DIMENSIONAL DIAGRAMS FOR TEACHING MULTIPLE REGRESSION

Doug Stirling
Massey University, New Zealand

Many concepts in simple linear regression can be explained or illustrated on scatterplots. Similar diagrams for regression with two explanatory variables require 3-dimensional scatterplots. Appropriate colouring and dynamic rotation on a computer are needed to effectively show their 3-dimensional nature. Concepts such as multicollinearity, sequential sums of squares and interaction have no analogue in simple linear regression, so it is particularly helpful to illustrate them graphically. This paper gives several examples of concepts in multiple regression that can be illustrated well with 3-dimensional diagrams.

7D3: UNDERSTANDING REPLICATION: CONFIDENCE INTERVALS, P VALUES, AND WHAT’S LIKELY TO HAPPEN NEXT TIME

Geoff Cumming
La Trobe University, Australia

Science loves replication: We conclude an effect is real if we believe replications would also show the effect. It is therefore crucial to understand replication. However, there is strong evidence of severe, widespread misconception about p values and confidence intervals, two of the main statistical tools that guide us in deciding whether an observed effect is real. I propose we teach about replication directly. I describe three approaches: Via confidence intervals (What is the chance the original confidence interval will capture the mean of a repeat of the experiment?); Via p values (Given an initial p value, what is the distribution of p values for replications of the experiment?): and via Peter Killeen’s ‘_prep’, which is the average probability that a replication will give a result in the same direction. In each case I will demonstrate an interactive graphical simulation designed to make the tricky ideas of replication vividly accessible.

7D4: WHAT DOES DRAGGING THIS DO? THE ROLE OF DYNAMICALLY CHANGING DATA AND PARAMETERS IN BUILDING A FOUNDATION FOR STATISTICAL UNDERSTANDING

William Finzer
KCP Technologies, United States

Dynamic manipulation of mathematical objects in a computer-learning environment allows a learner to build an intimate, visceral relationship with those objects. Dynamic manipulation is direct and continuous. Dragging data allows the learner to experience the affect of data change on statistical measures and their visual representations such as the vertical line and the computed value in the plot above. A systematization of the very large set of opportunities for dragging data and the kinds of learning fostered is presented.

---

SESSION 7E: Technology-intensive curricula and instruction

7E1: USING SIMULATION TO TEACH AND LEARN STATISTICS

Beth Chance, Allan Rossman
California Polytechnic State University, United States

Technology, and simulation in particular, can be a very powerful tool in helping students learn statistics, particularly the ideas of long-run patterns and randomness, in a concrete, interactive environment. This talk will provide examples of the integration of simulation to enhance topics throughout an introductory statistics course through a combination of Minitab macros and specifically designed applets. Topics will include randomization tests for comparing groups, and sampling distributions of proportions, odds ratios, and regression coefficients. We will also highlight how simulation can motivate students to learn the more mathematical derivations. Feedback and sample work from students will be presented, as well as issues in designing effective simulation investigations.

7E2: DIFFERENCES IN STUDENTS’ USE OF COMPUTER SIMULATION TOOLS AND REASONING ABOUT EMPIRICAL DATA AND THEORETICAL DISTRIBUTIONS

Robin Rider
East Carolina University, United States
Hollylynne Stohl Lee
North Carolina State University, United States

This paper reports a comparison of two separate studies using the same task and simulation software but with different age groups and abilities of students who have had different curricula experiences. One study examined how middle school students used computer simulation tools to reason between empirical data and theoretical probability. The second study replicated the first with secondary school students who had just completed an Advanced Placement statistics course. This comparison includes the similarities and the differences in the way each group approached the task and used the simulation software, given their background and prior knowledge.

7E3: TEACHING SPATIAL STATISTICAL TECHNIQUES AND CONCEPTS

Richard Castle
The University of Brighton, United Kingdom

The last decade has seen a rapid increase in the use of Geographical Information Systems (GIS) and the analysis of spatial data is an important component of this development. Spatial statistics is a relatively young subject and, although there are useful textbooks on spatial statistics theory, there is virtually no literature on how to teach spatial statistical concepts and techniques. This paper suggests ways of teaching some of spatial statistical analysis without recourse to matrix algebra and vectors. By using the graphical features in Excel it is possible to illustrate and explain the concepts behind the statistical techniques in GIS. The interactive and dynamic features of Excel enable students to investigate the effects of changing the spatial location of the data and to develop an understanding of spatial dependence and its impact on Kriging and regression techniques.

7E4: STATISTICS VISUALIZATION WITH DYNAMIC GEOMETRY

José Alexandre dos Santos Vaz Martins
Instituto Politécnico da Guarda, Portugal

Students from this generation learn best by seeing. Nowadays, visualisation is extremely important to help young students to catch the real meaning of some concepts. Therefore, this paper explores the application of a dynamic geometry software (Cabri-Géomètre II) to illustrate basic statistical concepts (like mean, median and mode), their properties and graphical representation, in a way that allows the teacher to explore, discover and uncover those ideas that will get the messages to students and stimulate interactive work in the classroom. In this presentation a main goal is showing a way to approach statistics through the use of a computational tool, with emphasis in the visual exploration of statistical concepts and focus on the improvement of statistical literacy, reasoning and thinking.

---

SESSION 7F: Principles and theories for the design of learning technologies

7F1: AN ELABORATION OF THE DESIGN CONSTRUCT OF PHENOMENALISATION

Dave Pratt, Ian Jones, Theodosia Prodromou
University of Warwick, United Kingdom

The paper builds on design-research studies in the domain of probability and statistics. The integration of computers into classroom practice has been established as a complex process involving instrumental genesis (Verillon and Rabardel, 1995), whereby students and teachers need to construct potentialities for the tools as well as techniques for using those tools efficiently (Artigue, 2002). The difficulties of instrumental genesis can perhaps be eased by design methodologies that build the needs of the learner into the fabric of the product. We discuss our interpretation of design research methodology, which has over the last decade guided our own research agenda. Through reference to previous and ongoing studies, we argue that design research allows a sensitive phenomenalisation of a mathematical domain that can capture learners’ needs by transforming powerful ideas into situated, meaningful and manipulable phenomena.

7F2: HANDLING COMPLEXITY IN THE DESIGN OF EDUCATIONAL SOFTWARE TOOLS

Clifford Konold
University of Massachusetts – Amherst, United States

Designers of educational software tools inevitably struggle with the issue of complexity. In general, a simple tool will minimize the time needed to learn it at the expense of range of applications. On the other hand, designing a tool to handle a wide range of applications risks overwhelming students. I contrast the decisions we made regarding complexity when we developed DataScope 15 years ago with those we recently made in designing TinkerPlots, and describe how our more recent tack has served to increase student engagement at the same time it helps them see critical connections among display types. More generally, I suggest that in the attempt to not overwhelm students, too many educational environments managed instead to under whelm them and thus serve to stifle rather than foster learning.

7F3: LEARNING CHANCE: LESSONS FROM A LEARNING-AXES AND BRIDGING-TOOLS PERSPECTIVE

Dor Abrahamson
University of California – Berkeley, United States

The paper builds on design-research studies in the domain of probability and statistics conducted in middle-school classrooms. The design, ProbLab (Probability Laboratory), which is part of Wilensky’s ‘Connected Probability’ project, integrates: constructionist projects in traditional media; individual work in the NetLogo modeling-and-simulation environment; and networked participatory simulations in HubNet. An emergent theoretical model, ‘learning axes and bridging tools,’ frames both the design and the data analysis. The model is explicated by discussing a sample episode, in which a student reinvents sampling by connecting ‘local’ and ‘global’ perceptions of a population.

---

SESSION 7G: The role of simulations in Statistics education

7G1: CONSTRUCTING SIMULATIONS TO EXPRESS DEVELOPING STATISTICAL KNOWLEDGE

Lulu Healy
PUC, São Paulo, Brazil

This paper reports on an attempt to involve mathematics teachers, with a limited previous experience in exploring statistical concepts, in the collaborative design of computational tools that can be used for simulating data sets. It explores the constructionist conjecture that the design of such tools will encourage designers as learners to reflect upon the statistical concepts incorporated in the tools under development, since generating data-sets on the basis of different characteristics, such as average, spread, or skewness, necessitates the making explicit of thinking related to these notions and the construction of some sense of random processes. It describes how involvement in the design process involved participants in coming to see distributions as statistical entities, with aggregate properties that indicate how their data is centred and spread.

7G2: USING SIMULATION TO LEARN ABOUT INFERENCE

Tim Erickson
Epistemological Engineering, United States

Many statistics educators use simulation to help students better understand inference. Simulations make the link between statistics and probability explicit through simulating the conditions of the null hypothesis, and then looking at sampling distributions of an appropriate measure. In this paper we review how we use simulation to help understand hypothesis testing, and lay out the relevant steps. We illustrate how using simulation and technology can make these difficult ideas more visible and understandable, through making processes more concrete, through unifying apparently disparate tests, and through letting the learners construct their own measures to study phenomena.

7G3: REGRESSION MODELING IN COMPUTER-SUPPORTED LEARNING ENVIRONMENTS

Joachim Engel
University of Hannover, Germany

We consider the role of technology in learning concepts of modeling univariate functional dependencies. It is argued that simple scatter plot smoothers for univariate regression problems are intuitive concepts that- beyond their intended usefulness in providing a possible answer to more intricate regression problem – may serve as a paradigm for statistical thinking, detecting structure in noisy data. Simulation may play a decisive role in understanding the underlying concepts and acquiring insight into the relationship between structural and random variation.

7G4: USE OF VIRTUAL EXPERIMENTS IN TEACHING DESIGN AND ANALYSIS OF EXPERIMENTS

Paul Darius, Eddie Schrevens
K. Univ. Leuven, Belgium
Kenneth Portier
University of Florida – Gainsville, United States

The ability to design experiments in an appropriate and efficient way is an important skill, but students typically have little opportunity to get experience. Most textbooks introduce standard general-purpose designs, and then proceed with the analysis of data already collected. In this paper we explore a tool for gaining design experience: computer based virtual experiments. These are software environments which mimic a real situation of interest, and invite the user to collect data to answer a research question. The following prototype environments will be described: an industrial process that must be optimized, a greenhouse experiment to compare the effect of different treatments on plant growth, and an arcade style applet that illustrates the use of t-tests, regression and analysis of variance. These environments are parts of a collection called env2exp, and can be freely used over the web. They have been used in several courses over the last two years.