Integrating Statistics and Models Across the Social Sciences Curricula
A research project at Virginia Tech
supported by FIPSE, US Department of Education, under grant #P116B60201

ABSTRACT-- Faculty from the Social Sciences and Computer Science will produce computerized course materials that promote understanding and appreciation of statistics and mathematical models among undergraduate students in the social sciences. Our goal is to integrate statistical methods throughout the curricula, rather than isolate student contact with statistics to one or two courses as is common today. This will help students understand the role of statistics in the evaluation of hypotheses, and help students apply analytical thinking skills to claims of fact presented to them in their everyday lives. We will create an integrated courseware package including significant social science databases, visualization and analysis tools, and multimedia tutorials on statistical techniques and the role of models. The courseware will be flexible in that it will contain data suitable for use in a broad range of courses in the social sciences, and also allow students to import their own data. It will allow instructors to demonstrate particular statistical techniques or use those techniques to present information relevant to that class. Our courseware will also form a vehicle for integrating statistical material across courses within departments, and across departments within the University. The software will be created using Mathematica, a widely used mathematical software system. We will collaborate on this project with Wolfram Research, Inc., the creators of Mathematica. We aim to create an instructional package that will be used throughout the country in a variety of social sciences curricula, initially in geography, psychology and sociology.


Project Narrative

The Problem

Much social science research today involves testing hypotheses through statistical analysis of quantitative data. Thus, understanding and assessing conclusions made in the social sciences requires a familiarity with basic statistical techniques. Social sciences also make extensive use of mathematical models. Unfortunately, most college students reach graduation without a practical understanding of basic statistical techniques and the concept of a mathematical model. They often have little working knowledge of scientific methods. Such basics of statistical and scientific reasoning are not abstract concepts irrelevant to everyday experience. Rather, a misunderstanding of these basics has led to a citizenry that is largely unable to assess the validity of claims of fact presented in statistical form, or purporting to come from mathematical models. Such "facts" appear daily in newspapers, advertisements and political speeches.
Most social science curricula include a course in basic statistics, often as preparation for a course in research methods intended to give the student practical experience in creating and testing scientific hypotheses. The main problem does not seem to us to be in the content or quality of the initial statistics course. Rather, most students see little or no connection between the required statistics course and the rest of their curriculum. Nor do they see any connection between statistics and their ability to be critically analyze information outside the academic setting.

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Goals and Objectives

Our goal is that students understand the role of statistics in the scientific evaluation of hypotheses. We would like students developing hypotheses to know how to apply statistical techniques to evaluate these hypotheses. Likewise, when a student is presented with a statement of "fact," we want the student to be able to test whether that statement is supported by available data.
A coalition of faculty from three Social Sciences departments and the Department of Computer Science at Virginia Tech will produce course materials that promote understanding and appreciation of statistical and mathematical models among undergraduate students taking courses in the social sciences. The integrating concept will be models: what they are, why we use them and the underlying mathematics that drive them. These models will be developed with sufficient depth and flexibility to allow us to integrate statistical methods throughout the social science curricula, rather than isolate student contact with statistics to one or two courses.
The work outlined in this proposal will address some of the most basic problems in the teaching of statistics and quantitative methods to undergraduates in the social sciences. Presentation of statistical material is often concentrated in a single course, where it is detached from the subject matter context in which statistical concepts could be most clearly presented, and seen to be most powerful. Confining this material to one or two courses creates the impression that statistical concepts are somehow detached from the concepts most basic to a discipline, rather than essential components.
This separation is usually caused not by a lack of faculty expertise or interest as much as it is by a lack of effective teaching resources that permit instructors to present statistical material without lengthy digressions from immediate topics. Our effort will create a system with the flexibility to present relevant examples and concepts tailored to the specifics at hand, designed to minimize the effort required to use the package, and maximize flexibility to permit use with a variety of data, both in classroom and in laboratory contexts. By providing these capabilities, we hope that our work will lead to changes in curriculum, such that within courses, statistical material will be more effectively integrated with subject matter issues, that within departments, statistical concepts can be presented in a wider variety of courses, and within the university, that there will be greater collaboration among faculty in different disciplines. Virginia Tech is not unusual in its desire to become more cost effective through reducing redundancy in courses. By increasing cross-disciplinary collaboration, this project will help in such efforts.

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Potential Impact and Significance

By targeting the mathematical content of courses in the social sciences, we have a unique opportunity to greatly influence the understanding of mathematical models by a broad population of students. Social science courses, at all levels of the curriculum, naturally touch upon many models of complex systems. However, traditionally these courses have not stressed the importance of models, or quantitative aspects in general. One reason is that traditional classroom settings do not make it easy for students to interactively manipulate quantitative data. Fortunately, modern instructional technology provides an opportunity to provide sophisticated presentations of models and analysis techniques through interactive simulations and visualizations, multimedia presentations, use of computers to illustrate dynamic processes during lecture, and desktop publishing of new course materials.

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Procedure and Methods

The Project-- Our efforts will focus on creating an integrated software package including tutorials, visualization and statistical analysis tools, and supporting course materials. The system will be organized around two major databases and a selection of smaller databases that together contain data relevant to all of the social sciences involved. One database will be the General Social Survey (GSS), an annual survey of individuals which includes demographics (race, marital status, age, occupation, etc.) and hundreds of other items related to attitudes and behavior. The second database will be derived from Census Bureau information, including the 1990 census and the most recent City/County Data Book, which provides aggregate data at the county level for the United States. Finally, quasi-experimental and experimental databases will be selected from the Inter-University Consortium for Political and Social Science. Together, these databases provide a resource broad and deep enough to allow students to perform interesting class assignments, gain experience and confidence with research methods, and simply explore data to satisfy their own curiosity. In addition, we will provide support for students entering, analyzing and visualizing their own databases.
We will create multimedia tutorials that teach the statistical techniques and modeling issues relevant to most social sciences curricula. Students can be introduced to the database in one course, and subsequently build on their understanding to do more sophisticated analysis in later courses. For example, students in introductory courses may focus on what the database tells us about the behavior of people, while students in a research methods class might focus on choices of statistical techniques. The interdisciplinary character of the development team will promote greater collaboration and co-ordination between the curricula of the several departments, and lead to reinforcement of concepts.
Our instructional system must integrate three components. The database component will be derived from the various databases listed above, edited and reformatted as appropriate. The second component is an analysis system which allows flexible access to the databases, a wide range of statistical analysis on the selected data, and visualization of the results of the analysis. The third component is a multimedia tutorial on statistical techniques and the role of models. In addition, our project will produce a set of manuals, instructional aids and classroom exercises to support the software.
Our intention is for the courseware to be flexible and applicable in a number of instructional settings. In particular, it will not be a monolithic instructional course. Instead, students will be able to use the system to learn about and a apply a particular statistical function or analysis technique. Users will be able to apply the visualization tools to solve their particular problems. Instructors will be able to use the courseware to illustrate a particular point in class, or assign a small project using the courseware even if they choose not to make it a central part of the class.

The Role of Mathematica-- To create the system we envision, we must be able to integrate the three components of database, analysis and visualization tools, and online instructional material. We have considered implementing the entire system from scratch (actually, built on our existing software libraries created as part of Project GeoSim) [GIL94, GeoSim]. However, this would require re-implementing standard statistical analysis functions and an instructional presentation package. An alternative is to base the system on an existing statistical package such as SPSS or SAS. Unfortunately, these systems are rather inflexible outside their domain of statistical analysis, and have inadequate support for instructional presentations. Tutorial material could be created in a separate authoring system such as Authorware, but this leads to two major difficulties regarding integration. First, the students must alternate between the tutorial presentation and the analysis package: the two modes cannot be combined because the software supporting these two parts of the system does not allow it. Second, the programming team must keep the content of two separate systems synchronized during development, which is difficult if there is no connection supported by the development software. A more manageable approach, and the one we propose, is to use a package that provides a good compromise regarding ability to support all of the components required by our project.
Our solution is to base our project on the widely used Mathematica system from Wolfram Research, Inc [Wolf91]. Mathematica contains all of the necessary statistical analysis functions, and has excellent support for graphics. Since it includes a complete programming language, we can implement the database processing portions of the system directly within Mathematica. The system is also flexible enough to support programming of the visualization techniques described in the next section. Mathematica incorporates an interface for instructional material, called a "notebook." Notebooks provide a hierarchical organization of instructional material so that students can begin with a table of contents and expand those sections of interest. The statistical analysis functions are incorporated directly into the instructional presentation, so that students can examine the abilities of the techniques on actual data sets in a controlled manner. The interface will be designed so that students need no prior knowledge of Mathematica to use our courseware.
Finally, the resulting courseware will be able to run on all platforms supported by Mathematica, including MS-Windows, MacOS and UNIX.

The Role of Visualization-- Most statistical techniques, while implemented as mathematical formulae, have simple, intuitive interpretations. However, developing that intuition often requires that the technique be expressed in a visual manner. Likewise, relationships in data such as correlation and regression are often best spotted by humans through appropriate visualization techniques. Over the past few decades, visualization techniques for statistics have become increasingly important to scientists. The work of pioneers such as Tukey, Cleveland and Tufte [Tukey77, Cleve93, Tufte83] has been combined with the rise of computer graphics capabilities, resulting in many high-end scientific visualization systems. We believe it is time to harness the best of this technology for use in education. Note that this does not necessarily mean that sophisticated computational facilities is required. Charts, scatter plots and special purpose techniques such as the creative use of Venn Diagrams to visualize the concept of correlation [KB94] are popular. They convey the statistical concepts to the students, as well as forming analysis tools in their own right.
As an example of the power of visualization in statistical instruction, consider a small number of outliers which result in a Pearson correlation coefficient that differs appreciably in magnitude or even in sign from Spearman's rho for the rank order relationship for the same data. Understanding each of these measures of association and choosing between them is facilitated by scatter diagrams showing raw scores and ranks in which students see for themselves how Pearson's r may be affected by outliers and how Spearman's rho fails to distinguish between trivial and substantial difference between adjacent pairs of scores. Through such visualization, students will gain the experience needed to make informed choices when doing analyses for their own projects.
Effective visualization techniques are also important to allow understanding of data relationships within large, complex databases such as the GSS and Census databases to be incorporated in this project. Each of these databases contain thousands of records with hundreds of variables per record. We intend to take advantage of advanced visualization techniques that are becoming standard practice within the research community, but which are not now commonly used at the undergraduate level.
As part of our work for Project GeoSim, we developed a data browser for a county information database [Hines95]. This has given us experience with visualization techniques appropriate for the proposed project. To illustrate such techniques, we present three "views" for county data in Figures 1 to 3.

Figure 1: Visualization of spatial data via a map view.

Figure 1 shows a map view. The left side shows a map of the entire U.S. The right side shows an expanded view for a part of the country selected by the user. Counties are shown colored based on the quintile of the value or rank of the county under some variable (either a raw variable stored in the database, or a derived quantity). The map view provides a basis for understanding spatial effects.

Figure 2: Visualization of data distribution via a graph view.

Figure 2 shows a graph plotting the distribution of the same variable. This display illustrates distribution effects that may not be clear under the map view. Effects of distribution on statistical relationships are an important concept for the student to learn.
Figure 3 shows a spreadsheet view, which helps the user browse multiple variables for a record. Figure 4 illustrates the advanced visualization technique called "parallel coordinates," [Ward94] which allows for visualization of relationships such as correlation among multiple variables in a large database. Each column corresponds to a variable, sorted by value. The lines link the position of a particular record among the columns. The visual pattern presented by the lines provides information regarding correlation or reverse correlation. For example, to the extent that the lines show few intersections between two columns, there is visual indication that the variables positively correlated.

Figure 3: Visualization of multiple variablesvia a spreadsheetview.

Figure 4: The visualization technique known as "parallel coordinates." Variables A, B and C appear correlated, as shown by few intersections. Variables C and D appear inversely correlated, as shown by many intersections near the same point. Variables D and E show little correlation.

Alternatives-- There currently exist many systems for doing basic statistics, many easily understandable by undergraduates. Examples include SAS, SPSS, Stata and Statistica. While good at what they do (namely, allow for statistical calculation), they are not well suited for instructional presentation or visualization of large databases. There also exist special purpose systems for examining databases such as the 1990 Census or the GSS. There even exist computerized tutorials meant to teach basic statistical techniques. However, there is no comprehensive, integrated software package that combines significant and relevant social science databases with strong statistical processing power and advanced data visualization techniques suitable for classroom use at the undergraduate level. We will provide such a package, closely integrated with computer tutorials on statistical techniques and classroom exercises.

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Impact on Selected Curricula

This section comments on how the proposed software would be used in the three social sciences departments represented by the Principal Investigators of this proposal. It also serves to point out how the departments differ in their approaches to data analysis in particular and research methods in general.

Sociology-- In Sociology, research methods rely heavily on survey work and post hoc analysis. Students need the ability to compare data and find correlations. The result of their analysis is often descriptive in nature. Sociologist work with both group and individual differences. While the GSS data are directly relevant to Sociologists, the Census database will also prove to be a value resource.
Our Sociology faculty are presently reviewing whether to increase the number of credit hours for our Sociological Research Methods course from 3 to 4. We realize that the sheer volume of material covered in that course requires more time and effort than normally associated with 3-hour courses. The proposed courseware can further strengthen the Research Methods course. It will also allow us to place the Research Methods course earlier in the curriculum since the material will be easier for students to comprehend. In this way, students will gain familiarity with both the courseware and the research methods earlier, allowing us to use these techniques more fully in later classes.
Numerous courses in Sociology lend themselves to adoption of the proposed courseware. At the undergraduate level these courses include the following.

Psychology-- In contrast to Sociology, research methods in Psychology tend to be experimental or explanatory in nature. The approach is generally to form a hypothesis and then design a study or search a database to determine the validity of the hypothesis. Psychological research also tends to focus on individual differences. Both the GSS and Census databases will be useful to some degree to Psychology students. However, more than for the other departments, students and instructors will need the ability to enter their own databases, or use the specialized experimental and quasi-experimental databases provided with the courseware.
Two recurring problems with psychology majors is that many have little understanding of the relationship between psychological research and statistics, and are not readily able to apply statistical principles to research problems. One reason is that the required statistics and research methods courses are not formally integrated when students take these courses in their Sophomore year. Instead, students are expected to integrate and apply statistics and research methods when they take the senior-level psychology courses that require completion of a research project.
The courseware will allow instructors to actively reinforce the understanding of statistics and research methods in the content courses taken prior to the senior-level courses. Instructors will be able to simultaneously demonstrate the relationship between statistics and research methods. Instructors can enter data sets of their choosing to compliment the content areas covered in lecture. In doing so, instructors can increase understanding and retention of statistics and research methods, and better prepare students for the senior-level application courses. When our majors reach their senior-level research courses, they will already be able to use the courseware to visualize and analyze their data.
Some relevant courses in Psychology include:

Geography-- Statistical practice in Geography tends to concentrate on post hoc approaches to data analysis. Thus, a student or researcher will wish to search a database to reveal interrelationships among variables. In contrast to Sociology and Psychology, analysis in Geography often concentrates on aggregate data. The US Census database is clearly ideal for study by Geography students.
Our Geography faculty has a long-standing commitment to teach statistical applications throughout its curriculum. Geography majors are required to take the statistics course in social science applications offered by the statistics department. Unlike the other departments, Geography majors do not take a separate Geography course devoted to statistical research methods. Distributing research methods topics throughout the Geography curriculum has been slowed by the absence of a convenient, flexible vehicle for presenting this material in a variety of formats, by faculty with differing interests and perspectives. The proposed courseware will address this problem.
While statistical topics are applicable to most Geography courses, the following provide good examples.

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Institution and Investigators' Background

This proposal was created by a team of faculty from four separate departments. Together, we have extensive expertise in developing and evaluating educational software, a variety of quantitative methods in the Social Sciences, and educational outcome evaluation. Cliff Shaffer was Project Director for Project GeoSim, jointly sponsored by FIPSE and NSF and winner of an Ames Undergraduate Computational Science Education Award. GeoSim consists of several simulations and tutorials for use in introductory geography classes. John Carroll is a widely known expert in Human Computer Interaction, with extensive experience designing and evaluating help and instructional systems. Jim Campbell, Neil Hauenstein and Bradley Hertel represent discipline-specific expertise in Geography, Psychology and Sociology, respectively. They each have extensive experience with teaching quantitative methods and research skills in the social sciences. In addition, Dr. Hauenstein has experience with academic outcome assessment and evaluation of intervention projects in the private sector.
Virginia Tech is currently in the third year of a four year initiative to provide all our faculty with personal computers suitable for a wide range of multimedia and instructional technology. Another part of this initiative is a major effort to install computers and the necessary projection equipment in all classrooms to support CAE presentations. Already, five classrooms have been converted into special labs where each student has a computer at his or her desk to allow for interactive educational exercises. Thus, Virginia Tech has a demonstrated, continuing commitment to computer aided instructional technology.
Wolfram Research, Inc. (WRI), the creators of Mathematica, have agreed to provide considerable support for this project. Their personnel will provide expert assistance as we design and program the system. They will also provide summer internships for our personnel at their facilities in Champaign, IL. This will allow for increased collaboration between Virginia Tech and WRI. WRI will also aid in project dissemination (see below).

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Statistical Content

We currently plan for the following statistical content to be included in the system.

  1. Levels of data and central tendency
  2. Dispersion and distributional characteristics
  3. Sampling
  4. Drawing inferences about two means
  5. Testing for significant relationship between and among categorical variables
  6. Analyzing strength of association between categorical and ordinal variables
  7. Analysis of variance: analyzing relationship between and among ordinal or continuous dependent variables and dichotomous or categorical independent variables
  8. Bivariate regression and correlation
  9. Multiple regression analysis

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For this project we need to evaluate both the "usability" of the software and also its "learning efficacy" [CR]. With respect to usability, the software must convey and facilitate tasks and operations that the user wants to accomplish; it must provide appropriate feedback; it must evoke and sustain the user's motivation, it must support error recognition, diagnosis and recovery. With respect to learning efficacy, the experience of using the software must effectively guide problem-solving and learning. Software can be attractive, pleasant, and productive but fail to stimulate effective learning and retention. Conversely, it can incorporate good educational content and yet be too difficult or unpleasant to use.
Scriven's monograph on curriculum evaluation emphasized the contrast between pay-off and intrinsic evaluation [Scri67]. Measuring task times and error rates are examples of pay-off evaluation. Enumerating and analyzing the design features of a tutorial package would be an intrinsic evaluation. Scriven observed that pay-off evaluation often produces solid facts with indeterminate causal interpretations. Intrinsic evaluation produces detailed interpretations of features, rationale, and tradeoffs but often with little empirical grounding. Scriven urged that the two approaches be combined: intrinsic evaluation can guide the detailing of pay-off evaluation plans and the interpretation of results [CR].
Scriven's monograph also originated the distinction between summative and formative evaluation. Summative evaluation seeks to gauge a design result, while formative evaluation seeks to identify aspects of a design that can be improved. These three distinctions (usability/learning efficacy, formative/summative evaluation, pay-off/intrinsic evaluation) define a comprehensive evaluation space for instructional software. Our evaluation plan attempts to address this entire space.

Formative evaluation-- The first phase of evaluation involves documenting and guiding development of the project from the perspective of users. Our approach will integrate intrinsic and pay-off methods, in a style Scriven called "mediated" evaluation [Scri76]. We have employed this approach to formative evaluation in prior instructional development projects [CSR].
Intrinsic evaluation. As the databases and software tools are developed, we will create and maintain an explicit design rationale for the system [MC96]. We will enumerate the typical and critical tasks and scenarios to be supported by the system for students and instructors, for example, the what-if scenario in which a student has worked through an analysis project using an installed data set and wishes to edit the data set and repeat that analysis. We will analyze the potential user consequences for key system features and relationships within each scenario context. For example, allowing learner-initiated what-if explorations enhances motivation and depth of cognitive processing, but also increases the variety and severity of errors (which in turn complicates the tutorial and help-system).
This design rationale is our intrinsic evaluation and will serve as a formative planning aid, helping to keep considerations of usability and learning efficacy in view from the very inception of the work. For example, the what-if scenario mentioned above suggests that users be able to run two (or more) analyses at once to compare results.
Pay-off evaluation. We will also use the design rationale to guide and interpret pay-off formative evaluations. For example, classifying a sequence of learner actions as an instance of what-if exploration will engage our analysis of that type of scenario in interpreting the observed events. Later in the project, the design rationale will be used as an issue base to create summative pay-off evaluations that comprehensively assess the key design features and usage scenarios of our software [CR].
Our main pay-off evaluation method in the formative evaluation phase will be thinking-aloud [NS72]. This method consists of systematic, non-directive prompting during learning activities to encourage learners to articulate their plans and concerns while these are still actively being pursued, and to clarify the basis for specific actions they undertake. We have extensive experience with this approach to formative evaluation.

Summative Evaluation-- A large part of the summative pay-off evaluation will involve assessments of students and faculty using the courseware. The evaluation criteria for this phase of the project can be classified into immediate and long-term measures. Immediate criteria refer to those evaluations occurring during or shortly after use of the courseware. Long-term criteria refer to measures collected one or more years after implementation.

Immediate Criteria-- Reaction Measures. Reaction criteria are used to assess attitudes about the learning intervention [Gold]. Two types of reaction measures will be developed. First, general reaction measures will be developed to assess both student and faculty attitudes about the classes using the courseware. Data will be collected on these general reaction measures both before (baseline) and after (post-intervention) the courseware is implemented. The comparison between baseline and post-intervention general reactions will indicate the effect that the courseware had on general beliefs about the course, student satisfaction when taking the courses using the courseware, and faculty satisfaction about using the courseware.
Second, specific reaction questionnaires will be developed to measure both student and faculty attitudes about the courseware. Responses to specific reaction questionnaires will be collected only in classes using the courseware. The focus of these specific reaction questionnaires will be satisfaction levels associated with specific features of the courseware. These data can be used as formative measures to assist with decisions about modifications to the courseware after initial implementation.
Learning Measures. Learning criteria are used to assess the extent to which students acquire the learning objectives targeted by the intervention. Such criteria must be objective and quantifiable indicants of learning. The learning criterion developed for this project will be a content-valid standardized achievement test designed to measure knowledge of the statistical principles fundamental to the behavioral sciences. This test will be designed to be used across all social science disciplines involved in the project. Prior to implementation of the courseware, baseline knowledge data will be collected by administering the test in classes targeted for future use of the courseware.
In subsequent semesters, post-intervention performance on the statistical principles test will be collected in classes using the courseware. Comparisons of baseline knowledge to post-intervention knowledge will indicate the extent to which the courseware affected initial learning of statistical principles.

Long-Term Criteria-- The completion of a long-term evaluation of the courseware is not possible under the proposed three year schedule. Nonetheless, baseline data necessary for a long-term evaluation of the courseware will be collected with intention of completing the evaluation after the FIPSE grant expires.
Retention Measures. Ultimately, a major goal of the courseware is to increase the statistical sophistication of behavioral science graduates. In order to assess our success on this goal, the retention of the statistical knowledge of graduating seniors will be measured both before and after implementation of the courseware. Statistical knowledge will be measured using an alternative form of the statistical knowledge test described above. During the time the courseware is being developed and implemented, baseline data will be collected from graduating seniors who have not used the proposed courseware.
Two years after implementation of the courseware, post-intervention performance of graduating seniors will be assessed. If post-intervention performance is better than baseline performance, then this suggests the courseware was helpful in increasing the statistical sophistication of behavioral science graduates.
Curriculum Revision. A second major goal of the courseware is to affect the behavioral science curricula. To assess this goal, post-intervention modifications to departmental curricula requirements will be monitored. Interviews will be conducted with the relevant faculty to determine the role of the courseware in stimulating any curricula revisions. Also, baseline syllabi will be collected from courses targeted for implementation of the courseware. These baseline syllabi will be compared (within instructor) to syllabi used after implementation of the courseware. Instructors who modify their syllabi after implementation of the courseware will be interviewed to determine the effect of the proposed courseware on course revisions.

Independent Evaluation-- To insure that our materials are applicable to a wider audience than Virginia Tech, and to serve as an independent check on our summative evaluation, we will recruit members of the corresponding Social Science departments at nearby Radford University. Radford is primarily a four-year, teaching-oriented University, and so provides some diversity to contrast with Virginia Tech. We successfully worked with faculty at Radford during Project GeoSim. While the details have not been completed, we include a letter from one faculty member to show that we have begun the process. A part of our budget is allocated to support Radford faculty.

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Dissemination of Results

The software resulting from this project will be available via the Internet, both from our site and from MathSource, WRI's Internet distribution for Mathematica related software. WRI has also agreed to distribute the software as part of MathSource on CD-ROM. The software will be demonstrated at a variety of conferences, including discipline specific conferences and meetings on educational technology.
Based on our successful experience with disseminating Project GeoSim software, we believe that we have a demonstrated ability both to produce software of value to a wide educational community, and to distribute it effectively.

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Fall 1996

Spring 1997

Summer 1997

Fall 1997

Spring 1998

Summer 1998

Fall 1998

Spring 1999

Summer 1999

Continuing after grant

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[CR] J.M. Carroll and M.B. Rosson, Managing evaluation goals for training, to appear in Communications of the ACM, July 1995.
[CSR] J.M. Carroll, M.K. Singley and M.B. Rosson, Toward an architecture for instructional evaluation in Proceedings of the 1991 International Conference on the Learning Sciences, L. Birnbaum, Ed., Association for the Advancement of Computing in Education, Charlottesville VA, 1991, 85-90.
[GeoSim] L.W. Carstensen, Jr., C.A. Shaffer, R.W. Morrill and E.A. Fox, GeoSim: A GIS-based simulation laboratory for introductory geography, Journal of Geography 92, 5(Sep/Oct 1993), 217-222.
[Cleve93] William S. Cleveland, Visualizing Data, AT&T Bell Laboratories, Murray Hill, NJ, 1993.
[Gold] I.L. Goldstein, Training in Organizations, Brooks/Cole Publishing, Pacific Grove CA.
[GIL94] D.T. Hines, J.M.A. Begole, C.A. Klipsch and C.A. Shaffer, The GeoSim Interface Library (GIL): Programmer's Manual, Computer Science TR 94-31, VPI\&SU, December 1994.
[Hines95] D.T. Hines, Computerized Simulations for Geography Instruction: Sense of Place, Master's Project Report, Virginia Tech, Blacksburg VA, 1995.
[KB94] D. Knoke and G.W. Bohrnstedt, Statistics for Social Data Analysis, 3rd Ed., F.E. Peacock, Itasca IL, 1994.
[MC96] T.P. Moran and J.M. Carroll, Design Rationale: Concepts, Techniques, and Use, Lawrence Erlbaum Associates, Hillsdale, New Jersey, 1996.
[NS72] A. Newell and H.A. Simon, Human problem solving, Prentice-Hall, Englewood Cliffs, New Jersey, 1972.
[Scri67] M. Scriven, The methodology of evaluation, in Perspectives of curriculum evaluation, R. Tyler, R. Gagne and M. Scriven, Eds. Rand McNally, Chicago, 1967, pp. 39-83.
[Tukey77] John W. Tukey, Exploratory Data Analysis, Addison-Wesley, Reading, MA, 1977.
[Tufte83] E.R. Tufte, The Visual Display of Quantitative Information, Graphics Press, Cheshire CT, 1983.
[Ward94] M.O. Ward, XmdvTool: Integrating Multiple Methods for Visualizing Multivariate Data, in Proceedings of Visualization'94, Washington, DC, October 1994, 326-333.
[Wolf91] S. Wolfram, Mathematica: A System for Doing Mathematics by Computer, 2nd Edition, Addison-Wesley, 1991.

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Table of Goals



Improve statistical comprehension of students Compare baseline studies to outcomes using learning measures
Greater retention of statistical knowledge Compare graduating students in current courses to graduating students in revised courses on retention measures
Improve students' ability to apply statistical concepts to practical problems in their disciplines Actual classroom exercises combined with testing as part of summative evaluation of learning measures
Improve integration of statistical content throughout curriculum Analyze syllabi and interview faculty before and after for integration
Reduce duplication in courses Analyze syllabi and interview faculty regarding duplication
Produce materials that will prove valuable to other Universities Conduct evaluation procedures at Radford University

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