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Embedding web applications into a learning process for courses in quantitative methods and economics.


Teaching quantitative courses such as Management Sciences, Statistics or Economics, in colleges and universities requires not only passing the knowledge of the subject to students, but also applying the right pedagogy such that students can better learn through experimentations of the models. This form of engagement creates self-motivation and leads to enhanced 'exploration' of the course contents (Pidd, 1997).

Traditionally, the application of mathematical modeling in learning is based on static resources such as textbooks, pictures and graphs, calculators, and even pencil and paper, to assist learners in locating and further processing of the information imbedded in analytical formulations. However, in the environment where learners have to construct a mental representation that accurately represents the content depicted in the model, most learners do not actively participate in this process adequately. Although this pedagogy has been successful in many ways, developments in computer information systems allow for a dynamic learning environment and should be included as part of the resources or tools that can be used to assist in learning complex abstract models. Thus, respective learning tools, including those accessible online, have a unique motivating effect that helps learners assume a new role as initiative takers (Gries & Gries, 2001).

With the advent of information technology, the availability of resources and cognitive tools has exploded. Students are increasingly exposed to an array of sophisticated learning resources and technology tools such as hypertexts, streaming video, and visualization tools. Thus, in today's digital age saturated with multi-media environments, students pay less and less attention to the printed form, which looks to them too archaic. New technologies are impacting student behavior and even learning styles to the extent that it affects their attention span in a classroom. Therefore, the way learners interact with resources is changing qualitatively, and the success of their learning is increasingly dependent on how effectively they utilize diverse resources, which has been noticed in previous, early studies (Hill & Hannafin, 2001; Nesbit & Winne, 2003).

Providing an interactive platform to involve students in learning abstract concepts related by formulas and functions is an important part of teaching courses in quantitative methods and economics. Typical subjects that can benefit from interactive technologies are linear programming, queuing (waiting line) models, decision analysis, statistics and regression analysis, forecasting and many other topics that are important components in the business curriculum.

Most quantitative concepts can be interactively modeled to allow for observational studies conducted by the user (student) under different sets of constraints. One example of such approach is the use of online games. The objective of this research is primarily creating a web learning platform but also to define and measure processes of an interdisciplinary project with common objectives.

In this study, the authors discuss a simple web based interactive platform for specific topics in quantitative methods and economics courses in business curriculum, and report on the interdisciplinary effort to implement such platform.


Only a few quantitative business courses take advantage of the Internet for interactive learning of mathematical concepts and applications, and the literature on this subject is almost non-existent despite a rapid increase in educational content of the Internet. Institutions are placing more course materials on-line to supplement and sometimes even replace classroom instructions altogether. In addition, recognizing potential new marketing opportunities, universities are placing entire college degrees on the web to attract new students from around the world (University of California at Berkeley, 2011).

Already over a decade ago Hamalainen et al. (1996) and Robin & McNeil (1997) pointed out that education had the potential to be the key application in electronic commerce. However, they warned that new technology alone would not make these new web-based tutorials and learning modules more effective, forecasting that we can expect only marginal improvements in student performance if web developers continue to re-implement traditional and conventional models borrowed from the classroom. Their prediction was based on a review of the offerings of web-based educational content that were mostly tutorials that passively transmitted information or data. By itself, more technology will not make education more efficient. Other authors (e.g., Wolfe, 2001) supported this view, calling for new innovation modules of production, presentation and delivery that would take advantage of the Internet's power that emphasize the capability of the learners to participate.

According to some researchers (e.g., Janicki & Liegle, 2001), "the current web-based educational tutorials are generally poor in educational content", especially in usage of interactive media. As Murray (1996) pointed out: "Over a decade ago, the World Wide Web was a relatively new technology and the early adopters were individuals skilled in programming and HTML, but not necessarily knowledgeable about educational concepts." Most educators have never had a course in learning theory and as a result their web-based offerings are lacking in real content based on such theories (Murray, 1996).

On the other hand, complicating the issue of effective web-based training material is that those professionals who are experts in learning theories (traditional teachers) often lack the technical skills to implement a web-based course. It has been noticed long ago (Bork, 1986) that many of the computerized educational offerings provide poor learning opportunities, as they are merely the "translation" of books and lectures into an electronic format. Schank (1993) complained that the offerings were not very good, and added that there is a need for these modules to be based more on learning concepts. His viewpoint is that many of the tutorials on the web were analogous to simply "turning the pages" in a textbook. He noted that the reason that learning modules have not achieved their full educational potential is that information is not learning and that many of these systems present information and data, and do not necessarily teach.

Another problem of web offerings is the cost and time of development, because each offering is generally an independent effort. The developer must start from scratch at significant cost and skills. Hansen (2008) presents a research at how online learning contributes to the goal of preparing students for professional jobs that offer little or no opportunity for training by facilitating the process of knowledge transfer. Although he did not specifically look at interactivity of material online to assist learning of quantitative concepts, the results indicate the usefulness of online courses in Principles of Marketing for developing skills leading to the application of classroom knowledge to real projects (Ping, 2007).

Currently existing are authoring systems that provide a limited set of templates for developers. Examples are WebCT, ANGEL, ToolBook, Director, AuthorWare and TopClass. These tools provide significant file management and some limited HTML assistance so that an average educator can create web-based course content without the need for a deeper knowledge of the underlying technology. However, a major weakness of these systems is that they do not provide assistance to a developer to create learning content based on learning principles or pedagogy.

A variety of Internet-mediated simulation games have emerged during the course of the past years. At this point, however, the uses at academic institutions of gaming simulations that are run completely over the web seem very few. Overby et al. (2000) reviewed the file transfer wit computer simulation software, which is then run on a stand-alone PC. Dessouky et al. (2001) discussed a methodology for developing a web-based factory simulator for manufacturing education. More recently, Mak and Palia (2005) discussed collaborative virtual environments, such as online forum and chats, and 3D Multi-User Virtual Environment, for learning and potential of integration with business simulation systems and games to provide a task oriented approach system for teaching and learning.

There are several offers from software vendors, which fit well into the business market. One example of a game that uses the Internet for uploading decisions and downloading results is the Capsim Business Simulation (2010). The game is categorized as a PC and web-oriented game. Another example of such game is the Stock Market Game--SMG (SIMFA, 2010) being used for students in grades 4 to 12 as well as postsecondary students. The SMG is now available on the web and is sponsored by the Securities Industry Foundation for Economic Education.

One important observation is that the performance of students in online courses decreases when it contains technical information. Face-to-face courses were found to be superior for learning technical information such as statistics (Kartha, 2006). Similarly, Anstine and Skidmore (2005) found that after adjusting for course selection factors among students the learning results obtained in online courses in economics were inferior to that of traditional courses, providing support for the idea that online delivery may be less successful for technical or quantitative courses. Mixed findings in this regard are reported recently by Sendag and Odabasi (2009)


To accomplish the goals of web-based interactive labs outlined in previous sections we need to build an educational model of the web-based course delivery system. In the network view, the system consists of the following three components as presented in Fig. 1 below:

* a server providing interactive examples (models) to illustrate educational concepts;

* courses at remote sites that incorporate these interactive models in the course materials and allow web-based access;

* student clients (equipped with laptops, workstations, mobile phones, etc.), who are taking respective courses, which incorporate specific interactive models.


The interactive models are built into a server controlled by the developer, who is at the same time the service provider. Particular instructors who teach web-based courses decide, which specific models they want to use in these courses. There is no restriction on who can incorporate what model into which course--it's all under control of an instructor, just like textbook selection and a choice of other course materials, some of which may be local to the course. Students can use any computer with Internet connection to access any of the interactive models, but they have to comply with a particular course Instructor's ruling, for which exercise they will get credit. This model combines instructional design concepts from the educational and instructional technology fields with those of the information systems and web-based design research. The logical operation of the web-based course delivery system is illustrated in Figure 2. The server provides a number of examples illustrating specific applications of quantitative models from a number of theories used in business courses, such as: linear programming, queuing theory, Bayesian networks, linear regression, etc. It has a number of characteristics, which determine its properties from the perspective of a user: access level (student, instructor, developer), access scheduling, reporting, sound, animation, etc.

The course website is under the control of instructor and can be used in a number of typical quantitative methods courses, such as Statistics, Management Science, Operations Management, Quality Control, Project Management, Economics, etc. It is up to the Instructor, to select specific models from the server to fit best his course needs, and assign to the students to enhance the learning process. The characteristics of the course website, related to the services, may include:

* modules/models selection

* variables choices

* time frame for running the model

* due dates

* quizzes and tests

* other constraints.

Students review material in real time and learn important concepts through interaction and graphical display of information, graphs, and video based lesson instructions.



Typical examples of interactive exercises that can be used in any Quantitative Methods course or in an Economics course, or even in an Econometrics course, are outlined in the sections below.

Economics--Illustrating Concepts with a Quadratic Equation Solver

Any course in Economics must teach simple models of the behavior of economic variables and their functional relationships, interactions and dynamics. The simplest models in use for the basic economic variables, such as supply and demand, are linear or quadratic. Thus, it makes sense to develop interactive exercises even for these models illustrated by simple formulas.

Sample Problem #1.

For a certain product whose price p (p > 0) depends on one hand on the demanded quantity q (q > 0) according to a linear demand equation:

p = a * q + b

where a<0; and on the other hand on the supplied quantity according to a non-linear

supply equation, for example:

p = square_root(b + q)

one can calculate a market equilibrium according to the quadratic equation:

[a.sup.2] * [q.sup.2] + (2*a*b--1) + ([b.sup.2] - b) = 0


Illustrating these concepts interactively would provide a great value to the student, specially if some additional notions, such as interception points or area under the curve can be interpreted in economic terms. A sample user interface for such calculator is presented in Figure 3, and the actual website to play with it is available at this link:

Quantitative Methods--Illustration of Linear Programming

Linear Programming is a typical topic in quantitative course theory students have to conceptually grasp before moving to more advanced concepts. Multiple business and economic problems can be expressed as a set of linear equations of inequalities. Linear algebra is normally a prerequisite for this topic, but interactive examples and exercises can significantly help in understanding most of the problems.

Sample Problem #2.

Frames Inc., a small manufacturer of sports equipment and supplies, wants to determine the number of baseball bats to produce in order to maximize profit over the next season. Constraints affecting production quantities are the production capacities in four departments: cutting, turning/trimming, finishing/inspection, and packaging. For the 8 weeks season, 630 square feet of cutting area, 600 hours of turning and trimming hours, 708 hours for inspection and packaging, and 135 pounds of packing material are available.

For the following notation: B = number of standard bats C = number of professional grade bats Z = total profit and the total profit contribution $6 for a standard bat and $9 for a professional bat, the profit contribution function is given by

Z = 6*B + 9*C.

We want to maximize the contribution function, therefore we are looking for max (Z = 6*B + 9*C)

subject to the following production constraints:

7/10 * B + 1 * C [less than or equal to] 630 CUTTING AREA in squared feet)

1/2 * B + 5/6 * C [less than or equal to] 600 TURNING AND TRIMMING (in hours)

1 * B + 2/3 * C [less than or equal to] 708 INSPECTION AND PACKAGING (in hours)

1/10 * B + 1/4 * [less than or equal to] < 135 PACKING MATERIAL (in pounds) B, C > 0

A sample illustration how variables B and C can be connected using interactive dragging of respective points via the web interface is shown in Figure 4, and a corresponding illustration of interactive linear computations is shown in Figure 5. Respective online examples can be accessed via the following links: for the example in Figure 4, and for the example in Figure 5.



Econometrics--Illustration of a Monte Carlo Method

In more involved statistical models in econometrics, concepts of probability and probability distributions play a crucial role. One specific statistical technique used in simulating economic behavior is the Monte Carlo method (Creal, 2009). It is particularly useful in forecasting or predicting outcomes of activities that involve uncertainty. Therefore, interactive explanation of principle of the Monte Carlo method may be particularly beneficial in higher level courses on Quantitative Methods. An example of an interactive learning site is presented in Figure 6, and the actual website is accessible via the following link:


With the advent of the Internet an added dimension of convenience is now available to teaching complex business and economic models. Due to the ubiquitous nature of the World Wide Web, which is accessible today from any home computer and mobile device connected to the Internet, it is critical that academics explore and take advantage of this technology to improve course delivery. Web based interactive exercises as proposed for a quantitative course in business or economics should be made easy for the learner to use, be easy to facilitate learning and be highly interactive to take advantage of the web's capabilities. The student can then concentrate on the content and learning in the web exercise without getting too diverted by the mechanics of computations.


While first experiences with using interactive web-based exercises seem to be very positive with respect to student learning, three kinds of issues need closer attention to make the learning process smoother and more effective. First, there are plenty of technical issues involved in preparing the web representation of exercises and placing them on the server. These involve the choice of a specific technology (Java, Flash, ASP, etc.), computational power of the server (memory size, disk space, etc.), network connection speed, and others. Secondly, a close cooperation between the Instructor and the Web Developer is needed to resolve these problems, with multiple iterations to fix bugs and upgrade the exercises, for which a significant amount of time and effort is needed if the results are to be meaningful. Finally, new measures of teaching effectiveness need to be developed, to assess and evaluate the results of the learning process, in particular, comparison criteria with traditional delivery methods must be elaborated. Acknowledgments

This project has been funded in part by a grant SBAHQ-10-I-0250 from the U.S. Small Business Administration (SBA). SBA's funding should not be construed as an endorsement of any products, opinions, or services. All SBA-funded projects are extended to the public on a nondiscriminatory basis.


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About the Authors:

Elias Kirche (Ph.D. in Operations Management, 2002) is an Associate Professor of Computer Information Systems in the Lutgert College of Business at Florida Gulf Coast University. He is a member of the Decision Science Institute and the Production and Operations Management Society. His research interests include: supply chain optimization models, empirical research and theory testing. He is a recipient of Aspen Technology scholarship to develop Advanced Planning and Scheduling (APS) case studies. He can be reached at:

Teresa Tharp holds a Doctorate in Business Administration (DBA) from Argosy University, in Sarasota, Florida (2009). She teaches Economics at Valencia Community College in Orlando, Florida. Her research interests include macro- and microeconomics issues, as well as distance education and web-based learning. She can be reached at:

Janusz Zalewski (PhD. in Computer Science, 1979) is a Professor in the Computer Science program at Florida Gulf Coast University. He previously held academic positions at Embry-Riddle Aeronautical University and University of Central Florida. He worked on projects for the Superconducting Super Collider, Lawrence Livermore National Laboratory, NASA, FAA and Air Force Research Labs. His research interests include software engineering, computer networks and web-based education. He can be reached at:

Elias Kirche

Florida Gulf Coast University

Teresa Tharp

Valencia Community College

Janusz Zalewski

Florida Gulf Coast University
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Author:Kirche, Elias; Tharp, Teresa; Zalewski, Janusz
Publication:International Journal of Education Research (IJER)
Article Type:Report
Geographic Code:1USA
Date:Sep 22, 2011
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