Teacher Authored Simulations: A Proof of Concept
Janice S. Tyler
The proposed topic of this research exercise is testing whether a practicing teacher can write a computer simulation program, under normal working conditions, and the simulation still enhance the student learning experience. In narrowing the research to my area of practice and interests, the project came to focus on a simulation of an archaeological project that would lessen math anxiety while introducing concepts in an applied and interesting context. This proposed project required a review of the literature on math anxiety, computer simulation, programming with Visual Basic for Applications, and the use of simulations in teaching archaeology. County regulations will essentially prohibit “Beta” testing the software on students in county schools, but some of the officers of the Society for Georgia Archaeology expressed an interest in testing the software when it is completed.
Teacher Authored Simulations: A Proof of Concept
The growing importance of computer simulations is clearly illustrated by the following observation:
Today if [someone] says he understands how a complex system works, it is fair to insist that he demonstrate this by programming a computer to imitate its behavior…If he can not do this then his understanding is certainly incomplete and perhaps illusorily (Grodins 1965, 143;cited in Johnson,1978, 176).
Is it reasonable to extend Grodin’s assertion into a call for full time teachers to write ad-hoc instructional simulation programs? Educational planners have long recognized that simulations can be powerful instructional tools (Price 1991). However, the programs, even simulations of school neighborhoods such as Dethlefsen’s (1982 ) study, seem to be nearly always created by professional programmers or university academics rather than teachers. Cantrell (1997) called for teachers to use a variety of software applications to enhance mathematics instruction including spreadsheets. However, she did not call for teachers to go the extra step and incorporate VBA programming to enrich Excel spreadsheet applications. The International Society for Technology in Education (ISTE) is developing National Education Technology Standards for Teachers (NETS-T), yet it does not hold teachers to a specific level of programming competency (ISTE 2003). Teachers are not typically trained to program by the colleges of education. They do not write software application code as part of their classroom practice, and the ISTE is not raising the bar for them to program. Despite this tremendous inertia of being at rest when it comes to teacher programming, it could contribute tremendously to professionalize public education.
This project will gage the difficulty of preparing instructional simulations under the life conditions of a practicing teacher and as such it is both exploratory action research (EAR)[i] and participatory action research (PAR) (Merrifield 1997). The spirit of the PAR approach is crystallized in the masthead of Focus on Basics: …dedicated to connecting research with practice, to connecting teachers with research and researchers with the reality of the classroom, and by doing so, making adult basic education research more relevant to the field (National Center for the Study of Adult Learning and Literacy, 1997). The PAR association may be preferable to the Collaborative Action Research (CAR) described by Sagor (2000) as PAR advocates tend to take a less strident tone, and they call for a close association between professional researchers, teachers, and the general community (Garner 1997). Citations to researchers less bellicose than Sagor may facilitate acceptance of a teacher’s research within a wider community of researchers.
In terms of software engineering this study is a “proof of concept” i.e. a demonstration of technical feasibility. Proof of concept studies are based on preproduction models (Scottish Endowment, 2003). The Northwest Academic Computing Consortium (NWACC) uses four criteria in evaluating submissions for its Proof of Concept Awards; impact, innovation, feasibility, and technology transfer to education and other fields (NWACC, 2003). The presence of VBA in MS Office Applications makes the study feasible (Getz and Gilbert 1997). It would have probably taken less time and effort to propose to do a survey to identify reasons why teachers do not program and then suggest policy changes. However, there was a significant possibility that such a survey would be counter-productive and simply reinforce the status-quo rather than promote change. Successful proof of concept projects often lead to change through the presentation and demonstration of new technology or new applications of existing technology.
This proof of concept exercise, the demonstration of the feasibility of teacher authored instructional simulations is grounded in four broad areas of prior research, (a) math anxiety, (b) computer simulations, (c) programming and application development in Visual Basic for Applications (VBA), and (d) simulations in archaeology and instructional resources for archaeology in the middle grades. Four relevant facts emerged from this (admittedly very rushed and superficial) review of the literature. First, math anxiety is a recognized psychological condition, and experts in the field are popular speakers on the lecture circuit (Tobias 2002). Second, there seem to be only limited simulation resources available that focus on archaeology that support instruction across the curriculum. The third fact to immerge is that the general public and teachers in particular, underutilize the computing power available to them in the form of Visual Basic for Applications (VBA). The fourth fact to immerge, is a corollary of the third and presents a significant challenge for programming educators. That is, there is a low level of expectation for teachers to be instructional programmers. Hopefully, at some point in the future, if this project is successful, one outcome of its outcomes will be a greater teacher awareness of the power they literally have at their finger tips, but do not use.
Recent research on the cognitive dimension of mathematical thought has important implications for middle school math teachers who practice in culturally diverse schools. Performance on mathematics tasks is mediated by both extra-curricular cultural factors (Campbell and Xue, 2001) and stress (Ashcroft and Kirk 2001). These recent findings strongly indicate that teachers can enhance students learning math by accommodating cognitive practices that are embedded in students’ culture and by providing learning situations that can lower math anxiety.
Campbell and Xue compared the cognitive processes engaged in the execution of arithmetic tasks by non-Asian Canadians (NCA), Chinese Canadians, raised and educated in Canada (CC), and Chinese university students (CA) who came to Canada as exchange students. The Chinese Canadians reported engaging cognitive processes more similar to those reported by the Chinese university students than the non-Asian Canadian university students. Campbell and Xue attributed this pattern to extra-curricular cultural factors.
Ashcroft and Kirk (2001) reported the findings of three experiments that extended previously demonstrated connections between memory, stress and proficiency in carrying out math tasks. Their first experiment essentially replicated prior research linking adverse life outcomes related to anxiety associated with mathematics. Students with math anxiety were found to take fewer math courses, and make lower grades in the classes they did take. They were also found to perform less well on mathematics tests. These findings were consistent with trends recognized by Tobias (1978), Ruedy and Nirenberg (1992), and other previous researchers.
The second of Ashcroft and Kirk’s (2001) experiments revealed that even students who have a math competence when working with paper and pencil exhibit an adverse effect of math anxiety on working memory when students were asked to perform mental arithmetic tasks and then recall a series of letters that had been presented to them before the were given the arithmetic problem. The third experiment was similar to the second in that it indicated that math anxiety impeded students working memory and detracted from their proficiency in carrying out mental operations within a task context that included mental arithmetic.
While clinical researchers have been able to document cognitive and even physiological responses associated with math anxiety, treatment of the condition has been more or less illusive. If successful double-blind clinical trials have been conducted that demonstrate therapeutic efficacy of any particular treatment of math anxiety, its publication has been obscure. Several folk-remedy style responses have been suggested based on anecdotal evidence. Curtain-Phillips (2002) writes, “For instance, a new concept can be taught through play acting, cooperative groups, visual aids, hands on activities and technology.” Ellen Freedman (2003) has a popular web site that lists ten was to reduce math anxiety:
1. Overcome negative self-talk.
2. Ask questions.
3. Consider math a foreign language -- it must be practiced.
4. Don't rely on memorization to study mathematics.
5. READ your math text.
6. Study math according to YOUR LEARNING STYLE.
7. Get help the same day you don't understand.
8. Be relaxed and comfortable while studying math.
9. "TALK" mathematics.
10. Develop responsibility for your own successes and failures.
Santa Monica College (2003) sponsors an on-line annotated bibliography with links a wide variety of on-line resources related to reducing math anxiety. One of the links is to OnLineCollegePrep.com, an education service that offers a free on-line interactive set of programmatic lessons to help students master anxiety in academic settings. The lessons explaining the learning process and stress the need for the student to reduce anxiety by taking control of her learning through an understanding of the various learning styles. A common theme in the anxiety reduction literature is a need for the student to be able to take control of the learning process.
The use of computer simulations could combine Curtain-Phillip’s call for the use of technology to address math anxiety in a way that accommodates the general need of afflicted students to assume control of their learning experience. However, commercially prepared simulations are often expensive to purchase, commonly demand the latest in hardware and operating system technology, and require a fairly long learning curve for the teacher to master sufficiently to use them effectively in the classroom. If teachers could produce simulations, more or less on the fly then they would be tailored to the teacher’s system and instructional needs, and at negligible cost.
Even in the early days of desk top computing during the 1970s and 1980s simulations were recognized as especially powerful teaching instruments (Price 1991). However, during this period, hardware and software limitations lead authors to focus on “programmed instruction” with a focus on repetition and reinforcement drills rather than simulations. None the less, there were still efforts to integrate simulation applications into the teacher’s tool kit because of its potential to engage students in higher order cognitive skills (Holzman, Glazer, & Pellegrino, 1976; Gange, Wager, & Rojas, 1981; Smith, 1989).
The current situation in programming is one of rapid change. To understand what is going on and what will likely develop over the short term it is helpful to review the history of computer simulations as a series of three evolutionary “forks in the road.” The first fork was between analog and digital computing. The second fork was the split between simulations with continuous time structure and those with discrete time structure, often referred to as discrete event models. The final fork is the distinction between “artificial reality” and “artificial life” both of which employ artificial intelligence. In artificial reality the user interacts with a dynamic simulated environment while in artificial life, the user studies the results of interactions among large numbers of interacting artificial entities. Advances in software and hardware may keep the fields of artificial life and artificial reality from drifting completely apart.
Analogue computers were based on physical relations and changes which digital simulations were numeric expressions of relations and change. Slide rules were analogue calculators that came to be displaced by digital hand calculators. Developments during the Second World War led left digital computers as the clear leaders. Later, the rise use of object oriented programming and fractal algorithms so enhanced simulations that it is sometimes hard to remember old efforts to simulate with physical objects and to appreciate the power of recent advances. In the old days, the Army Corps of Engineers simulated river tributary systems by wiring together a series of transformers on a map. Transformers were placed over the junctures of tributaries and the river. The flow of electricity through the system modeled the flow of water through the river basin. Today, using Geographical Information Systems software such as the ARC View extension BASINS, developed by the USCE river flow patterns are modeled digitally, more accurately and in more detail. German hydrographers have modeled the Rhine in 3-D digitally.
The next evolutionary fork separated simulations based on continuous and discrete models of time. At first, continuous time simulations had the advantage. They could accommodate structured sets of equations and were adopted to classical Game Theory models (Davis 1983) and support practical simulation problems such as simulating falling objects and trajectories of diving airplanes. However, the introduction of random number generators gave a clear advantage to discrete time models. The random number generators allowed programmers to introduce chance events into the program and this made it possible to create much interesting and realistic simulations.
While continuous time modeling have come to dominate some applications in physics and engineering, in most fields of simulation related to decision making, the discrete event programs proved to be far superior. The contrast between the two becomes clear when we consider Milstein’s (1974) attempt to use continuous functions simulate the American war in Viet-Nam with Thompson’s (1977) early discussion of modeling dynamic processes with discrete structures. Even though Milstein only modeled the war between the time of the 1968 Tet Offensive and the Invasion of Cambodia there were difficulties in the use of continuous functions that would accommodate an escalation of conflict and then reverse to a diminution of conflict. In contrast, Thompson’s introductory discussion showed that models of dynamic feedback systems, based on discrete events could be designed in such a way that the output results served not only as new input into a set of structured functions, but also changed the changed the controlling relationships and functions of the system. When program output creates changes in the structuring functions, then complex cycles, extinctions, and other phenomena can be simulated.
Later, with the introduction of random number generators it was possible for programmers to produce a powerful variety of programs known as “Monte Carlo” simulation. In a Monte Carlo simulation, life is a game of chance as programmers introduce elements of the “unexpected” at the beginning or end of each time period. In stead of just estimating the position of a diving torpedo plane at a given instance the use might experience his gun jamming, or have to respond to his ship sinking due to the strike of an unanticipated submarine torpedo. Program designers use the term “Monte Carlo” to describe discrete event programs that used random number generators to introduce chance events or factors . The introduction of Monte Carlo programs made simulation training much more interesting.
Eventually, simulation programs that attempt to allow the user to interact with aspects of the real world came to be labeled “virtual reality.” Authors of the earlier virtual reality simulations tried to create a virtual world in which the user of the application was able to practice a training skill in the safe environment of a computer lab. Examples of such simulations developed for school related activities included dissection of a virtual from and pioneering on the Oregon Trail (Price 1991). The earlier virtual reality simulations were not very visual, and the modeled conditions were typically communicated to the user through the use of text print outs and later text displays. Flight simulators were among the earliest of the simulations to use graphics to communicate the modeled circumstances to the user.
Random number generators and Monte Carlo programming allowed programmers to introduce weighted probabilities to their programs. Suppose a pioneer wagon train had a choice of crossing a river or going overland. The programmer could introduce a given probability weight that a percentage of the party would drown as a flash flood strikes during the crossing. On the other hand, if the user opts for the river crossing, and the programmer could write in a probability weight that the party will be struck by a blizzard, become snow-bound and starve like the Donner Party. And for good measure, the programmer could introduce a probability weight that the wagon train would be attacked by a war-party of Cheyenne Dog-Soldiers in either case. With random number generators, programmers were able to turn their virtual worlds into a casino-like games of chance, and the term Monte-Carlo simulation has been with us ever since.
By the mid 1980s cellular automata programs, another kind of dynamic system simulation became popular as software and hardware advanced to the degree they could accommodate parallel distributed computation models in problems involving large groups. So the general system state could be determined by the summation or thousands of unique decisions and actions of thousands of simulated decision makers - and each decision maker’s decisions could be influenced by the decisions of her neighbors while also influencing the decisions of those around them. These simulations accommodated feedback to a degree that Wiener (1949) could not have imagined when he defined the field of cybernetics or mechanistic feedback and system control. Advances in structural and object oriented programming, combined with advances in mathematics supported an explosion in simulation of complex interactions of interacting populations. Eventually, this type of programming came to be called “Artificial Life.”
Programming with Visual Basic for Applications (VBA)
If a teacher reaches the conclusion that she is going to write simulations of her own, one of the first decisions she must make is what development soft ware to use. Every teacher who access to the Microsoft Office suite of windows based applications has been blessed with ready access to a very powerful object oriented programming language, yet very few of realize it. Visual Basic for Applications, VBA, is embedded in all the MS Office products, waiting to be used, but, sadly ignored.
At one level it is surprising that anyone uses VBA because it is not typically covered in MS Office Application user guides and manuals. There are three ways why the literature fails to support accessibility for VBA. First it is ignored by most of the user guide books for MS Office suite applications. Furthermore, volumes on Visual Basic 6 and Visual Basic Net do not typically address the intricate nuances of programming with the Office application objects (for typical examples see Balena, 1999, Stephens 2000).
In some cases application guides of about one thousand pages devote only one paragraph or less to the topic. Some popular examples of these types of manuals are Chester and Alden, 1997; Rutledge and Mucciolo, 1999; Petroutsos 1996). To begin to comfortably write code in VBA the novice needs to invest in three types of manuals: a beginners guide that covers how to insert Active X controls into an application like Word or Excel and then attach VBA code to the inserted object. Then specialized manuals are needed for working with the unique objects associated with each application. Then a general application development manual is needed to develop software that engages more than one of the Office applications.
The application objects of the Microsoft Office Suite are quite different from one another in terms of their properties and their methods(Getz and Gilbert, 1997). The Excel object and its set of associated objects are very different than the objects associated with Word or Access (Walkenbach, 2000). It is possible for teachers to create applications call upon more than one application – say, Excel, Power Point, and Word (Simon, 2002). While starting on the learning curve, it would be essential that the teacher and novice programmer acquire a general application development manual for VBA and the MS Office suite. The scope and power of VBA now goes beyond Microsoft products, and any software that is developed to COM specifications can incorporate VBA as an embedded script-programming language. One of the more spectacular examples of VBA inclusion is ESRI decision to make VBA the programming language of its newest version of ARC-View, one of the more popular (and powerful) of the GIS applications (ESRI 2002).
There have been a few, hard to find, VBA manuals like Boonin’s (1997) Using Excel Visual Basic for Applications. But VBA remained obscure as the old hands in Excel such as Chester and Alden continued to focus on traditional “macros” rather than try to discuss VBA. Much of the obscurity associated with VBA could be overcome by having teacher oriented sites post detailed descriptions of the application objects, their methods and properties. The lack of easy access to object documentation would probably be the biggest obstacle a teacher would face were she to try to take up writing her own simulations at the present. Once the documentation is obtained, writing code becomes, if not trivial, then at least a manageable exercise. To support the spread of VBA based programming it will be helpful, and perhaps necessary for one or more teacher centered web pages to post the code and documentation of teacher authored simulation software.
Archaeology deals with story of humanity across space and through time as read in the physical remains resulting from human activity. Anything that calls for the interpretation of measurements of dynamic processes across space and through time, is calling for the use and application of mathematics. Some of the most fascinating simulations created have been done by archaeologists and anthropologists for archaeologists and anthropologists. Steven Lansing’s classic 1991 study and simulation of the interface of landscape engineering, economics and ritual cultural in Bali stands out as a stellar academic exercise that did not reach down below the university (and probably graduate school ) level. As early as 1978, Johnson commented that a computer simulation “…is still more rigorous than the loose constructs anthropologists usually refer to as models.” Johnson computer simulations as being particularly helpful conducting virtual experiments and exploratory pilot projects, not in instructing school children. Gatewood (1992) described computer simulations as being essential “if the types of processes we study are truly complex, and /or and they can only be understood probabilistically, then simulations enable us to reach a depth of understanding that goes beyond whatever case-specific data we may be able to assemble.” Gilbert and Doran (1994) include a rich, complex, and diverse set of fifteen papers on simulation that reinforce Gatewood’s comment above. Modern discrete event simulations developed in object oriented languages allow the novice simulation program to explore processes through complex mathematical models that would be difficult to apply, if not impossible with out computer simulations (Roberts et.al., 1983; Beltrami, 1993 and Fishwick 1995). Even though MS Word is a word processor, the VBA embedded in it will support a development of a simulation based on the intermediate to slightly advanced mathematics described in the works of Betrami and others cited above.
Despite the rich use of simulations of archaeological simulations to further professional research, if one discounts the Laura Croft “Tomb Raider” interactive games, there have been relatively little simulations developed to teach archaeology in the publics. There are a few elementary survey and excavation simulations available through the Internet. Perhaps the most robust archaeological simulation developed for public school education is Excavating Occaneechee Town, produced by the Department of Anthropology of the University of North Carolina. This application is not available on line but CDs with the simulation can be purchased from the University of North Carolina. An excellent review on-line by Dean Snow is available in the electronic version of Journal for Multi-Media History at http://www.albany.edu/jmmh/vol1no1/occaneechi.html. In this simulation the student is required to do historical research using scanned archival documents and maps before undertaking up excavation. The budget is tight and it is impossible to dig the whole site. The student must select wisely (and with a bit of luck) and record carefully to draw accurate and valid conclusions about the prehistory of the site.
A fortunate set events and circumstances made selection of a specific archaeological project to simulate less challenging than expected. The Georgia Ports Authority recently encountered an extremely important colonial archaeological sites on the banks of the Georgia side of the Savannah River a few mile upstream of the city of Savannah while developing a huge new transport ship unloading facility. Among the features encountered were the remains of a trading post operated by Mary Musgrove who played a pivotal role in the founding and early development of the Georgia colony. While the remains could not be saved. It was impossible to change the construction plays to save the site, but before it was destroyed, the Ports Authority contracted with Southern Archaeological Services, Inc. to carry out salvage excavations to extract as much information about the Grange site as time and funding would permit. The month of May is Archaeology Month in Georgia and the Ports Authority produced a video of the project and an associated instructional packet that was authored by Rita Flose Elliot (2003). The Society for Georgia Archaeology collaborated with the Ports Authority in distributing the video and teaching packets to its membership and schools around the state.
One of the activities in the teaching packet is a board-game activity. While the board game format is interesting migration of the simulation to an electronic format would potentially enhance its potential as a teaching instrument. To ensure that this work will be authentic, that is, to ensure that it is carried out under conditions of a teacher’s life and with resources readily available to teachers whose schools are facing budget shortfalls, I will use the free teaching packet mailed to the middle schools and the embedded VBA in Excel. As many teacher do not have ready access to MS Access it will not be used. Furthermore, to accommodate the strict time constrains that teachers live under no attempt will be made to incorporate PowerPoint or Word. This summer I will not be able to test the effectiveness of the simulation (assuming I succeed in creating it) because of the time required to have research projects by the County Central Office. According to Board of Education Policy, in DeKalb County, Georgia surveys and observation studies done in public schools for college class projects are supposed to be submitted to the central office for approval – by a committee of county employees with Ph.D. degrees – in a process that takes thirty working days. The simulation would have to be submitted with the proposal. However, some of the officers of the Society for Georgia Archaeology have expressed an interest in Beta testing the simulation over the summer.
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[i] As far as I have been able to determine the “exploratory action research (EAR)” has not been used in the literature, but I suspect that it is out there, lurking somewhere and I just have not been able to find it.