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Towards Dynamic Modeling of aTeaching/Learning Process Part 3:The Simulation Model*

N. EFTEKHAR and D. R. STRONGMechanical & Industrial Engineering Department, University of Manitoba, Winnipeg, Manitoba, Canada.E-mail: [email protected]

In this part of the study, first the STELLA language software, as an operational manifestation ofthe system dynamics approach, is introduced and discussed. Then the general model of the teaching/learning process is translated into the STELLA stock and flow equation of a system dynamicsmodel. Although the gist of the teaching/learning model is common for both form-oriented andfunction-oriented learners, because of their totally different approaches to learning, two separatebase models could be built and run concurrently. The rest of the paper deals with the description,analysis and results of the base models and the implementation of the different policies to improvethe behavior of these two systems.

INTRODUCTION

IN THE PREVIOUS PARTS of this study, in linewith step 1 and step 2 of the system dynamicsapproach, a system for the teaching/learningprocess was defined [1]. The building blocks ofthe system, their constituent parts, and theirrelationships were theorized and described. Then,the main parts of the system were converted into aunified diagrammatic representation. Furtheranalysis of the literature search, uncovered newknowledge about student's learning and resulted indevelopment of a new theory and the introductionof two different types of learners with two distinc-tive approaches to learning: form-oriented learnersand function-oriented learners (Form-FunctionTheory of Types [2]).

The proposed form-function theory of types,provides a new ground for analyzing, under-standing, and re-engineering of the teaching/learning processes. This theory is based on a`systems as cause' thinking approach and, hence,looks at the systems or processes as the cause oftheir performance as opposed to their performancebeing merely determined by outside forces. Thistheory, principally, demands this study to developa separate model of the teaching/learning processfor each type of learner.

To investigate how a learner and a teacher reallywork and interact with each other over time, asimulation model should be constructed and runaccordingly. In fact, the model should be basedon the interaction between three major sets ofcomponents in the system:

. the learner's learning abilities and motivation;

. the teaching system's characteristics, and

. the nature and quality of the subject matter.

The answers to two fundamental questions raisedfrom the interaction of the above forces, namely:what should be taught to whom; and how shouldit be taught should be found in dealing with sucha model. This is achieved by using a systemdynamics approach and employing a computersimulation program (STELLA Research Soft-ware). Thus, STELLA software will be introducedand discussed briefly. Then, two different basicstructures for the form and function learners areconstructed in the STELLA language. The basemodels are run and the results are comparedwith observed realities to validate the models. Anumber of policy variables are used to improveand to enhance the situation. For instance, it willbe shown that the teaching/learning process maybe enhanced by the careful choice of the learningmaterial (subjective, objective, and procedural)that the teaching system presents.

The results of this experimentation indicate thepower and effectiveness of using industrial engi-neering modeling techniques in the field ofnon-physical (non-rigorous) variables of educa-tion. Moreover, and more importantly, theproposed Form-Function Theory of Types intro-duced by this study, facilitates the better under-standing of the mechanism of learning from oneside and teaching from the other side.

STELLA LANGUAGE SOFTWARE

The STELLA software language is built arounda progression of structures. Stocks and flows are atthe lowest level and are the fundamental buildingblocks of the structure. Infrastructures, which vary* Accepted 21 May 1998.

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Int. J. Engng Ed. Vol. 15, No. 3, pp. 168±190, 1999 0949-149X/91 $3.00+0.00Printed in Great Britain. # 1999 TEMPUS Publications.

in size and complexity, are the next step in pro-gression. They are built up from various combina-tions of stocks and flows. Feedback loops are thefinal step in the progression and are the relation-ships that link stocks to flows in various ways. Inso doing, they enable infrastructures to exhibitinteresting dynamic behavior [3].

This section provides an overview of each step inthe progression of the fore-mentioned structures.In fact, this overview will prepare the ground forunderstanding what the `structure' looks like ateach level, how each structure behaves, and over-all, how a STELLA model works. To be moreefficient, in discussing each step, this study usesexamples from the non-physical variables that, oneway or another, are parts of a teaching/learningprocess in real life [3].

The building blocksComponents, or the building blocks, of the

system are the first progression of the structurein the STELLA software language. There are fourbasic building blocks in the system: the stocks,the flows, the converters, and the connectors. Aconcise description of each of these componentsfollows [4].

1. Stocks. Stocks are basically accumulations.They collect whatever flows into and out ofthem. The default stock type in STELLA is the`reservoir.' A reservoir passively accumulates itsinflow, minus its outflows. Any units, which flowinto a reservoir, will lose their individual identity.Reservoirs mix together all units into an undif-ferentiated mass as they accumulate. In a teaching/learning process, for instance, the student knowl-edge is an accumulation that varies as the processof teaching/learning proceeds.

Three other stock types are available in theSTELLA software, but only two of them;`conveyors' and `ovens' are used in this study. Aconveyor can be thought of as a moving sidewalkor a conveyor belt. Stuff gets on the conveyor,rides for a period of time, and then gets off. Thetransit time for a conveyor can be either constantor variable. Both capacity and inflow limit canconstrain entry to a conveyor.

On the other hand, an oven may be thought as aprocessor of discrete batches of stuff. The ovenopens its doors; fills (either to capacity or until it is

time to close the door); bakes its contents for atime (as defined by its outflow logic); then unloadsin an instant. By contrast, stuff that enter these twostocks (conveyor and oven) do retain both theirmagnitude and time-of-arrival identity.

Stocks, in general, can be referred to as systemstate variables. Figures 1(a), (b) and (c) show areservoir, a conveyor, and an oven type of stocksrespectively.2. Flows. The task of flows is to fill and drainaccumulations. Mathematically, they are theinstantaneous rates of flows that represent themeans by which the system is controlled andrepresent activity points in the system. In fact,without flows, no change in the magnitude ofstocks could occur. So, stocks and flows areinseparable components. They form the minimumset of structural elements needed to describe thedynamics of a system. Figure 2 exhibits two typesof flows that are used in the STELLA program;uniflows and biflows. In Fig. 2(a), the unfilledarrow head on the flow pipe indicates the directionof the uni-directional flow. Clouds represent infi-nite sources or sinks for flows as illustrated in thediagram. Also, Fig. 2(b) shows a bi-directionalflow (biflow), which is used to transport thingsboth into and out of an accumulation. The second,shaded arrow head on this flow points the direc-tion of outflow. Uniflows will assume only non-negative (i.e., inflow) values, but biflows can takeon any value.3. Converters. Converters are auxiliary functionsand serve a utilitarian role in the software. Theyhold values for constants, define external inputs tothe model, calculate algebraic relationships, andserve as the repository for graphical functions. Ingeneral, they represent the decision processes inthe system. They are called `converters' since theyconvert system states to system activities (or inputsto outputs). Figure 3 shows the symbol thatrepresents converters in the STELLA mapping.4. Connectors. As their names suggest, the job ofconnectors is to connect model elements. In fact,connectors are links that connect all of the compo-nents to each other. In so doing, they eventuallyform arcs that influence the flows (which regulatethe system). The only restriction of connectors isthat one cannot drag it into a stock. The only wayto change the magnitude of a stock is through aflow. Figure 4 shows how a connector looks inSTELLA software.

Fig. 1. Stock types: (a) a reservoir; (b) a conveyor; (c) an oven.

Fig 2. Flow types: (a) a flow (uniflow); (b) a biflow.

Fig. 3. A converter.

Fig. 4. A connector.

Towards Dynamic Modeling of a Teaching/Learning System Part 3 169

InfrastructuresAs stated earlier, stocks and flows are the

principal building blocks of the STELLA softwarelanguage. However, irrespective of how manyflows are attached to it, a single stock system canself-generate only a very limited set of dynamicbehaviors. In order to produce a more complexdynamic pattern, it is essential to assemble sets ofstock/flow combinations. These sets of combina-tions are called infrastructures. They exist in anessentially infinite variety. For the purpose of thisstudy's modeling, it is important to recognizethat infrastructures will generally define the rangeof characteristic behavior patterns that a model ofteaching/learning will be capable of exhibiting.

In practice, infrastructures typically appear in alimited number of generic forms. Each genericform has certain dynamic behavior. Five maingeneric forms are recognized in STELLA softwareas follows:

1. First-order linear infrastructure: a simplecombination of a compounding and a drainingprocess (Fig. 5). (Note: In a compoundingprocess, the stock serves as the basis for pro-ducing its own inflow while in a drainingprocess, the stock serves as the basis forgenerating its own outflow.)

2. S-shaped: a self-reinforcing growth processthat eventually is under control by somegrowth constraint.

3. Overshoot and collapse: accumulations do notmake a smooth transition from growth tosteady-state. Instead, they grow rapidly, reachtheir maximum, and then decline to a newsteady-state value.

4. Oscillation: an oscillatory behavior producedby a minimum of two stocks while each servesas a catalyst for producing the other stock'sflow.

5. Main chain: represents a sequence of stagesthrough which stuff flows while the specific

nature of the flows varies, depending on thespecific situations being modeled.

Taken as a whole, these generic processes will helpthis study to operationally specify the teaching/learning processes that it seeks to represent withthe software. A model of a teaching/learningprocess will generally employ a combination ofall of the above types. An example of the genericstructure of the first-order linear infrastructure isshown in Fig. 5. The system is called `first-order'since only one stock is involved. Also, it is `linear'since the constant proportionality between thestock and its flows gives rise to the term linearÐwhich refers to the algebraic form of the flowequation.

As the diagram shows, the stock is fed by acompounding process (as defined and formulatedin the figure). It is depleted by a draining process.Both the compounding fraction and the lossfraction are constant, which means that bothcompounding and draining flows are proportionalto the amount of the stock.

A first-order linear infrastructure can exhibitthree distinct behavior patterns, dependingupon the relationship between the compoundingand loss fractions. When the two fractions areconstant, and the compounding fraction is greaterthan the loss fraction, the infrastructure exhibitsexponential growthÐthe compounding processwill dominate the behavior. In each cycle of theprocess, more will be added to the stock than willbe taken away. As the stock builds, both inflowand outflow will grow larger. In relative terms,however, the inflow will always be greater than theoutflow. The net rate of growth in the stock issimply the difference between the compoundingand the loss fractions. On the other hand, when thecompounding fraction is less than the loss fractionin this infrastructure and both are constant, the netrate of decline is the difference between the lossand the compounding fractions. Finally, when the

Fig. 5. Example of first-order linear infrastructure.

N. Eftekhar and D. Strong170

two fractions are equal, the stock will remainconstant. The draining flow is equal to thecompounding flow, so no change will occur inthe stock.

Feedback loopsWhile infrastructures define the range of

dynamic behavior patterns that a model is capableof exhibiting, the particular kind of feedbackrelationships that exist within the infrastructurewill determine which of these patterns is realized.A feedback relationship is a closed-loop circle ofcause-and-effect. Feedback loop cause-and-effectalways includes at least one stock and one flow.This is because stocks are conditions that give riseto actions (or flows of activity) that in turn changeconditions. However, it is really the current stateof conditions, relative to some target level for thecondition, that inspires conditions to change.Thus, feedback loops could be viewed as relation-ships that generate goal-seeking behavior. Goalseeking is a fundamental activity in which alldynamic systems engage. In fact, goal seeking iswhat enables conditions within a system to remainon course. When deviation occurs, feedback rela-tionships inspire and direct corrective actions tobring conditions back in line.

There are two types of feedback relationships:negative (counteracting) and positive (reinforcing)feedback loops. When any variable in a negativeloop is changed, then the loop causes that variableto readjust in the opposite direction. The negativeloop produces self-regulating change (controllingand restorative behavior). Figure 6 illustrates acommon counteracting feedback process. In theloop, the level_of_effort is being used to regu-late the level_of_performance. If performancefalls below the level that the student has set as hisor her target, then effort should go up. A higherlevel_of_effort leads to an increased level_of_performance. So, an initial decrease in per-

formance propagates a signal around the loop,which leads to an increase in performance. Theloop thus acts to counteract the initial change.

It should be noted that the loop also couldcounteract change in the other direction. That is,if performance rises above target levels, effort willbe scaled back so as to return performance targetlevels.

By contrast, positive (reinforcing) feedbackprocesses compound change rather than counteractit. When any variable in a positive loop changes,the resulting interactions cause that variable tochange further in the same direction. The positiveloop, in other words, characteristically producesself-reinforcing change (unrestrained growth).

Figure 7 is an illustration of how a typicalreinforcing feedback process works. The better astudent performs, the more confident she or hefeels. Subsequently, the more confident s/he feels,the better s/he performs. However, as mentioned inthe counteracting feedback relationship, the loopalso may change conversely. That is, the lessconfident one feels, the worse one performs andsubsequently, the worse one performs, the lessconfident one feels.

As the diagram indicates, in the case of areinforcing feedback loop, the goal or target_level_of_performance is linked to the level ofself_confidence. The link means that whenself_confidence rises, the target for level_of_performance follows suit and vice versa. Then,as performance adjusts to the new target level,self-confidence responds accordingly.

Combining counteracting and reinforcingfeedback loops

In fact, it is the interaction and shifting domi-nance between the two types of feedback relation-ships that generates the dynamic character of asystem. Figure 8 is an effort to combine the two

Fig. 6. A simple counteracting loop.


previous examples and to show the way that theresulting system behaves. As the diagram indicates,now it is self_confidence that sets target_level_of_performance and target_level_of_effort. That is, how confident a student feels,determines both how well s/he thinks s/he shouldbe able to perform as well as how much effort s/heputs out in order to achieve that level ofperformance. Level_of_performance feeds backto determine self_confidence, and level_of_effort feeds back to determine level_of_performance.

Now, if this set of relationships is allowed tooperate with the STELLA software, the behaviorof the system will depend on the initial levels ofconfidence, performance and effort as well asthe strength of the relationships between self_confidence and the two targets. For example, if adecline in self_confidence causes a larger decline

in the target for effort than it does for performance,then the system accelerates downward.

However a decrease in self_confidence hasonly a minimal effect on the target_level_of_effort, the counteracting feedback loopwhich ties level_of_performance back tochange_in_effort will have a chance to operate.This loop will act to boost the level_of_effortwhich, in turn, will increase the level_of_performance. An increase in performance, thenwill inspire a rise in the level of self_confidenceaccordingly.

Worth mentioning is that there are a lot of `ifs'in these scenarios. The `ifs' depend on the relativestrengths of the feedback relationships that areinvolved. This simple example emphasizes thefact that it is difficult to make accurate predic-tions about the performance of systems involvingextensive webs of feedback relationships.

Fig. 7. A simple reinforcing loop.

Fig. 8. Combining reinforcing and counteracting feedback relationships.


MODELING SOFT VARIABLES IN ATEACHING/LEARNING PROCESS

Modeling of a teaching/learning process requirestotal involvement with variables that are internalto both learners and teachers. Variables likestudent's abilities and motivation or quality ofteaching are not entities that can be measured orcomputed. In fact, since they are non-physical(soft) variables, they could not get numeric orprecise values. Despite this reality, however tech-nically, there is a mechanism for tackling such aproblem. The mechanism could be found in thefundamental distinction that exists betweenmeasurement and quantification [5].

Measurement, by definition, means `assessingthe magnitude of'. The result of the assessment isoften expressed numerically. All physical quanti-ties or `hard' variables like height, volume andweight have their pre-defined units-of-measures.On the other hand, quantification means, `assign-ing a numerical index to'. While assigning aquantitative index usually is a pre-condition tomeasuring something, the two activities are notthe same. The interesting point is that one canquantify anything.

Fortunately, in the case of a teaching/learningprocess, it is not necessary to measure all of thesoft variables in order to be able to use them in the

simulation model. That is, the study will assigna numerical index to each of the non-physicalentities that are involved in the system. Forinstance, to quantify student motivation, theresearch will assume that 0 represents the completelack of motivation and 100 represent as muchmotivation as is possible for a student to have. Asimilar quantitative index would work equally wellfor the effort that students put into a learning taskor the interest they have in the subject matter.Likewise, to quantify the rate of knowledgeacquisition, the research will assume 0 representsthe complete absence of effort to learn and 100represents as much knowledge as is possible for astudent to acquire for a given period of time.

Doing this will cause this study to act in arigorous manner about the relationship eachvariable bears to other variables in the teaching/learning system. Hence, the more this study tries toquantify, the better the desired model resemblesthe real one. In addition, this will enable the studyto solidify all the soft variables and simulatethem to examine their role in the dynamics of ateaching/learning process.

This study, based on the discussions and find-ings in the previous parts [3, 4], proposes twoseparate models for the components involved in ateaching/learning process. That is, a system for aform-oriented learner and a separate system for a

Table 1. Defined variables for the proposed models of teaching/learning process

ProposedModel Stocks Flows Converters

Form-orientedlearners

hooks_under_developmenthooks_for_repetitionhooks_in_memoryquantity_of_infointerest_in_subjectexpectancy_level_of_effortlevel_of_performance

taking_ (information)completing_ (the hooks)repeating_ (hooks ofinformation)lecturing_change_in_quantity_of_infochange_in_expectancychange_in_effortchange_in_performancewaste_

type_of_info: memory_info, relrote_info,relreal_info, procedure_real,procedure_rotelearning_reinforcers:testing_ : (rote_type, clsd_prbm_slvg,opn_prbm_slvg),quality_of_teaching,other_reinforcersinterest_in_use,interest_in_grade,impact_of_other_valuesavailability_,student's_perceived_availability,forecast_adjustmentprior_knowledge, amount_learned,productivity_,coding_.waste_fraction,learning_style_compatibility,constraints_.willingness_, mark of desire_,perceived_assessmenttarget_info, adjustment_fractionallocated_time_factor

Function-orientedlearners

relationships_under_studystructures_to_formstructures_in_memoryquantity_of_infointerest_in_subjectexpectancy_level_of_effortlevel_of_performance

taking_ (information)evaluating_ (information)finishing_ (the structures)lecturing_change_in_quantity_of_infochange_in_expectancychange_in_effortchange_in_performancewaste_

Same as above


function-oriented learner. It is noteworthy that thegist of the main structure for both models is thesame and only the main chain within each model isdifferent.

Table 1 shows the list of the soft variables thathave been defined and considered within the twomodels. Each soft variable is represented by one ofthe main building blocks of the STELLA software(stock, flow, or converter). As the table depicts,each model is composed of exactly fifty soft vari-ables with most of them being common in bothmodels. Note that this is a good number for aSTELLA model. In fact, a model with this numberof variables is neither too complicated to beunmanageable nor too simple to be unacceptableas the representation of the reality.

Each model uses eight stocks and nine flowrates. The remaining variables have been definedby the converters. All of the stocks except twoare reservoir types. These two stocks; hooks_for_repetition and structures_to_form, areConveyor and Oven type stocks respectively.

On the other hand, four flow rates (out of totalnine flows) are biflow types. These flows representvariables that can `change' values in eitherdirection (e.g., change_in_quantity_of_infoand change_in_effort).

LEARNING MODEL OF A FORM LEARNER

In this section, the STELLA model of a teach-ing/learning system for a form-oriented learnerduring a short time period (such as a class lecture)is presented. The role of each variable in themodel is highlighted, the nature of the interactionsbetween different variables within the entire system(feedback loops) is described, and finally, thebehavior of the system will be discussed.

Description of the base model for a form learnerThe system flow diagram for the learning

process of a form-oriented learner is as shown inFig. 9. The diagram has been constructed bySTELLA simulation language software and repre-sents all the variables presented earlier in Table 1.Basically, the variables within the system can berecognized in three sets of components: compo-nents of the teaching system, components of thelearning side (the form learner) and the compo-nents of the subject matter. Note that the compo-nents of both the teaching system and subjectmatter are at the top and the right end of thediagram. The remainder of the diagram includesthe components that represent the characteristicsof the learner (learning, motives and performance).The definition and description of each variablehave been given in the List of Equations (Appen-dix). Worth mentioning is that the STELLAequations created from Fig. 9 in the List ofEquations are two types. The first types are stocklevel equations (which are generated by the soft-ware directly from the diagram) and their asso-

ciated initial conditions. The remainder are theflow and converter equations that are generatedby the modeler.

Referring to Fig. 9, the main chain infra-structure at the center of the diagram representsa sequence of stages through which the informa-tion flows in the learning side of the system.Apparently, the specific nature of flows vary,depending on the specific situation of each typeof information. The chain is fed by a single flow(taking_). The cloud on the left-hand side ofthe flow of taking_ depicts the boundary ofthe model. It represents an infinite source for thetaking_ flow, as shown. (For the purpose of thismodel, it does not matter what is in the cloud.)The flow of lecturing_ (teaching system) isgoverned by two main variables: type_of_infoand change_in_quantity_of_info. Type_of_info is composed of five different types of incom-ing info (as introduced and discussed in Part 2 ofthis study [2]). In fact, the composition of thetype_of_info determines the type of the teachingsystem or the teacher. If more weight is given tomemory_info or relrote_info (relationship roteoriented information), the teacher is most likely aform-oriented teacher. Other potential possibilitiescan be created and used in the model by changingthe composition of type_of_info. The governingeffect of type_of info on the flow of lecturing_has a subsequent impact on the learning_style_incompatibility (which has its relevantimpact on the learning side as will be discussedlater).

In the present base model, the flow of taking_ iscapturing each piece of issuing information fromthe teaching system (flow of lecturing_) andplacing it into the mind of learner (stock ofhooks_under_development). Therefore, the flowof taking_ depends upon the flow of lecturing_from one side, and coding_ (suitability to becategorized and connected to the hooks alreadystored in the amount_learned), and the learner'sown forecast_adjustment from the otherside. The flow of waste_ drains the stockof hooks_ under_development at a rate thatis determined by the level of the stock itselfand the waste_ fraction. Waste_fraction isthe product of constraints_ (that include allimpeding factors, whether internal or externalto the student, that lead to waste in the process ofthe knowledge acquisition) and learning_style_incompatibility.

Flow of completing_ takes the hook ofinformation from the stock of hooks_under_development and places them in the stock ofhooks_for_repetition. This flow is under theinfluence of four variables: the level of the directupstream stock, the learner's interest_in_subject, interest_in_grade, and interest_in_use [1]. The learner's interest_in_subjectis represented by a stock and flow combinationwhile the other two types of interest are shown byconverters. It is assumed that the magnitude of the


learner's interest_in_subject may vary duringa lecture period while this is not so for the othertwo.

As shown in the diagram (Fig. 9), a conveyortype stock represents the state of the hooks_for_repetition in the mind of a form learner. Inter-estingly, by assigning different inflow limits andcapacities to the conveyor, different types of form-oriented minds can be detailed and modeled.Subsequently, the flow of repeating_ gets therepeated hooks off the conveyor and stores themin the stock of hooks_in_memory. The flow rate ofrepeating_ is adjusted by the level_of_effortthat the learner puts into the task. The impact_of_other_values (all the remaining task values)reinforces the flow of repeating_. Finally, thesum of total number of hooks_in_memory andprior_knowledge are represented by the amount_learned. Needless to say, all of this entities havebeen already defined in the first part of the study[1].

The other five stocks (shown as boxes in thediagram) are quantity_of_info (given by theteaching system), interest_in_subject, level_of_effort, expectancy_, and level_of_performance. Each of these stocks allows theseparts of the system to have initial values. Thesestocks change in value according to the amount

they receive or lose since their bi-directional flowscan get both positive and negative values.

To simplify the model, only two most importantlearning_reinforcers namely quality_of_teaching (shown on the top right of Fig. 9)and testing_ (shown on the left end of Fig. 9)have been defined in the model. Learning_reinforcers is modeled by a graphical functionof type_of_info and quantity_of_info. On theother hand, testing_ comprises of rote_type,clsd_prbm_slvg, and opn_prbm_slvg compo-nents [2]. In fact the other less important types ofexternal reinforcers have been represented by asingle converter as other_reinforcers [1].

Also, to have a more solid model, two newcomponents,productivity_ andavailability_,have been conceptualized and introduced in themodel. Note that the learner's productivity indicatesthe level of his or her learning effectiveness in theacquisition of new information. It is defined asthe ratio of amount_learned to prior_knowledge(output to input) and, as pointed out, influencesthe learner's performance during the learningprocess. Availability_, on the other hand, hasan important inter-relational role between thelearner's available knowledge and his or herproductivity_ from one side, and the impact oflearning_reinforcers on availability_ (of

Fig. 9. System flow diagram for a form-oriented learner.


the current knowledge) from the other side.Availability_ connects the main chain of thestudent' learning abilities to three importantdimensions of expectancy_, level_of_effort,and level_of_performance.

The remaining components, willingness_,mark_of_desire, perceived_assessment, stu-dent's_ perceived_availability, forecast_adjustment, allocated_time_ factor, target_info and adjustment_fraction, represent theother important characteristics within a teaching/learning system and are defined and detailed inthe List of Equations (Appendix) based on theprevious discussions made in Part 1 and Part 2 ofthe study [1, 2].

FEEDBACK MECHANISMS

Several feedback mechanisms are included inthe model (Fig. 9). Four of these loops have adetermining effect on the resulting behavior of thesystem. Two loops are acting merely in thelearner's ability (to learn) side. One loop is actingin the student's performance side (that demon-strates the impact of subject matter). And the lastloop, which is the largest loop is acting in theteaching system side.

The learner's ability (to learn) mechanismsThe first mechanism acts along the main chain

running from the stock of hooks_under_develop-ment to the stock of hooks_in_memory, and fromthere to the amount_learned and to the coding_and finally back to the flow of taking_. Thislinkage closes a feedback loop in which as theamount of incoming information (lecturing_)increases, the form-oriented learner will takemore and make more hooks_under_development.This leads to a higher rate of completing_ (thehooks and strings of information) and subse-quently, more hooks_for_repetition. A highernumber of hooks_for_repetition, inevitablyincreases the rate of repeating_ and theamount of hooks_in_memory respectively.Amount_ learned will increase and accordinglycauses an increase in the categorizing andcoding_ ability of the form learner. This, inreturn, will facilitate the flow rate of taking_. Thereinforcement of taking_ is one of the feedbackmechanisms included in the model for responding tochanges in amount of incoming information. Thus,the feedback loop starts with an increase in theamount of hooks_under_ development and feed-back to taking_ makes it increase more. Thisphenomenon is the characteristic of a positivefeedback loop that tries to reinforce the process.As stated in the previous sections, when anyvariable in a positive loop changes, the resultinginteractions cause that variable to change furtherin the same direction. The positive loop, in otherwords, characteristically produces self-reinforcingchange (unrestrained growth).

The second mechanism acts in parallel to thefirst one, keeping the same track but diverts fromhooks_in_memory to availability_. Thus, anincrease in hooks_under_development, ultimatelyincreases the hooks_in_memory. The result is anincrease in availability_ (of the information)that gives rise to a higher student's_perceived_availability. A higher perceived_avail-ability, subsequently, decreases the student'sforecast_adjustment. This, in return leads toa negative impact on the flow of taking_ anda subsequent decrease in the hooks_under_development.

Summing up, the loop starts with an increasein the hooks_under_development and the feed-back to hooks_under_development makes itdecrease. This phenomenon is typical behaviorfor a negative feedback loop. As mentioned inthe previous sections, when any variable in anegative loop is changed, then the loop causesthat variable to readjust in the opposite direction.The negative loop produces self-regulatingchanges (controlling and restorative behavior).And so, an initial increase in the number ofhooks_under_development propagates a signalaround the loop, which leads to an eventualdecrease in the level of this stock. The loop thusacts to counteract the initial change.

In summary, it is obvious that the overallbehavior of the learning ability of the learner isalmost the result of the interaction between thesetwo feedback loopsÐa positive feedback loop thatacts in the `coding_' side and a negative feedbackloop that acts in the `availability_' side.

The student's performance mechanismThe other feedback loop that has a major effect

on the behavior of the overall learning system actsalong the student's `performance' side (down to theright of the diagram). This loop may either act as anegative or a positive feedback loop. The way itworks depends upon the direction (or the resultingdirection) of changes in the involving biflow rates.

This loop starts with the stock of hooks_in_memory. Note that an increase in hooks_in_memory, concurrently, increases the amount_learned (by the student). This, in turn, increasesthe student learning productivity_ and avail-ability_ (of the knowledge) respectively. Theresult is reinforcement in the positive direction ofchange_in_expectancy which subsequently leadsto an increase in student's expectancy_ for ahigher achievement. The increase in expectancy_has a direct impact on the student's expectedmark_of_desire, and at the same time, on thewillingness_ [1]. However, if change_in_ perfor-mance and change_in_effort biflows tend to bein the positive directions, then they result in sub-sequent increases in level_of_performance andlevel_of_effort respectively.

On the other hand, mark_of_desire andwillingness_ are the target levels for level_of_performance and level_of_effort respectively.


Therefore, the rate of change in each biflowdepends directly on the difference between thevalue of each reservoir and the value of the corre-sponding target level. Eventhough, an increasein level_of_performance reinforces the positivedirection of change_in_effort which subse-quently increases level_of_effort. The increasein level_of_effort, strengthens the rate ofrepeating_ and generates more hooks_in_memory. Needless to say, the resulting effect is atypical behavior of a positive feedback loop. Asmentioned earlier, when any variable in a positiveloop changes, the resulting interactions cause thatvariable to change further in the same direction.

Two points are worth mentioning. First, thebiflow of change_in_effort is under the influenceof allocated_time_factor. This converter repre-sents the time dimension of the effort that astudent puts into different learning tasks. Second,the biflow of change_in_expectancy is underthe influence of testing_. Note that testing_,as discussed in the previous part of the study [2],comprises of three major types of questions:

(1) rote_type (true/false, multiple choice andshort/long answer questions),

(2) clsd_prbm_slvg (closed problem solving typequestions) and

(3) opn_prbm_slvg (open problem solving typequestions).

The value of testing_ in the model is defined bythe following relation:

Value of testing �� wr � r� wcps � cps� wops � ops

wr � wcps � wops

where

wr � weightpercent of rote type questionswcps � weight percent of close problem solving

type questionswops � weight percent of open problem solving

type questionsr � value of the rote type questions in the

teacher's viewcps � value of closed problem solving questions in

the teacher's viewops � value of open problem solving questions in

the teacher's view

In the base case of the model, it is assumed thata form-oriented teacher represents the teachingsystem. It is obvious that, form-oriented teachersnormally intend to ask questions or take tests withhigher weight percentages of the types of questionsthat they prefer the most (i.e., more rote typeand less open-problem solving type). Conversely,function-oriented teachers normally intend to askquestions and take tests while they give moreweight to the open problem solving and closedproblem solving type questions.

In the meantime, each of these types has its valuein the teacher's view: form-oriented teachers assign

higher values to rote type questions while function-oriented teachers assign higher values to theproblem solving types questions. By assumption,the following values (out of 5) have been con-sidered for each type of question in a form andfunction's view respectively and may be used in thebase model:

Rote typequestions

Closed-problemsolving

Open-problemsolving

Form teacher 5 3 0Function teacher 0.5 3 5

Since both the form teacher and the form learnerprefer the first two types of questions, the better atesting_ represents these two types of question,the higher the expectancy_ of a form-orientedstudent, and the higher s/he sets his or hermark_of_desire. Subsequently, the higher s/hesets his or her mark_of_desire, the better s/heperforms. But as it was mentioned in the counter-acting feedback relationship, the loop also maychange conversely. That is, the less testing_represents the form student's preferred questiontypes (if say, for instance, the teacher is afunction-oriented individual), the lower his or herexpectancy_ for a better achievement and subse-quently, the less his or her mark_of_desire andthe worse s/he would perform.

The teaching side mechanismThe largest feedback loop mechanism acts

along the `teaching_' side (top left) of themodel. This loop, again, may either act as anegative or a positive feedback loop. The way itworks depends upon the direction (or the resultingdirection) of changes in the involving biflows. Thisfeedback loop could be tracked as described below.

The `teaching_' loop starts with the stock ofquantity_of_info. The level of this stock (thetotal accumulation of information presented atany time) is controlled by rate of change_in_quantity_of_info. The biflow of change_in_quantity_of_info may change its direction ineither positive or negative side to regulate thelevel of the stock, based on the amount oftarget_info (as is preset by the teaching systemfor each lecture, here for instance in the basemodel, say it is set as 200 pieces of information)and adjustment_fraction (as is adjusted by theteaching system based on the feedback receivedfrom the student's level_of_performance).

As the level of quantity_of_info increases,provided that type_of_info is at its appropriatevalue for a form learner, thequality_of_teachingincreases. The increase in quality_of_teachinghas its reinforcing effect on the student'slearning_reinforcers and subsequently onthe student's availability_ (of knowledge).The more the availability_, the greater the


expectancy_, the higher the mark_of_desire, thebetter the performance, and finally, the larger isthe adjustment_fraction. This means a higherflow rate of information to the stock of quantity_of_info. (Note that for the sake of having a neatdiagram, the connector that links level_of_performance to the adjustment_fraction is notshown in Fig. 9).

It is worthwhile to notice the role of type_of_info in the teaching_ side of the model. Infact, it represents what is flowing, via lecturing_,from the teaching system to the learning side(learner). The different types of informationwithin a lecture were recognized and classified intwo sets; `main set' and `testing (auxiliary) set,' [2].At this side, the model shows the types ofinformation that include in the `main set' namelymemory_info (memorizing typeÐrote info),relrote_info (relationship type infoÐroteoriented), relreal_info (relationship type infoÐreal), procedure_real (procedure type infoÐreal)and procedure_rote (procedure type infoÐroteoriented). The four types of the `testing set' havebeen reduced to three types and are shown asconstituents of testing_ in the right end of thediagram (Fig. 9). They are part of learning_reinforcers like the quality_of_teaching_and other_reinforcers that were dealt withearlier. The value of type_of_info is determinedby the following formula:

Value of type of info �

� a� wa � b� wb � c� wc � d � wd � e� we

wa � wb � wc � wd � wd:

where

w � weight percent of each type of information inthe lecture presented by the teaching system

a � memorizing type informationb � relationship type infoÐrote orientedc � relationship type infoÐreald � procedure type infoÐreale � procedure type infoÐrote

In the base case of the model, it is assumed thata form-oriented teacher represents the teachingsystem. It is obvious that form-oriented teachersnormally are giving lectures with higher weightpercentages of the types of information that theyprefer the most (i.e., memory type, relrote, andprocedure-rote). Conversely, function-orientedteachers prefer these three types of informationthe less and are presenting lectures with higherweight percentages of relreal and procedure-real.In the meantime, each of these types has its valuein a teacher's view. Form-oriented teachers assignhigher values to a, b and e while function-orientedteachers assign higher values to c and d. Byassumption, the following values (out of 5) couldbe considered for each type of information in aform and function's view respectively and may beused in the base model:

type_of_info Form teacher Function teacher

memory_type 5 1relrote 4 2relreal 1 5procedure_real 1 5procedure_rote 5 1

In general, the last two feedback loops describedabove act on two sides of the model (teaching andlearning) and due to the bi-directional effect oftheir biflow rates, seek eventually either goalmaintaining or a growing pattern. At the sametime, some smaller loops exist in the model thatbehave locally and generate their limited effect onthe system. Consequently, the overall behavior ofthe teaching/learning process is the resulting beha-vior produced by all of the mentioned loops.

BEHAVIOR OF THE SYSTEM

Referring to Fig. 9, and List of Equations(Appendix), it can be seen that the simulationstarts with an initial stock of hooks_under_development at 0 hooks, a prior_knowledge of10 hooks about the subject matter, an initialinterest_in_subject of 0.01 (1%) and an initialquanity_of_info of 0 hooks. The other initializa-tion values are as defined and assumed in the Listof Equations (Appendix). The time horizon for themodel is assumed to be 45 normal minutes, namelythe length of a regular lecture.

As the lecture starts, the flow of lecturing_sends the desired quantity_of_info to the mindof the learner. The form learner begins to receivethe information at the rate of taking_. At thisstage, as each piece of information moves to thestock of hooks_under_development, it will beclassified, coded, and adjusted as well. The stockof hooks_ under_development represents the lear-ner's short-term memory (STM) in real life. To beconsistent with the reality, the model assumes thatsome information is leaked from the stock and hasgotten lost during the information taking processat the flow rate of waste_. As discussed earlier, therate of waste_ is controlled by waste_fraction.Again, as mentioned earlier, the value of waste_fraction is determined by two factors: learning_style_incompatibility and the amount ofconstraints_ . Note that the lower learning_style_incompatibility (say, for instance, bothteacher and learner are form-oriented individuals),the smaller the waste_fraction, the lower the rateof waste_ and the higher is the level of hooks_under_development.

Therefore, as lecturing_ proceeds, the flow oftaking_ sends more hooks to the stock of hooks_under_development. The flow of completing_takes the information from the upstream stockand places them as the completed hooks in thestock of hooks_for_repetition. The rate ofcompleting_ is reinforced by three factors: the


level of student's interest_in_subject (shownas a stock), and the amount of both interes-t_in_grade, and interest_in_use (shown asconverters). If the type of information receivedby the form-oriented learner is compatible withhis or her preferences (almost rote types), thenlearning_style_ incompatibility between theteaching system and the learner would be at itsminimum. Again, the lower the value of lear-ning_style_ incompatibility, the lower thewaste_fraction, and the less is the variation inthe level of student's interest_in_subject.

The stock of hook_for_repetition is repre-sented by a conveyor type stock. The time that ittakes that each piece of information finds itslocation in the episodic memory of the learner'slong-term memory (LTM) has been considered asa variable. The in-flow capacity and transit timefor the conveyor vary for different form-orientedlearners. The maximum inflow capacity for thehooks_for_repetition in the base model isassumed to be at most 20 hooks of information.Also, the transit time (the time it takes that eachpiece of information gets off the conveyor) for theconveyor is assumed to vary. (Refer to the List ofEquations in Appendix)

The flow of repeating_ takes each hook ofinformation from its upstream stock and afterrequired repetition implants it into the student'sLTM (hooks_in_memory) as a permanent trace.The rate of repeating_ is regulated by the stock ofstudent's level_of_effort and is reinforced bythe impact_of_other_values. Note that three ofthe student's perception of task value (interest_in_subject, interest_in_grade, and interest_in_use) have been already defined and modeled inthe diagram (Fig. 9). The impact of the remainingsix values (pride in future profession, self-worth,

security in future job, social obligation, band-wagon effect and association with something onelikesÐas discussed in Part 1 of the study [1]) arerepresented by a single converter for the sake ofsimplicity.

Maximum level of both hooks_under_development and hooks_for_repetition happenbetween minute 8 and 9. This can be found fromFig. 10 (graph of base run for a form-orientedlearner). This fits the reality quite well, especiallywhen one notices the large amount of new infor-mation that is usually presented by the teacherright at the beginning of each lecture. Normally, asthe lecture proceeds, the rate of the presentationof new information decreases and the content ofthe lecture, more or less, is focused around theexpansion of the topics that are presented in thebeginning of the lecture.

The maximum level of hooks_in_memoryhappen at the end of the simulation period and isapproximately about 15 hooks. The maximuminterest_in_subject is about 0.7 (out of 1.0)and again happens at the end of the lecture. Also,the level_of_performance reaches its maximum;60 out of 100, at the end of the period. (See Fig. 10.)

The simulation may be run for the analysis ofother variables as well. Note that Fig. 11 demon-strates a second graph of base run for the other fivemajor variables. As shown in the graph, the flowrate of waste_ reaches its maximum at minute 7and then keeps descending at an almost uniformrate as the lecture proceeds to the end. The reasonwhy the rate of waste_ is at its maximum at minute7 may be found in the large amount of newinformation that is normally delivered by theteaching system in the beginning of the lecture.The sharp ascending pattern of the graph for thefirst 7 minutes fits nicely with what is happening in

Fig. 10. Graph of base run for form-oriented learner (Part I).


the reality. Interestingly, as the teacher gives moreexplanation about the topics (learning objectives),which this usually happens after first 5±7 minutes,the rate of waste_ then decreases.

Two variables, amount_learned and produc-tivity_ follow a common track. Both variablesshow a continuous increasing trend. These twovariables have been defined, simply by using thecognitive algebra concept, as below:

amount_learned � prior_knowledge

� hooks_in_memory

productivity_ � amount_learned/

a prior_knowledge

Note that the simulation begins with prior_knowledge of 10 and hooks_in_memory of 0hooks. This means that the initial productivity_is equal to one. At the end of lecture, the form-oriented learner acquires 14.5 more hooks andconsequently the productivity_ ratio increaseto 2.45.

Also, the flow of taking_ starts at an initial rateof 0.7 hooks per minute and ends at a rate of0.2 hooks per minute. In the mean time, thequantity_of_info delivered by the teachingsystem starts at 0 and is accumulated at the finallevel of 200 pieces of information by the end of thelecture. The patterns of behavior of these twovariables over time seem very promising. As thelecture proceeds, the learner gets more detailedinformation about the topics at hand, becomesmore familiar with the subject matter, and con-sequently adjusts (reduces) his or her rate oftaking_ accordingly.

As mentioned earlier, the behavior of any othervariable can be simulated and tracked on thesimilar graphs (or tables). The graph of base run

in Fig. 10 shows the behavior of all of the variablesinvolved in the simulation model over 45 minutesof a typical lecture period. The interested readercan refer to this table and observe how eachvariable within the base model changes valueminute after minute.

EXPERIMENTAL RUNS

A number of experiments were carried out withthe simulation model in line with the step 4 and 5of system dynamics method [1]. The intention wasto examine different policy alternatives and deter-mine which policies show the greatest promise. Thealternatives were chosen mainly from the experi-ence of the analyst and also from intuitive insightsgenerated during the first three stages of the systemdynamics. Although, in a complex system liketeaching/learning, there would be many competingcriteria for defining failure or success, neverthelessdifferent scenarios of favorable performance mightbe identified. In addition, the better alternativebehaviors would often come from changing thesystem base structure.

To be concise, only four experiments arediscussed in this section. These simulation experi-ments were carried out to gauge the effects ofprior_knowledge, memory_info, and rote_type(questions) as policy variables on the learningbehavior of the form-oriented learner. All ofthese variables have been chosen intentionally.Prior_knowledge represents one of the student'strait variables in the model, while memory_infoand rote_type represent the characteristics ofsubject matter and teaching system respectively.

. Experiment 1: A sensitivity analysis was made ofthe student prior_knowledge for 10, 20 and 30

Fig. 11. Graph of base run for form-oriented learner (Part 2).


hooks of information to gauge its effect on therate of completing_ (Fig. 12).

. Experiment 2: A sensitivity analysis was made ofthe memory_info for the weight factor of 5, 10,and 15 to gauge its effect on the productivity_of the form-oriented learner (Fig. 13).

. Experiment 3: A sensitivity analysis was made ofthe memory_info for the weight factor of 0, 5,and 10 to gauge its effect on the level_of_perormance of the form-oriented learner(Fig. 14).

. Experiment 4: A sensitivity analysis was made ofthe rote_type (questions) for the weight factorof 0, 5, and 10 to gauge its effect on the student'sexpectancy_ for a mark_of_desire (Fig. 15).

Effects of other policy variables like interest_in_subject, learning_style incompatibility,quality_of_teaching, level_of_effort, andother_reinforcers have been investigated aswell. However, the discussion of results of theabove four experiments (next section) wouldsuffice and serve the purpose of this study.

Results of experimentsTo examine the results of the above experiments,

the data at four points of interest (minutes 11.25,22.5, 33.75 and 45.0) were extracted from Figs 12,13, 14 and 15 respectively, and tabulated as shownin Table 2. The similar results of the base run arealso included, so then the changes in the learning

Fig. 13. Comparative graph for experiment 2.



`behavior' of the form-oriented learner would bemore obvious.

Rate of completing_, productivity_, level_of_performance, and expectancy_ are taken asthe measures of change in the behavior of thesystem. These choices look reasonable as every-thing runs on the rate of acquisition of knowledge(here, in this case, on the rate of completing_ newhooks of information in the memory). Besides, thelevel of the acquisition of knowledge could beevaluated based on the productivity_, level_of_performance, and the expectancy_ of theform-oriented learner (for his or her mark_of_desire).

The results of Experiment 1 indicate that, thehigher the initial level of prior-knowledge aboutthe subject, the lower the student's rate ofcompleting_ would be. This means that a form-oriented learner with more prior_knowledgeabout the subject at the beginning of the lecture,is more `efficient' in absorbing the new incomingpieces of information and hence, is more relaxed inprocessing the information (here, read it as: slowerin the rate of completing_ hooks of informationin his or her memory).

The difference in the rate of completing_ ismore evident at the beginning of the lecture. Asshown in Fig. 12, for all of three runs, the rate of




completing_ reaches its maximum in the first tenminutes of the lecture and then keeps decreasingfor the rest of the lecture. Note that this patternof behavior is quite consistent with what happensin reality in the teaching/learning environments.Upon beginning a lecture, the teacher usuallystarts with the presentation of the topicsand introduction of the learning objectives.Then, s/he uses the rest of the time of class, toexpand around each topic and to go into thedetails. The student, on the other side, knows wellthat s/he must build more hooks of informationin the beginning to hang the other informationincoming later onto them. (Refer to Part 2 of thisstudy, Figs 3(a) and (b) and see the example shortlecture experiment that shows how a form-oriented learner treats incoming information inthe beginning of the lecture [2].)

Comparing the values of completing_ atminutes 11.25, 22.5, 37.75, and 45 implies anotherfinding. With a prior_knowledge of 10 hooks(base run), a student has a harder job to do incontrast with a student with a prior_knowledgeof 20 or 30 hooks. In fact, as the prior_knowledgeabout the subject increases, the rate of com-pleting_ shows a more promising pattern ofbehavior. For instance, the rate of completing_for a student with prior knowledge of 10 (Run 1in Experiment 1) varies in a larger span than ofthe student with a prior_knowledge of 20 (Run2 in Experiment 1) or 30 (Run 3 in Experiment1). This can be seen in the diagram of Fig. 12.The rate of completing_ for Run 1, starts at 0 inthe beginning, reaches its maximum (0.50) atminute 7, and ends up with 0.21 hooks per

minute at minute 45. Compare these values withthe values of completing in Run 3. Here, the rateof completing_ starts at 0 in the beginning,reaches its maximum (0.18) at minute 8, andends up with 0.15 hooks per minute at minute45. What are the differences? The form-orientedlearner in Run 3 has an average completing_rate of about 0.15Ð0.18 hooks per minute overthe whole period of the lecture except for the firstfew minutes, (which is normally expected). This,of course, may be interpreted as less pressure onthe student's mind and more stable behavior inthe process of knowledge acquisition. Run 2shows a similar pattern to Run 3.

On the other hand, according to the results ofExperiment 2, as the teacher puts more value onthe memory_info and delivers a lecture with ahigher content of memory type information, theform-oriented learner's productivity_ would behigher. As shown in Fig. 13, doubling thememory_ info content (from 5.00 to 10.00)would result in, more or less, about 10% increasein the student's productivity_. Even anotherincrease (this time 50%) would give a betterproductivity_ (Run 3 in Table 2). Again, thisfits very well with the reality if one notices that aform-oriented learner is highly productive when s/he receives information in his or her type ofpreference. Worth mentioning is that if theteacher uses other rote type information likerelrote_info and procedure_rote in his orher lecture, the pattern of the behavior wouldbe similar to that shown in Fig. 13. Conversely, ifthe teacher gives a lecture with more stress onrelreal and procedure_real, the form-learner

Table 2. Results of sensitivity analysis

Measure of behavior Minute 11.25 Minute 22.5 Minute 33.75 Minute 45

Base run (prior_knowledge � 10.0)completing_productivity_level_of_performanceexpectancy_

0.461.454.970.01

0.311.8859.600.05

0.242.19

38.380.23

0.212.45

51.440.66

Experiment 1 completing_prior_knowledge: Run 1 � 10.00Run 2 � 20.00Run 3 � 30.00

0.460.260.18

0.310.230.17

0.240.210.16

0.210.180.15

Experiment 2 productivity_memory_info: Run 1 � 5.00Run 2 � 10.00Run 3 � 15.00

1.461.651.73

1.902.122.32

2.202.482.73

2.452.752.98

Experiment 3 level_of_peformancememory_info: Run 1 � 0.00Run 2 � 5.00Run 3 � 10.0

4.904.975.05

7.709.60

14.0

16.037.3344.0

42.051.4475.0

Experiment 4 expectancy_type_of_info: Run 1 � 0.00Run 2 � 5.00Run 3 � 10.00

0.080.090.10

0.100.150.38

0.150.501.40

0.0221.303.12


definitely will be in trouble and his or herproductivity_ will decrease.

Experiment 3 is to gauge the effect of the sameinput variable (memory_info) on the student'slevel_of_performance. As shown in Fig. 14, ifthe teacher uses no memory_type_info in his orher lecture, the form-learner's achievement fallsbelow the `passing zone' and is about 42%. Insuch cases, the teacher most likely is a function-oriented individual and the form-oriented studentwill be at risk. In contrast, as the teacher usesmemory_type info with 5 or 10 weight factors,the student's level_of_performance increases to51.44% and 75% respectively. Interestingly, thedoubling of memory_info content (from 5 in Run2 to 10 in Run 3) results in about 50% increase inthe student's level_of_performance. The modelassumes that the continuous assessment of thestudent's achievement during a lecture is feasibleand practical.

Experiment 4 is complementary to Experiment 3and demonstrates the effect of different types oftesting_ on the student's expectancy_. Testing_could be occasional short oral questions during thelecture or a written short quiz. The important issueis the type (orientation) of testing_. If the teacherasks no rote_type questions (memory orientedyes/no, true/false, short/long answers qestions) inhis or her testing_, the form-oriented learnerpresumes a lower level of expectancy_ for success(in getting a passing grade). In this case, theteacher most likely is a function-oriented indivi-dual and hence, the form-oriented student wouldbe definitely at risk. Apparently, as the teacheruses rote_type questions in his testing_, say forinstance at a weight factor of 5 (Run 2 of Fig. 15),then the student's expectancy_ rises considerablyand results in a higher mark_of_desire accord-ingly. Furthermore, if the teacher doubles theamount of rote_type questions (Run 3 of Fig.15), the student's expectancy_, more or less,increases by 150% (Table 2). Once more, one canobserve the role of different types of issuinginformation by a teacher; whether they are partof `main set' or `auxiliary' (testing) set (as definedin Part 2 of this study [2]), on the student'sachievement.

LEARNING MODEL OF A FUNCTIONLEARNER

Description of the base model for a functionlearner

As mentioned in the beginning, the system flowdiagram for the learning process of a function-oriented learner is the same as Fig. 9 except for themain chain of the model. (Refer to Table 1:Defined variables for the proposed models ofteaching/learning process.) To be brief and toprevent mentioning repetitive material, in thissection, only the main differences are discussed.

The main chain of the system flow diagram forthe learning process of a function-oriented learneris shown in Fig. 16. The definition of each variableexcept for the main chain is the same as describedin the List of Equations (Appendix). The definitionof each variable in the main chain is given as thefollowing.

Referring to Fig. 16, the main chain infrastruc-ture represents a sequence of stages throughwhich the information flows in the mind of afunction-oriented learner. Note that the specificnature of flows varies, depending on the specificsituation of each stock. The chain is fed by asingle flow (taking_). A non-conserved system isdemonstrated by the stock of relationships_under_study. The cloud on the left hand side ofthe flow of taking depicts the boundary of themodel. It represents an infinite source for thetaking flow, as shown. (Again, for the purposeof this model, it does not matter what is in thecloud.)

In this model, flow or taking_ is receiving eachpiece of the incoming information from the teachingsystem and placing it into the mind of the function-oriented learner (stock of relationships_under_study). The flow of waste_ drains thestock of relationships_under_study at a ratethat is controlled by the level of the stock itself andthe waste_fraction (not shown in the diagram).

As shown in the diagram, an oven type stockrepresents the state of structures_to_form in themind of a function-oriented learner. Two interest-ing points are worth mentioning. First, by assign-ing different capacities and fill time to the oven,

Fig. 16. Main chain of the system flow diagram for a function-oriented learner.


different types of function-oriented minds can bedetailed and modeled. Capacity tells how muchinformation the oven can hold. The oven will closeits doors and begin processing its contents whencapacity is reached, or fill time is expiredÐwhich-ever comes first. Note that both capacity and filltime may be assigned small or large values, and so,make the analyst's job easy or difficult. Second,oven cook time (processing time) can be set to aconstant or it can be made variable. In so doing,different situations can be defined for a function-oriented learner. For example, if the teacher is aform-oriented individual and delivers memory-type information rather than relationship-typeinformation (which is the student's more preferredtype of information), the oven can be set to uselong fill times and small capacity to representcapacity constrained situations.

Finally, the flow of finishing_ completes thelearning task by taking each would-be-structurefrom the stock of structures_to_form andplacing it into the stock of structures_in_memory. The flow of finishing_ is under thedirect influence of the amount of the structures_to_form and level_of_effort (not shown in thediagram). In other word, acquisition of knowledgeis viewed as student effort-based activity as well.The function-oriented type student acquiresknowledge when s/he puts effort into the learningtask over a certain period of time (as defined).

Feedback mechanismsThe same number of feedback mechanisms as

was discussed for the model of form-orientedlearner are included in the model. Similarly, twoof these loops have a major effect on the resultingbehavior of the learner. Also, as discussed earlier,both of these loops act in parallel along the mainchain, running from the stock of relationships_under_study to the stock of structure_in_memory, and from there each diverts in a differentdirection. For the sake of brevity, the material willnot be repeated here.

Behavior of the systemThe behavior of the system is the same as dis-

cussed in the previous section for the form-orientedlearner. By assigning initial values to each of thestocks and converters, the simulation model maybe run. The initialization values could be definedand assumed in the same way as described in theList of Equations for the form-oriented learner(Appendix). The time horizon for the model isassumed to be 45 minutes, that is, the length of aregular class lecture.

The only main difference between the twomodels is the nature of the pieces of informationthat is flowing through the main chain. In the caseof a form-oriented learner, the nature of know-ledge was based on the hooks of information. Incontrast, in the case of a function-oriented learner,the nature is based on the structures of informa-tion. The STELLA model has properly taken

care of this difference. The use of a conveyor-type stock in the form-oriented case and an oven-type stock in the function-oriented case, accountfor this major difference.

ASSUMPTIONS AND SIMPLIFICATIONS

The proposed form-function model of teaching/learning in this study is the first attempt in a chain ofmodels that may evolve from this study later. Thestructure of the present model provides a principalbackbone for the future models that necessarily willhave more complicated components and linkages.However, while the present model includes all themajor variables of a teaching/learning process, it isfounded on a few assumptions to maintain itssimplicity at this stage. These assumptions as wellas simplifications are as follows:

1. Because of the imprecise non-physical nature ofa teaching/learning process, any attempt tomodel this process in a quantitative mannermust be influenced by the subjective experi-ences, backgrounds, and beliefs of the modeler.Therefore, in the system dynamics model pre-sented here, one must expect a degree of sub-jectiveness in the selection of variable valuesused in the equations. The values are based onthe `best judgment' of the authors. Clearly, anyother researcher might end up with a differentset of values. This in no way invalidates thiswork.

2. Since modeling is an emerging process, any`model' represents only one of a sequence ofmodels, that provide insight to the situation andform a basis for continued evolution. Themodel worked on in this study is presented inthis spirit. This model is to be viewed as avehicle that can be used to identify the impor-tant dimension of form-function orientationfor implementing policies and tracing theresulting behavior of a teaching/learningprocess.

3. The focus in the proposed model is mainly onthe learner or learning side of the system. Thereason can be seen in the fact that the twoother sides of the system (teaching system andsubject matter) have complementary roles in ateaching/learning system and serve the learningside. Hence, the characteristics of the teachersystem and the subject matter are not definedand detailed like the learning side in the pro-posed model. Each of these sides should bedetailed and worked out in a sub-model withits characteristics' constituents.

4. The obtained results are valid only for theparticular student under the conditions andlimitations defined in the boundary of thesystem. Each individual student, whetherform-oriented or function-oriented, has his orher particular traits that in similar situations


may give or not give rise to identical pattern ofbehavior.

5. The only student's task value that is representedby a stock-flow combination in the proposedmodel is interest_in_subject. The two othermajor student's task values namely, interest_in_use and interest_in_grade have beenintroduced by simple converters. Although, itis assumed that these two values remainconstant during the time of study (i.e., duringa 45 minutes normal lecture), nevertheless, thisassumption is not so far from reality. Consider-ing their negligible change in short-term, thesevalues can not vary much to any extent during alimited lecture period.

6. Also, all of the other values (pride in futureprofession, self-worth, security in future job,social obligation, association of the task withsomething one likes, choice of subject, andbandwagon effect) are presented with a singleconverter (other_values). Each of thesevalues is a complex variable that demands tobe defined separately and be assigned anappropriate weight factor. Needless to say,some of these variables have reciprocatoryinter-relationships with each other.

7. Willingness_, despite its complexity, also hasbeen represented by a single entity. This majorlearning driver should be demonstrated inits own stock-flow combination. To reducethe weight of this inadequacy in the presentmodel, willingness_ is defined as a graphicalfunction and is represented by a graph thatis a function of changes in the student'sexpectancy_.

8. Only two external reinforcement factors,quality_of_teaching and testing_ (methodof assessment) have been defined in the model.The other five factors (institutional factors,nature and content of the task, feedback fromthe teacher, satisfaction with the university, andinterpersonal relations) are represented by asingle converter (other_reinforcers). In amore complete model of teaching/learning,these factors should be represented by separateentities. Also, the interactions between thereinforcement factors themselves have notbeen shown (i.e., effect of quality_of_teaching on testing_ and vice versa). How-ever, the effect of these interactions in the shortterm (during a lecture period) is minor and maybe neglected.

9. `Knowledge' is the sole content of all of theflows and stocks that are located on the mainchain of the model. It is assumed that the unitof knowledge taking, knowledge processing,and knowledge storing for a form-orientedlearner is well represented by `hooks ofinformation.' On the other hand, the unit ofknowledge taking, knowledge processing, andknowledge storing for a function-orientedlearner is assumed to be well represented by`structures.'

Other miscellaneous assumptions and simplifica-tions that have been made include but are notlimited to: absence of some environmental vari-ables in the model; continuity of testing_; intro-ducing productivity_ (that seems somehow inconflict with the basic concept of productivity);availability_ (that does not seem to be a perfectterm for the concept it represents); simpleapproach to the definition of amount_learnedand some other minor items.

SUMMARY AND CONCLUSION

The modeling effort made on the learningprocess in this study is a unique combinationof educational metrics and engineering simula-tion programs. On the one side, the workconsists largely of inferences drawn from avail-able educational experience and viewpoints withan absence of a defensible, universal mechanism.On the other side, it heavily relies on a series ofactivities drawn from a methodology of systemdynamics to build a solid engineering frameworkfor the reinforcement and improvement of theprocess.

The sensitivity analyses discussed earlier inthis study, demonstrate that the behavior of theproposed model seems quite persuasive andpromising. At the same time, the four exampleexperiments attest the strength of the systemdynamics approach in predicting changes inbehavior of a learner due to using differentpolicy actions.

Two dynamic models of teaching/learningworked out by this study are based on continuousphase-type movement of information from theissuing origins (different types of teachingsystems) to the receiving destinations (differenttypes of learners). The main result from themodels reveals that the advance knowledgeabout the types of teachers and learners (form-function orientations) warrants an efficient re-engineering of the teaching/learning system. Inother word, the types of learners and teachers,whether they are form-oriented or function-oriented, has a major impact on the performanceof the system.

The important characteristic of the methodol-ogy used here is its power to show the insight ofthe system or the understanding of what ishappening in the system. As one can observe,unlike methodologies that focus only on an idealfuture condition for a system, system dynamicsreveals the way one arrives at the present andthen, in a later step, the path that leads toimprovement.

The simulation tests described in this study,determine which policies show the greatest promiseand how the study can work toward a consensusfor implementation of the policies. Influence of acombination of two or more policies on the


behavior of the system can be examined as well.For instance, in the model of a form-orientedstudent, a learner at prior-knowledge of 20 inter-acting with a type_of_info of 10 (issued from theteaching system) can be taken as an alternativeoption. In general, by comparing the resultingbehavior of the learning system under differentoptions, the most appropriate policy or course ofaction can be identified. This step would eventuallydirect the study to the last step of system dynamics[1]. In fact, this study is now at a position that canmake a conclusive statement related to the resultsof the experiments. The conclusive statement willclarify the standpoint of this study on how one canimplement changes in the policies and structure ofa teaching/learning system for the purpose of itsimprovement.

One can thus conclude that: the base model for ateaching/learning system and all of the experimentsperformed by the study on the base model, werestrongly under the influence of the form-functiondimension of the learners and the teachers. Thisdimension is so powerful that it has a primary rolein analyzing any teaching/learning process.

The intensive literature search by this studybears witness to the many dimensions and aspectsthat exist in the field of teaching and learning.However, what this study has done is to highlight adimension that by itself takes into account all ofthe other dimensions (i.e., lecturing, discussion,demonstration, etc.).

ImplicationsThis study can help decision-makers select a

performance parameter that will optimize a givenpolicy variable in a teaching/learning process.The effect of system configuration (form-functionorientation of individuals) on the performance ofthe system can be used to influence the design ofthe system before the planning stage is imple-mented. This information is critical in developingan efficient system in both academia and industry.

For technical learning it is extremely importantthat the learning structure emphasizes function-learning orientation. The required degree or inten-sity of the function-learning orientation for eachtechnical discipline may be considered as an inter-esting area of research. The field of engineeringeducation has the necessary and sufficient capacityfor further investigation in this area. Besides, inother fields, analysts and researchers have to find asimilar measure (or measures) regarding to whatextent the learning structure should emphasize onform-orientation.

Lastly, with the discovery that this study hasmade, it is predictable that the education andindustry sectors, in general, develop a more cost-effective human resources strategy on the one side,and higher quality products on the other side. Thechallenge is that each organization starts from itsown employees and examines their form-functionorientations to specify whether they fit the natureand requirement of their particular jobs or not.

REFERENCES

1. N. Eftekhar, Strong D., and O. Hawaleshka, Towards dynamic modeling of a teaching/learningprocess: 1Ðthe unified theory, Int. J. Eng. Educ., 12, (6), 1997.

2. N. Eftekhar and D. S. Strong, Towards dynamic modeling of a teaching/learning system 2: formsand functions, Int. J. Eng. Educ., 14, (6), 1998.

3. Barry Richmond et al., An Introduction to System Thinking: STELLA Research. HPS Inc., NH(1996).

4. S. Peterson and B. Richmond, STELLA Technical Documentation, HPS, Inc., NH (1996).5. N. Eftekhar and D. S. Strong, Dynamic modeling of a learning process, Int. J. of Eng. Educ. (Full

paper is available on: http://www.ijee.dit.ie/articles/999995/article.htm)


APPENDIXList of equations


Nassereddin Eftekhar is a professional engineer who received his Ph.D. from the Mechan-ical and Industrial Department at the University of Manitoba in Winnipeg, Canada. Heholds a B.Sc. in Chemical Engineering from Abadan Institute of Technology, Iran, and anM.Sc. in Industrial Engineering form Sharif University of Technology, Tehran. His maininterest is in systems analysis (system modeling simulation).

Douglas R. Strong is a professional engineer and is a professor in the Mechanical andIndustrial Engineering Department at the University of Manitoba, Winnipeg, Canada. Hereceived his Ph.D. from the University of Toronto in 1976. His primary research interest isin the analysis of manufacturing processes using modeling and simulation techniques. Hiscurrent research work is in the field of cost analysis of the manufacturing and serviceindustries which is supported by several industries.


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