A Concept Model for Learning.

C. VAN DIJKUM [1]

An attempt to define a proper relations scheme between instruction and learning, and to establish the dynamics of learning in relation to modern political concepts as study-fairness

For years, it has been attempted within educational science to establish the process of learning. A lot is known about instruction, but as to learning and acquiring knowledge and insight, we still know very little. A lot of research is conducted on methods of instruction, but very little on learning with learning tools. In this article, an attempt is made to do so. Discussions should then be: how can a learning process be turned into a model? And, how can learning be modeled? First, there should be a conceptual model with the basic entities and the relations between them. Recently, a committee of the Ministery of Education and Science introduced the political concept "study-fairness," an extra reason to lay down the points of application of these concepts in a larger, meaningful context and an understandable model so that each concept can be applied in the overall learning process. In this article, we want to construct a clear and irrefutable model, an analogon, to describe the phenomenon of learning. This mi ght, in the long run, help us identify the fundamentals of learning. We consider learning as a student activity, and instruction, on the other hand, as a relatively static condition. (Not to be confused with the traditional teacher role.)

In this article, we investigated the more dominant relations between a number of modem concepts, which present today's policy makers, educational science, and learning tools technology. Concepts such as study-fairness and motivation should be embedded into a coherent frame so that an unambiguous and consistent model is created that can be reproduced. Designers of learning tools want a qualitative and quantitative insight into learning or, at the least, into learning behavior. In this article, we wanted to find reproducible insights and answers to questions such as: how is it that some learning tools have a motivating effect on a certain type of student? What exactly is learning? How does study-fairness of the curriculum and the learning tools available influence independent learning? How do these matters apply in the learning process? Learning can be epitomized in four words: assessing, executing, and becoming interested, and it always starts by doing something.

Traditionally, little fundamental research has been performed in education: theories on deterministic models that can establish and predict phenomena during learning and instruction. Conceptual learning models such as mathematical equations or analogons are rarely seen, in particular. A lot of research is performed in relations between design variables and learning effects in, for instance, teacher-student instruction situations or computer-based learning. However, it cannot always be traced with which one and how much success, not to speak of researchers who express their findings in terms of mathematical models.

We would like to find answers to research questions such as: how can motivation reduce aversion against learning? It appears that motivation to attend "boring" classes increases if good learning tools have been included in the curriculum. If the class offers "differentiated learning tools," it will help the student be motivated to study a subject thoroughly. Then, there are questions such as: which forms of instruction and forms of feedback in simulation are best suited to promote the motivation to learn? Or a more topical question: how can good learning tools increase the study-fairness of lessons? How can study-fairness be increased and, thus, help to eliminate aversion in the learning processes?

Definition: model-driven (computer) simulation (MDS) is an open, interactive learning environment (here)--based on a reality model--whereby the underlying mathematical model will ultimately determine how it will react on an action of a user (here: a learner).

Definition: an intelligence computer cimulation (ICS) is model-driven simulation with a rule base to monitor the dynamic behavior of the model at every simulation step (dt), and gives a special kind of (extra) feedback to the user, besides the usual feedback. (Figure 5).

Definition: a learning model (LM) is an unambiguous, established model or analogon (as yet qualitative) of phenomena (usually knowledge increase) as it occurs when using learning or instruction tools.

Anderson, R.C. (1977) advanced a thesis in the form of a differential equation. It was called a "learning equation." The public, at that time, named it "the knowledge increment" in Atkinson's learning equation. The theoretical basis for it lay in the "broadcast process." It studied how information through the media is transferred, and how information is diffused in a population of N persons. Parameter "a" can be taken as the percentage of the total population that is converted every time the (same) piece of news is broadcast.

If we consider how the acquisition of knowledge or learning takes place, then a curve can be sketched--under influence of instruction or reading of a text--as indicated in Figure 1. Anderson's learning model has been known for years, as described by Anderson (1983). This learning model gives a model-like deterministic description of "learning or knowledge increase." A closer analysis of this model reveals a differential equation of the type: dq/dt=a(I-q), in which I is the input (stimulus), for instance an instruction; output q the actual knowledge, and in particular its level; and dq/dt is the increase of q in time. The "increase" in this equation equals a constant percentage of what remains, that is, what a person still has to learn (I-q). The analogue solution for such equations is not considered here. We want to perform a simulation study (on a PC) and, therefore, the differential equation on its own is already sufficient.

How does the learning process work? How fast do people absorb? Is absorbing the same as learning? Which parameters are responsible for this? Intelligence? The qualitative level of instruction? The goals one sets? How does the process of forgetting work? This figure shows that learning is the accumulation of knowledge, and forgetting is the reverse. We assume that there is an incentive somewhere, or that someone has set himself to target (top figure) (input). This figure is qualitative if we consider these curves quantitatively. We see time constants that are different for each person and in each learning situation, as indicated in the bottom figure.

This model also occurs in the "diffusion comparison" of the "broadcast process" (Vos & Min, 1997), and in the increase of the load and voltage in a capacitor:

du/dt=(1/RC)*(E-u). (Figure 9.)

The feedback model about diffusion by Spada and Kempf (1977) have that same structure. Kommers (1990) describes something similar in his thesis, the model of Anderson's "the architecture of cognition." That model contains the equation da/dt=n-p*a. That is a differential equation. All of these models are characterized by a first-order differential equation in which the increase of the modeled variable (d.../dt) is determined by a stimulus (an input variable, for instance: I, E or n) by a person's characteristics (a parameter) and the actual value of that variable. In Anderson's model, this parameter is called "intelligence" (a, or in our case, 1/RC). If we consider all these models they are, in fact, analogous to each other. This article wants to keep that analogy and proposes, on top of that, a new model. That new model will also contain the parameters of motivation, study-fairness, forgetting, and being able to choose yourself from a differentiated offer of learning and instruction tools (the incentives). S ee also the (stochastic) models of Bush and Mosteller (1995).

Within educational science, electronic learning tools have even more impact. At first, there was only the linear learning tools such as instruction films through TV stations or video recorders. Now there are interactive dynamic, multimedia learning tools on CD ROM, CD-i or the World Wide Web (Web).

A wants to tell B something, or B wants to know something from A. The question is, however, does it work and does B remember everything?

The first one is based upon the idea of "supplying" instructional tools. The second one is a kind of "demand" idea for instruction. It is striking how little we know of the learning effects that these media have on students. Within (traditional) educational science, we know a lot about instruction, but little about absorption, processing knowledge, and acquiring insight. That is, we know little about active learning and the accompanying learning processes, resistance, and how motivational design variables can be anticipated.

Knowledge is absorbed by a student, but when is it easy and when is it more difficult, and how do you get the best results?

Instructional tools are usually tuned to so-called open learning environments. Little is known about the actual way to learn and the way the brain functions. One of the things that is lacking in contacts among researchers is a proper, valid model of learning and the accompanying learning process. We know that good learning tools reduce the "resistance against learning." We want to make that explicit here, and discuss old essential ideas about forgetting" and "remembering" of Meerling. On top of that, we want to discuss new ideas about how to remove resistance to boring lessons by using learning tools--for instance, multimedia computer simulations or games--to create something that other tools can't. Such an approach might bear fruit in the scope of discussions about a "supply of learning tools that is as varied as possible." Only recently, B. Richmond published a paper on the Internet on "content assimilation." The combination of these types of learning tools, together with more traditional boring instructio n tools, might yield successful cooperation. We want to enter this discussion based on a conceptual model; an analogon. For then, everyone knows what we are talking about--in a qualitative sense--and where exactly in the whole process our learning and instruction tools become effective. Then, we can map research variables and conditions (in a qualitative way). We hope to collect qualitative data some time in the near future.

At present, it is not popular to model learning processes. Many educators consider it a waste of time. Schmidt (1998) conducted a study into models, and came across the "modal model," a model that recognizes two components: one component for the short-term memory, and the other for the long-term memory. This model is based on ideas (according to Schmidt, 1998) on forgetting by Ebbinghaus (Schmidt, ORD '98 conference 1998, Enschede). Research into effects of learning and a useful scientific discussion about it are only feasible if the actors and dynamics are clearly set out. With such a model, one can indicate how much learning tools are effective and to where they they lead.

INSTRUCTION VERSUS LEARNING

For years, we tried to understand the process of learning with learning tools such as simulation programs. We know a lot about instruction, but only little about learning and acquiring knowledge and insight. The right balance between open learning environments and instruction is essential in simulation. To start with, there should be a model with the basic issues. This is what this article is trying to achieve. The research should be on how to build a model of the process of learning: how can it be modeled? We want to construct a clear, irrefutable model, an analogon so learn how this phenomenon can be described and, hopefully, to understand it better.

The model should also establish a background about how learning takes place with learning tools. In the recent years--while we were working on learning tools for simulation--we have begun to understand what is actually achieved in students with simulation. Essential is motivation and the drive to further study, rather than knowledge transfer.

Theories on instruction are widely different from theories on learning. Experts in this field, the "learning technologists," have developed good ideas that are often compatible with ideas from the traditional world of instruction: "the instruction technologists." This, of course, has to do with the fact that instruction is the supply side because it has something to offer and learning is acquiring knowledge by the user, the demand side in education. The "demanding and supplying of information" are traditionally two sides of the same coin. Ideologically, however, they are two entirely different fields of science. This becomes obvious when one compares the ideas of Gagne (1965) and Romiszowski (1981) with those of Van Parreren (1978) and Papert (1980). The latter two had student-control as learning paradigm.

In the world of educational technology there are two different fields: that of learning technology and that of instruction technology. Properly speaking, there are designers of learning tools and designers of instruction. It is essential for the understanding of the analyses below that a clear distinction is made between learning tools and instruction tools. In principle, learning tools do not contain any knowledge or very little whereas instruction tools do. In this article the learning and instructional function are clearly separated and analyzed in a different way.

Learning and forgetting; knowledge accumulation and residual knowledge. A student sets a goal. When it has been achieved, the learning stops, and the level of knowledge, skills or insight for which the student set to achieve have been reached.

Our idea starts with proper distinction between the several types of educational software. A clear distinction should be made between learning and instruction tools. Learning tools such as simulation systems have the effect that, given a proper case, the user will acquire a good attitude with respect to the subject and want to continue attending a class or reading a book.

Thesis: There is a big difference between learning and instruction tools.

Thesis: Instruction tools are one-way environments; learning tools are two-way environments.

An example that illustrates this essential difference between instruction-rich and instruction-poor is the classroom for a chemistry practicum: there is no knowledge transfer other than the fact that manuals are studied. Opposed to that is a course on television, where knowledge is transferred when taught in a specific way, though there is little or no interaction. These are the two extremes: learning tool versus instructional tool.

If a simulation functions properly, the user will become motivated to do a further study in a (boring) book or in a (boring) continuation course. Learning tools should be seen as work environments--just like practicums--where you learn how to handle already acquired knowledge. Pieces of the jigsaw will automatically fall into place if all goes well and a proper casuistry is used. In our model, instruction is seen as a "source from which someone can drink."

Thesis: Learning tools should motivate to real learning and further study

The primary goal of a learning tool such as a computer simulation program should be motivation for possible further study in boring books or dull lessons. A computer simulation program should increase insight into a matter. Students should be taught to think in a wider perspective: they should see the cohesion between things. Present knowledge and insights should be strengthened, and the learner should learn to think in terms of conceptual overviews. There is one part of our model that stimulates this motivating process. If motivation is zero, nothing is learned, and if motivation is maximal, people learn fast.

Computer simulation programs "teach by doing." Because one is working on a task or case, one learns. A simulation environment is a "do" and "work" "environment" at the same time. Computer simulation programs and other learning tools are important to organize a curriculum in such a way that students are offered differentiated learning tools. This guarantees the individual student that the right learning course can be followed. They help break the curriculum's or learning program's monotony. It is purely for personal change (optional) and because some students can be better motivated this way (possibly because of the different approach or perhaps because of their visual or auditory preference for the one or the other learning tool).

THE CONTINUATION OF THE LEARNING PROCESS

It has been suggested earlier by Min (1992; 1994) that proper instruction is absolutely essential for a bare learning tool such as "common" simulation programs. There should at least be some good assignments or cases provided with a bare model-driven computer simulation.

Min poses in one of his articles (a testable hypothesis) that learning with a learning tool should be set in motion by proper instruction (texts, pictures, instruction, or video instruction). A well-proportioned learning tool with proper feedback (textual, graphic, and/or dynamic) should advance that learning process.

The following figure actually represents a simplified version of the above complex situation. It shows how a learning process is "set going" by incentives (all kinds of instruction) and "is kept going" by all kinds of feedback such as messages, intelligent video fragments, growing graphs, etc. Learning is obviously a feedback system in which "one learns until the desired level is achieved" (Min, 1992; 1994; 1996).

Thesis: Setting a learning process in motion (with a "bare" learning tool content-wise) takes place (or should take place) by proper instruction (in the form of assignments, booklets, cases, self-instruction, etc.).

Thesis: Keeping a learning process going (with a content-wise "bare" learning tool) should be achieved by proper textual and graphic feedback.

Input and output process for a learning process that should be kept going. Schematic idea about "parallelism" and the "Pi-theory" of Min on the input side and on the output side of a "learning process." On the input side of a learning environment, a lot of instruction types and/or formats are possible and, on the output, a lot of model-driven feedback forms are possible. The following rule applies to all designers: the asynchronic simulation processes on the "input side" and on the "output side" of this learning environment all need to be in the user's view, and must be presented parallel (Min, 1994).

A poor and non-intelligent learning tool can never keep a learning process going. If one has scored sufficiently, a new challenge should be presented in the form of an assignment or a case. We then go around in a full cycle. An instruction will then be "input" for the learning process, and the output on an intervention into a learning tool is feedback on the action of the learner.

Definition: Parallelism is a concept that is applied by designers of work and learning environments. As much information as possible (and desirable) is presented as large as possible. Everything can be compared to everything else and the (brief) memory of the user does not need to be consulted. (The automatically large screen of SUN computers and control rooms of operators illustrate this).

Definition: The Pi theory is a design theory which--from cognitive psychology--offers an explanation of why the concept of parallelism is essential in combined learning and instruction tools. (Looking back, this theory can explain why MS-DOS computers failed as learning tools for the greater part.)

LEARNING MODELS

In 1992, Min carried out a pilot research project into "learning models" (LM) in computer simulation.

One of the five "learning models" for a qualitative idea of how students learn in simulation learning environments

Such an LM is not identical to a "model for learning." It has set the concept aside for something quite different. That is why in this article, we have systematically used the description, "a model for learning," or rather, "a model in respect of learning." Mm presents five learning methods that can be applied in learning with computer simulations. These methods are: (a) discovery learning, (b) learning by doing exercises, (c) guided discovery learning (with intelligent computer simulation; ICS), (d) problem-oriented discovery learning (similar to problem solving), and (e) learning by doing--scientific--experiments (Min, 1992).

At the time, he distinguished five educational types of usage of (model-driven) simulation programs (also acquired by research) and, thus, there were five types of learning, too. Those models were called LM. Those five models had been drawn up based on observations of learning behavior. The experiments were carried out in observation rooms at Educational Science. They were filmed by three video cameras, and 20 test persons participated. Analyses of the tapes took one year. Through those, the qualitative learning models could then be converted into quantitative learning models. Later (in 1996), students also carried out a pattern recognition study on the data. It yielded some useful results, but the material has not yet been exhausted. This was reported in 1992 (Min, 1992) (Groenewoud & Ter Burg, 1996) at the Health Education Conference, organized annually by the Dutch Society for medical education. However, it seems that there are similarities between the conclusion then and those of the present in this proj ect of how to draw up an analogon of learning. In the future, we hope to be able to illustrate the similarities between those two different approaches. For the present, there seems to be two different opinions. If we match it with ideas, the current diagrams are, in fact, feedback systems--which can be proven--then it should be quite possible to find those similarities. See in this respect, the pictures and text in the educational material of the course, "Systems approach in educational science," by Vos and Min (1997).

Definition: A learning model (not to be confused with a "model for learning") is a currency diagram in which the behavior of a learner who uses simulation programs can be recorded (however not explained) (Min, 1992).

A RESISTANCE-NETWORK AS A MODEL

Our thesis (hypothesis) is that instruction or an instruction tool can be compared with a voltage supply (or possibly a currency supply). The student can be compared to a control system (based on an integrating network) that is active until one knows something or can do it. The student can also be compared to the accumulation of a load in a "capacitor." The integrating network or "capacity" of a capacitor is an "analogon" for "acquiring knowledge" (including concepts such as intelligence or memory). Acquiring knowledge--or in this case, learning--can be compared with the charging of a capacitor or the final process in a feedback system on the basis of an integrating network (with a specific time constant).

The heart of the analogon--the transfer function from input to output--simulated on a PC. The transfer function of this model is of the du/dt=1/RC (E-u) type. You should realize that e=E-u. Here e=IN-OUT. The integrator will go on integrating until e0. At that moment, u=E or OUT=IN. So, this model could be a model for knowledge acquisition.

A slightly expanded model for acquisition of knowledge. Program LEARNING, version 2.0x. You see in this simulation program, in which the model for learning has been included, that there are a number of targets, which the student can set himself. You start at level 5 and choose level (or target) 6, 7, 8 ,9, or 10. In this example, one chose level 5 at the moment in time t=0, and on t=0.1 the target level was 9. (The beginning level of the student was 3.) You can see that the student reaches the levels after a certain amount of time.

Charging a capacitor is actually similar. See the mathematical equation of both systems; they are similar (they are analogous). There is an isomorphy (term found by Ashby, 1956) between the simulation model of a feedback system (that goes on doing something until e=0), the (classical) model for charging a capacitor, and a (conceptual) model of knowledge accumulation, that is, learning. We are aware of the specific limitations of these assumptions, but if you are not prepared to assume something, a model case becomes impossible to draw up. Such models and concepts are dealt with in the course Methodology with stochastic models in the curriculum of TO. Adaptation says that a student learns something every time (on top of what he already knows, that is, all through life one learns, and there is a continuous accumulation). (Vos, 1997)

We first (1994) saw our learning model as a link between a capacitor with a resistance. We think that an RC network is a good analogon for the basic principles in the voltage field between learning with a learning tool and the use of an instructor during that process. In this model, the capacitor is a "model" of the student.

The "capacity" of a capacitor can be compared to brains, memory, or intelligence. Thus, learning can be compared with charging a capacitor. If the capacity is large, then the capacity for learning is large. If the capacity C is small, the capacity to learn is also small.

It is natural that a student feels a certain resistance towards learning. That is the resistance R1. Both "wanting to learn while discovering" and "wanting instruction" are hard work. A learning tool can contain oral instruction, but a manual or an assignment may not always be clear. The resistance against that can be removed by means of a well-designed instruction tool. The resistance R1 represents the resistance that a teacher or an instructor notices in a student.

First type analogon: a capacitor. The student has a certain capacity and wants to learn. Wanting to remember (and therefore learn) is represented by a capacitor C; with a certain capacity for absorption. U is supply: matter (from a book) or instruction (spoken by a teacher). Supply, instruction, and matter are a "voltage" source or a "current" source. However, the transfer function here is of the type du/dt=1/RC (E-u) were R=R1. The instruction or instruction tool is assumed to be a voltage source (E) or currency source in our model. The point here is whether the student is susceptible for the instruction or not. Resistance R1 represents that resistance or reluctance. The reluctance to learn is usually strong. This also indicates that learning tools--such as simulations--begin at R1. Reluctance against instruction, reading, and attending classes becomes less. After a few sessions with simulation programs, the student is more susceptible to attending classes or instruction. (That is our thesis.) The demand fo r learning has grown. The student is crying out for information and/or instruction. He is more prepared to go to certain lengths and read books about the subject of the simulation than before. R2 is the leakage resistance that represents forgetting.

Second type of analogon a feedback regulation system. This is, in principle, the underlying system in learning as described by Scheiblechner and in 1997 by Vos and Min in their lectures for the course, "System approach in Educational Science," (1997) at the University of Twente. The student is offered an incentive and will continue until the difference between the "knowledge in the incentive" and the "knowledge in his head" is zero. The difference in a feedback system always goes to nil. The appropriate curve occurs in many places in social sciences, psychology, and physics. In reality, there is a multitude of stimuli. (See ahead in the text and the figures.) But there is also a multitude of targets and feedback systems. The sum and substance of all this activity and knowledge accumulation is, therefore, learning. If a person sets himself various goals (learning goals, etc.), you can use the term dynamic targets or standards. With single targets (or standards), one can continue to say a static target or norm .

Ditto, as above. This representation is similar to the representation Anderson (1977) gives in his learning equation. His model presents how the learning or knowledge increase could progress in a student in the time given an incentive b, the total material to be learned. For comparison, also see the model of diffusing equations in the broadcast model of Lave and March.

The second resistance--(R2) parallel to the capacitor--is the leakage resistance over the capacitor, and it symbolizes forgetting. The proper use of a learning tool will reduce the resistance against learning and will take effect on resistance R1. A proper instruction in a learning tool is important to get the learning process going. This is symbolized by a (voltage) source (source 1, source 2, or source 3). The model of how learning progresses under influence of the learning tool and instruction can be seen in Figures 12 or 13. Thus, this analogon has become a proper quantitative model for learning.

Summarizing, we can put a number of things that are essential in a learning process, knowledge transfer or knowledge acquisition, opposite their analogous components:

Instruction as a source or voltage supply (source); knowledge accumulation--the learning process--as a feedback system or a capacitor (C); communication as a stream (i); resistance against learning (i.e., motivation) as a resistance (R1); study-fairness as a resistance (in series) (R3).

It follows that Ohm's Law applies here as well. So U=i.R. As a resistance decreases or motivation increases, then learning will be easier. The resistance against learning (i.e., motivation to learn) (as a function of R1 or better 1/R1) can partly be removed by proper learning tools. The study-fairness (as a function of R3 or rather 1/R3) can increase by a proper streamlined management in the curriculum and an adequate and specific supply of instruction and learning tools. When the study-fairness increases and (here) the resistance against R3 decreases, learning will become potentially easier. Ohm's law says that with a certain voltage (U), the currency increases (I) when the resistance (or one of the resistances in series) decreases.

Thesis: Study-fairness is (according to the Wijnen committee of the Dutch government) the task of the universities to enable the student to deal properly and swiftly (with his limited time, incomprehensible timetables, incomprehensible learning texts and learning tools), and they should not make a learning process more difficult than necessary.

Thesis: A resistance to learning occurs when unnecessary barriers occur in the course of a study. Suppliers of education and designers of learning tools should keep the resistance against (their) education and (their) learning tools as low as possible from the very start.

Anderson (1983) indicates in his ACT model (adaptive control of thought) how knowledge (both declarative and procedural) is activated in semantic networks consisting of knots and sources, i.e., how knowledge diffuses. The difference with our model is that there is no (charge-) source, but there are various sources and influences (e.g., learning targets too) who will be interactive and activate one another, enabling complex transfer processes which can be turned into a model. Mathematically speaking, this means that we will come across matrices (Kommers, 1990; Vos, 1997). We will not now explore any further into this direction.

A qualitative model (analogon) about how instruction and knowledge absorption work can be visualized by means of the model from Figure 11 or 12 and reproduced dynamically.

Study-fairness is, in this model, in series with motivation. The higher the study-fairness, that is, the lower the resistance (R1), the better learning will proceed. The higher the motivation, that is, the lower the resistance (R2), the better someone's absorption of useful things (knowledge, information, insight and possibly wisdom). And vice versa, the higher the resistance in R1 and R3 (in series), the worse learning will proceed. Simulation increases motivation for learning of about the same matter from books. R1 and R3 are in series and reinforce one another. This is the same in reality: study fairness and motivation should be added up. The replacement resistance for resistances in series equals R1+R3.

A large (and differentiated) supply of (learning tools). It has been indicated here that a student chooses the instruction tools or knowledge sources. There is an enormous supply. Resistance against the one (e.g., against study fairness) is higher or lower than against the other instruction (or learning tool).

Resistance R1, as detected by the instructor in confrontation with a student, represents the resistance. The second resistance, R2, is the leakage resistance over the capacitor, and it symbolizes forgetting. The article by Meerling (University of Leiden, 1981) deals with a model (from 1880!) by Ebbinghaus, and it strongly stresses forgetting and not so much learning. His model is, therefore, a quantitative model (on an empirical basis) for forgetting rather than a qualitative model for learning, let alone an analogon for learning. Ebbinghaus models the so-called forget curve as pn=pl(1-a)[caret]n-l, where 'pn' represents the percentage of wrong responses, 'p1' represents prior knowledge, and 'a' intelligence, for example. In our view, the quantitative approach research has more or less come to a standstill. Apparently a more complete qualitative model should first be developed. His article suggests accuracy that, in our opinion, is not possible in this way (and certainly not at this stage of model formation about learning). However, the time for reconsidering a qualitative model of learning has come.

DISCUSSION

We shall deal with three models in the discussion: (a) the learning models, (b) the model of learning here proposed, and (c) a new approach of design: the design model.

Learning-models: Groenewoud and Ter Burg (1996) have developed learning models (LM) by Min (1997) in 1995, already. Initially, they were qualitative by nature. Now, he is working to become them more quantitative.

Model for learning: Our model for learning is characterized by an integrated system. It is best to take the analogon as a feedback integrator. It fits quite well and enables us to establish a relation with motivation and study-fairness; something which we have always aimed to achieve. The model with the capacitor, though adequate and simple, should be avoided in order to prevent unnecessary discussions.

The quality level of a product increases in time as well. The OKT model has a feedback loop in which the evaluation (measuring) is the most important part. If you include an evaluation--however small and simple--you secure yourself against risks, as in a system without a feedback like a feed forward system always has. Feed forward systems are quite useless in actuality, when there are interruptions or setbacks. When the measured quality matches the desired quality, the product or the solution are ok. (See literature about the theory of Quality Control of Juran, 1962.)

Design models. Figure 15 shows that design also knows something similar and, therefore, such a model can be established: a model for learning to describe the design cycle, an analogon for design. An educational solution always has (if all is well) a moment of 'measuring' (the evaluation) and a feedback loop which is followed so often until the measured value is equal to the desired value (b). A designer also wants a difference of zero.

A similar control system. The OKT model also has, in principle, the same control circuit as our model. The designing process has a dynamic similar to learning: accumulation of knowledge versus accumulation of the quality of a product (final target). If one turns the OKT model (left) one quarter turn, it becomes a feedback system with a measuring moment (the evaluation) and a feedback loop that is passed so often until the value measured is equal to the desired value (right). A designer (also) wants zero difference. The designer will continue to work on his product or solution until the desired result (goal) is achieved. There, e=o. Then the designer will stop.

Further research should reveal whether this model could offer a plausible explanation for a number of phenomena that are essential to understand in cohesion. It would also help solve the confusion about concepts, actors, and effects.

CONCLUSIONS

This model will need a lot more polishing and it will have to be discussed extensively. The model on design is, as yet, unfinished. The learning models have been investigated most often and are empirically based. The model can be tested online in our system, LEARNING. The influence of motivation and study-fairness (of Wijnen) on learning can be studied. We hope that this idea--and this model--will be of interest to others, and that whoever is active in this field will contribute to the discussion.

(1.) University of Utrecht The Netherlands

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References

Anderson, R.C. (1977). The notion of schemata and the educational enterprise: Schooling and the acquisition of knowledge, pp. 415-432. Hillsdale, NJ: Lawrence Erlbaum.

Bush, R.R., & Mosteller, F. (1995). Stochastic model for learning. NY: Wiley & Sons; London: Chapman & Hall.

Juran (1962, first version). Quality control. MIT, Cambridge.

Gagne, R.M. (1965). Conditions of learning. NY: Holt, Rinehart & Winston.

Groenewoud, U.A., and Ter Burg, J. (1996). Effect van mate van parallellisme op taakuitvoering en gepercipieerd gebruiksgemak. An internal research paper. University of Twente.

Kommers, P.A.M. (1990). Hypertext and the acquisition of knowledge. Doctoral dissertation, University of Twente. ISBN 90-9003937-2.

Mm, F.B.M. (1996). Parallelism in working-, learning- and doing-environments: The parallel instruction theory for coaching in open learning environments for simulation. Proceedings of EuroMedia 96; Telematics in a multimedia environment, Dec. 19-21, 1996; A publication of the Society for Computer Simulation International (SCS) (Eds. A. Verbraeck & P. Geril).

Min F.B.M. (1994). Parallelism in open learning and working environments. Britsh Journal of Educational Technology, (25)2, pp. 108-112. ISSN 0007-1013.

Min, F.B.M. (1992). Parallel Instruction. Educational Computer Simulation. Interactive Learning Intern., (8)3, 177-183.

Papert, S. (1980). Mindstorms: Children, computers and powerful ideas. NY: Basic books.

Romiszowski, A.J. (1981). Designing instructional systems. London: Kogan Page.

Schmidt, H. (1998). Personal communication at the Nationale Onderwijis Research dagen (Educational Research conference) in Enschede, the Netherlands.

Spada, H., & Kempf, W.F. (Eds.) (1977). Structural models of thinking and learning. Proceedings of the 7th IPN Symposium on Formalized Theories of Thinking and Learning and their implications for science Instruction. Vienna: Hans Huber Publ.

Vos, H., & Min R, (1997). Systeembenaderingen in de onderwijskunde (System approach in Educational Science) (courses 1997/98) (in Dutch). Reader, University of Twente, Enschede.

Vos, H. (1997). Methodenleer (Methodology) (courses 1997/98) (in Dutch). Reader, University of Twente, Enschede.