Description
In general usage, complexity tends to be used to characterize something with many parts in intricate arrangement. The study of these complex linkages is the main goal of complex systems theory.
Case Study on Teaching on Managing Complexity Using Complexity Management Tools
Abstract: This paper explains the design of the course: "Introduction to Systems Thinking". This design uses Complexity Management tools from Organisational Cybernetics in order to teach Systems Thinking in general, and Organisational Cybernetics to Manage Complexity in particular. This design attempts to articulate theories, tools, and practices of systems thinking in a context in which students can develop their autonomy. The implementation of this design is a game, which models a social system. In this way, students learn how to make decisions by themselves in a complex environment. Keywords: organisational cybernetics; education on managing complexity; simulating complex environments. Reference to this paper should be made as follows: Lammoglia, N.L., Bohórquez, J.C. and Zarama, R. (2008) 'Towards teaching on managing complexity using complexity management tools', Int. J. Applied Systemic Studies, Vol. 2, Nos. 1/2, pp.95-108. Biographical notes: Nelson L. Lammoglia is a PhD student in Engineering at the Universidad de los Andes since 2003. His current research interest is in building experimental and computational models of social systems in order to strengthen intuition in observing large-scale social systems. Juan Camilo Bohórquez is a PhD student in Engineering at the Universidad de los Andes since 2005. N.L. Lammoglia and he were teaching assistants in the "Introduction to Systems Thinking" course in the Department of Industrial Engineering at the Universidad de los Andes since 2004 until 2007. Roberto Zarama is an Associate Professor and Director of the Industrial Engineering Department at the Universidad de los Andes, Colombia, SA. He received his Doctorat d'Etat Français from the Ecole des Hautes Etudes en Sciences Sociales. He has pursued Postdoctoral studies at the Ecole des Hautes Etudes en Sciences Sociales and Oxford University. He was Professor for the "Introduction to Systems Thinking" course until 2007.
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Introduction
This paper describes an implementation of Organisational Cybernetics in teaching. We have been using this approach while in charge of the course in "Introduction to Systems Thinking" in the Undergraduate Program of Industrial Engineering at the Universidad de los Andes. This tool has been useful in teaching a systems approach to the observation of organisations. Our initial idea was that if we are teaching 'systems thinking', then we are already assessing the fact that there are different ways of 'thinking'. In this perspective, we should design different ways of 'teaching' and select among them. We think that teaching is not simply a process of transmitting information from a source to a target, but rather that it is a process of establishing a context (von Foerster, 1998; Reyes and Zarama, 1998; Zarama et al., 2004). In this way of seeing the process, students should be able to learn by themselves with the guidance of the teacher. Therefore, we understand learning to be an iterative process of structural coupling (Maturana and Varela, 1995) between a system (who learns) and its environment (whom he or she learns with). Bearing this in mind, we needed to align the methodology with the products and conceptual focus of the course. This implied designing an active methodology that employed systems thinking and that would evidence non-systemic approaches in practice. In this sense we wanted that the students, and the course as an autonomous system, would determine, and be responsible, of their own learning process. Here we are not only referring to the autonomy of the individual, but also of the working groups and the course as a whole. Finally, we required that the methodology - as it is indicated later on included activities beyond the time restrictions of the course. Because of the above, we fashioned a design for the course that attempts to:
• • •
articulate theories, tools, and practices (Aristotle, 1998) of systems thinking in a teaching-learning context generate a context where students develop their autonomy set the context in which students learn to use tools to manage complexity.
In order to achieve these goals, we designed the course as a game. This game simulates a social system. Students make their own decisions autonomously, but they are subjected to the rules and purposes of the course. We have implemented this design during each semester since the first semester of 2004. We have observed that we can manage more complexity without losing the cohesion of the course. We have also observed that most of the students learn how to deal with their own autonomy. They also learn how to coevolve with a dynamic environment in order to achieve their own goals. This paper is divided into six sections, which are constructed to show:
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the introduction of the text the reasons for using a game to teach systems thinking the rules of the game the strategies that students may follow to achieve the objectives of the course throughout the game, and the relationship between these strategies and organisational cybernetics
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• •
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a brief discussion of certain observed results some closing reflections.
Background
The purpose of the course is to introduce students to the Systems Thinking approach applied to Organisational Management. To that end, we expose them to several topics in order to guarantee that students have the broadest knowledge of these theories and tools. The contents of the course include: systems thinking theories, systems thinking tools, tools for modelling and simulating complexity, and simulation of social systems through the use of games and experiments. We cover all these topics in an introductory way. Oncoming elective courses deal with these aspects in greater depth. To cover all these contents, an average student should work 280 hrs during an academic period. For this calculation we assume that an average student spends four hrs working on an essay, six hrs programming a computational model and eight hours designing and implementing an experiment. However, as regulated by the university, the academic load that this course may demand from a student is 45 h of class attendance, and 90 h of individual work. This was one of the problematic limitations that we recognised when designing the course. Accordingly, we posed to ourselves the following questions:
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How can we enable the group (as a social system) to manage greater complexity than the sum of the efforts made by each isolated student? How can we lead the group to articulate the practices, tools, and theories of systems thinking? What tools can we ourselves use to answer these two questions?
We found the answer to these questions in organisational cybernetics. One way to manage complexity is to use attenuation and amplification mechanisms to effectively master the action in focus. Thus, we had to establish the context in order to guide students in relating to each other and in producing a social system. Therefore, a student does not have to work 280 h, but n students have to. In this way, we have 90?? n students' working hours to satisfy our requirement of 280 h of individual study. However, we had to guarantee the diffusion of this knowledge. For this, it was indispensable that we build an appropriate environment for students to develop their own autonomy.
"In this framework [cohesion] and autonomy are not opposites (Espejo, 1983). Viable subsystems with autonomy are necessary in order to implement the organizational tasks; in other words, it is necessary to have the 'amplification' provided by viable (autonomous) subsystems to make possible to control of the organization's outcomes. The above discussion suggests that in any viable system there is, in one form or another, a complementary between [cohesion] and autonomy. Thus the problem is to find criteria to make the most out of it." (Espejo, 1989, p.91)
According to the above, we can grant more autonomy for the students, all the while maintaining the necessary cohesion of the course. One can maintain it by means of certain rules. Some of these are not negotiable; students must accept the General
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Regulations of the university, the established topics of the course, the members of the teaching staff, and the transformation function of the points earned in the game into marks. Other rules may change, but they must be obeyed by all the participants in the game, including the teacher's staff. On the other hand, autonomy is granted in those aspects of procedure that make students responsible for their own learning process. One of these is the students' management of their own time. Students may also select which topics they want to focus on in their academic production. Although this latitude could generate failures in the learning process for some students, it may be understood as a tradeoff between thediscursive and practical domains (Giddens, 1986). Students may lose capacity in the discursive domain but gain it in the practical one. To implement these ideas, we had to model the course as a social system. We understand social systems as self-constructed objects (de Zeeuw, 2001) which are observable on the basis of differentiation (Luhmann, 1984). Because of this, a social system continuously produces the border between itself and its environment on its own. When an observer draws the boundary of the social system, he or she observes its structuring properties. Chief among the ideas that allow us to distinguish (SpencerBrown, 1969) social systems are their structuring properties, which correspond to their rules and resources (Giddens, 1986). These rules and resources are continuously produced and reproduced by the social systems themselves. For example, any university can be distinguished by the student-professor relationship which is invariant (Beer, 1993). On the other hand, we understand that games are collections of rules and resources, which establish how players are to relate to one another. We distinguish among rules as being constitutive and regulative (Searle, 1992).
"Constitutive rules [...] show the meaning and significance of the recourses required to play a game. There are three types of constitutive rules. [1.] The rules that establish the purpose of the game. [2.] The rules that establish the resources used. These rules establish where, with what, and by whom the game is played. And, [3.] the rules that establish possible action. That is to say, what is permitted and not permitted in the game. Constitutive rules build for a recurrent practice, which generates autonomy to the game and makes it possible for an observer to distinguish the game as well." Regulative rules institutionalize performance. [...] these are divided into two different kinds. [1.] Strategic [which] indicate specific standards for playing the game [...]. And [2.] Arbitration [which] seek to guarantee the game is being played according to what was institutionalized. Arbitration rules are divided into two kinds as well. [i.] Declarative rules, which establish what is true and false within the game. [ii.] Negotiation or assignation rules, which establish how discrepancies and disputes within the game are to be settled. Notice how the resourceful articulation of these rules is what creates cohesion for the resources to give institutionalism to the game, and also these rules provide for a recognizable practice of the same event due to the same institutionalism." (Bermeo, 2005)
Based on the above, it might be possible to model and simulate a social system into a game. This possibility can be assessed, because games and social systems are observable as self-constructed objects which produce rules and resources that allow them to be distinguished by an observer. In this way, simulating a social system as a game is participating in the continuous production, reproduction, and deduction of the same game
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(Zarama et al., 2004). And players, while playing the game, produce the social system they constitute. Summarising these ideas, we took as our starting point the principle that the demands of the course would be greater than the capabilities of the students. To facilitate this principle, we designed the course so that it would guide students to relate one another, while at the same time offering an environment in which students can develop their autonomy. However, to be effective, students must balance this autonomy with cohesion, which means that they have to act as a coherent whole system capable of handling more complexity than the one that the sum of the efforts of its separate parts could. We also expect that, during the implementation of the game, students will become familiar with the theories and tools of systems thinking on the discursive level. And we also assume that they will learn to work effectively within a complex environment by putting these theories and tools into practice. These are the objectives of the course design.
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The Pensajistan Game
The 'Pensajistan Game' has been implemented during each academic period since 2004. Due to the fact that students may turn in assignments developed during previous periods some, certain variations are necessary to prevent this kind of institutionalisation of the game. The version we are explaining in this paper corresponds to the course designed for the first academic period of the year 2006.
3.1 Context of the game
Pensajistan, Evomod, Pensaquira, URSSA, and Rumanda are States. They constitute the International Community of Nomad States (ICNS). At the beginning of the game, Pensajistan is ruled by the Emperor, who happens to be the professor of the course. The Emperor has signed, along with the other four States (teacher's staff), the 'International Agreement'. This is a series of regulations for international commerce and diplomatic relations among the States. Additionally, he has signed bilateral agreements, subject to the International Agreement. All agreements have rules on how they must be modified. Because of this, ICNS and its constituent States are self-referential systems. The Kingdom of Pensajistan may change its political system if:
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the majority of the people want a democracy or if one of the citizens wants another political regime another State supports the revolution the Emperor's Army is defeated (revolutionaries spend some resources according to the political regime that they want).
In a democratic revolution, the Constitution of the Systemic Republic of Pensajistan comes to power and the citizens (students) govern the State of Pensajistan. That is to say, they may modify all the rules of their own State so long as they do not contradict any international agreement.
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3.2 Constitutive rules 3.2.1 Purpose of the game
We assume that students want to get the highest mark. The university's marking system is numeric, with a discreet rating scale from 1.5 to 5.0 with intervals of 0.5. If a student gets a 3.0 or a superior mark, then he or she passes the course; otherwise, he or she fails. Based on this, Table 1 shows how the mark obtained in the course is related to achievements in the game of Pensajistan.
Table 1 Mark 5.0 4.5 Transformational function Readings achievement h$ 10,000 h$ 10,000 Computational achievement h$ 10,000 h$ 10,000 h$ 10,000 h$ 7500 4.0 h$ 10,000 h$ 10,000 h$ 10,000 h$ 5000 3.5 h$ 10,000 h$ 5000 h$ 5000 5000 3.0 2.5 2.0 h$ 0 h$ 0 h$ 0 h$ 0 h$ 0 h$ 0 Experimental achievement h$ 10,000 h$ 7500 h$ 7500 h$ 10,000 h$ 5000 h$ 5000 h$ 10,000 h$ 5000 h$ 10,000 h$ 5000 H$ 0 h$ 0 h$ 0 Individual achievement h$ 70,000 h$ 60,000 h$ 10,000 h$ 10,000 h$ 50,000 h$ 10,000 h$ 10,000 h$ 40,000 h$ 5000 h$ h$ 10,000 h$ 30,000 h$ 20,000 h$ 0 h$ 60,000 h$ 45,000 h$ 30,000 h$ 70,000 h$ 80,000 Total holons h$ 100,000 h$ 90,000
As Table 1 indicates, students must get five achievements: readings, computational, experiments, individual, and TOTAL holons. The schema implies accumulating as many holons in each cell as indicated in Table 1. The above description suggests that a student must work about one hour to earn h$ 1000. Holons (h$) are the monetary unit within the game of Pensajistan. The holons from readings, computational models, and experiments are earned by doing assignments (products in the game's jargon) corresponding to each one of these types of evaluation. The sum of accumulated holons in these types of evaluation corresponds to the individual achievement. The total holons is the result of adding the individual achievement and the holons earned or lost in the interaction with other students, via commerce mainly, within the framework of the game rules.
3.2.2 Resource rules
The only possibility of economic growth for Pensajistan is to export products (essays from readings, computational models, and experiment results) to the other States of ICNS. Inside Pensajistan it is a zero sum economic game. When a Pensajistan citizen exports a product, the importer pays for it and, besides, according to the product's quality, he or she grants a quality certificate or not.
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3.2.3 Rules of action
The rules of action state how holons can be obtained and accumulated. In this text we will only emphasise the five most important ways to earn and accumulate holons:
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When the revolution proves victorious in Pensajistan, the citizens take control of the State. Thus, they can collect taxes from the citizenry and the corporations they form. With these taxes they can pay salaries. The game allows up to h$ 20,000 from the salaries earned by public officials of the State to be valid for completing any of the course achievements. PRODUCING. When one or more citizens produce a product and export it, they can earn holons for the corresponding achievement and the quality certificate of the product. If a product is exported by more than one citizen, then all of them get the certificate, and the total payment for the product is divided into the number of exporters. To export, exporters must have received all quality certificates of the products which are prerequisites of the exported product, as indicated in Table 2. PURCHASING. When one or more citizens buy a product, they can improve and export it to earn holons (only 10% of these holons is part of the individual achievement) and the quality certificate of the product. In case it is exported by more than one citizen, they will all get the certificate, and the total payment for the product will be divided into the number of exporters. The purchased product must have been previously exported and paid for. SELLING. Citizens can sell their products to other citizens of Pensajistan. For this, one or more citizens form a corporation. To sell their products, they must previously have produced, exported, and received payment for them. At the end of the game, the stakeholders of the corporations receive the dividends of the corporations they formed. These holons add up to the total holons, but not for the individual achievements. ECASIS. In order to evaluate students, they can pay for exams. In this way they transform total holons into individual achievements. There is an exam for each level. These exams consist of 20 multiple choice questions about certain concepts discussed in the course. They have 30 ms to answer each exam. If a student answers correctly more than 80% of these questions, then he or she gets all the quality certificates of the corresponding level.
'Knowledge tree' Products Introduction Systemic On systems Games Complexity Emergence I SLL Quality requisites None None None None None None None Code L46 L47 L48 L51 L52 L53 L54 Products Fractals Six degrees A N.K. Science Networks VSM Struct. Theory Foucault Quality requisites L34 L36 None L47 L41, and L42 L41, and L42 L43, and L44
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Table 2 Code L11 L12 L13 L14 L15 L16 L17
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'Knowledge tree' (continued) Quality requisites Code None None L11, and L13 L11 and L12 L13 and L14 None L21 and L23 L21, and L23 T22, and T23 Inf. Theory L23, and T21 L36 Experiments L31 L31, and L35 E31, and L32 E34, and L33 L35, and L34 L55 T11 T21 T22 T23 T41 T51 T52 E31 E32 None Products Models Introduction Segregation Game of life Daisy World Sand model Fractals Learning Justice E33 None L32 L42 L43 L41, and T41 Quality requisites L43, and L44 None L9, L18, and L16 L19, L15 L36 L46, L45, and L48 L45, and L46 L23 L23,
Code Products L18 L19 L21 L22 L23 L24 L31 L32 L33 L34 Digital mantras Mathematica On complexity Emergence II Learning MAS Trust Causality Recursivity Altruism E34 L41 L42 L43 L44 L45 System/Env. Communication SSM Nexus Complexity
Burning forest L19, or L15
On managing complexity L21
and L22 L35
Daisy world T21, and L24 E41 E51 E52 E53 E54 Trust Networks SSM Daisy world
Communication L42
Table 2 shows the products' codes, names, and quality requirements for producing them. The product code has three digits. The first digit corresponds to the type of product: L for readings, T for computational models, and E for experiments. The second digit corresponds to the product level. The third digit is enumeration.
3.3 Regulative rules 3.3.1 Declarative rules
There are many regulative rules, not all of which need be described for the purposes of this paper. Therefore we shall mention only some of these. Each State is in charge of evaluating the quality of the products exported by students. According to this evaluation, the ICNS States fix the price of the products exported to them and decide whether or not to award the corresponding quality certificate. Additionally, the only valid accounting system is carried out by the Central Nomad Bank and the Superintendent of Securities. Such entities are managed by the teacher's course staff.
3.3.2 Negotiation rules
All controversies between any constituents of the State of Pensajistan are dissolved by the following instances: the Supreme Court of Justice of Pensajistan, the International Court of the ICNS, the chamber of commerce of the International Court, and, finally, by the Council of the Faculty of Engineering.
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4
Individual learning
If students want to be effective at the game and get the highest mark, then they must overcome the following two main challenges:
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managing their own autonomy performing the functions of politics, intelligence, and cohesion, along with learning the adaptation mechanism of the Viable System Model (VSM).
In this context we define autonomy as "the freedom of an embedded subsystem to act on its own initiative, but only within the framework of action determined by the purpose of the total system" (Beer, 1985, p.105). According to this guideline, whenever we let students decide when and what to produce by themselves, we assume that we are building the context in which students can be autonomous. When we designed the course, we believed that it was going to be relatively easy for students to master. However, this proved not to be the case. Managing their own autonomy turned out to be a heavy load for them; it was also not easy for most of them to start producing. It seemed that they needed somebody else to decide for them when and what to produce. As a matter of fact, the main student criticism of the course design was that there are no precise stipulations either for deadlines or for the work to be done. We have also observed that the sooner a student understands the rules of the game, the richer he or she will be. We also found that students concentrate their efforts in the 'here and now'. This implies that they do not carry out actions related to the intelligence function of the VSM. At the beginning of the game, the products exported by the students have no relation to a long-term strategy. Usually they export either the 'easiest' products or those that have bring the highest price. This strategy minimises costs and maximises returns in the short term, but it is not optimal in the long-term. Students typically do not know the prices of the products being exported, but they do know that there is a strong positive correlation between the level of the product and its price. Thus, a level-1 product pays around h$ 2,000, and in general any given product pays: (level + 1)?? 1,000 holons. In that sense, if they want to comply with the Computational achievement (see Table 1), then they can export at least one type-T product from level 1, and three more from level 2. And if they want to comply with the Experimental achievement, then they can export at least three type-E products from level 3. This means that they must have the quality certificates of L15, L16, L18 and L19 (see Table 2) to get the computational achievements, and must have the certificates of L13, L14 and L23 to get the to the same level. However, the most commonly exportedproducts at the beginning of the game are: L11, L12, L17 and L21. This has two consequences that damage their effectiveness in the game:
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this strategy allows one to reach only the achievement of readings, which implies a mark of 3.0 or less in the course the market of these products will be completely saturated, implying that those who produce and sell the products L11, L12 and L17 will only get h$ 500 or less for them because of the over production and the excess of competitors in the national market, while those who produce L15 and L19, for instance, will get profit from a short-term monopoly and may get h$ 1,000 or more at the moment of selling.
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On the other hand, the not-buying-improving-and-exporting strategy is inefficient in the long term. For instance, those who carry out the 'selfish' strategy will have to produce: L13, L14, L15, L16, L18, L19, L23, T11, T21, T23, T22, E31, E32 and E33 in order to reach each one of the achievements by themselves. If they obtain the highest payment for all of these products, they will have accumulated only h$ 40,000 of individual achievement after having produced 14 products! While if, instead of producing level-1 products, they buy them in the national market, improve, and export them, they will be able to accumulate h$ 70,000 of individual achievement, plus some more holons toward the total, after producing only 16 products as follows: L21, L23, L31, L35, L36, L41, L42, L52, L53, T21, T22, T23, T41, E31, E32, E33. This last strategy is clearly better than the first. Nevertheless, during the first half of the first semester of 2006 it was implemented by only five students out of 80! However, this strategy also has a problem. If it were implemented by all students, then it would saturate the market. If that happened, then it would be more difficult to accumulate the total holons. Because of this, it is necessary to implement the coordination function and the cohesion mechanism of the VSM, which will be explained in the following section.
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Systemic learning
Once the citizens of Pensajistan take control of the State, they constitute a higher level of recursivity. Dealing with this factor demands the use of the mechanisms described of viability of the VSM (Espejo, 1989). The members of the State have to deal with two environments: the environment outside Pensajistan (the other member States of ICNS); and the internal environment, that is to say, the citizens and corporations that constitute the State of Pensajistan. Their job in relation to the external environment is carried out through the adaptation mechanism. The main tool which the Pensajistani State can use to manage its external environment is negotiation with other States. During these negotiations, it is possible to lower tariffs, get benefits in products, and arrange fairs, among others. However, all of these negotiations are subject to what Pensajistan can offer. Therefore, the government of Pensajistan has to be capable of:
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knowing the main demands of their citizens generating enough cohesion within the system to be able to satisfy these demands.
For example, commercial fairs have proven to be a main mechanism of coordination and economic growth in Pensajistan. These consist in short periods of time (a day or less when they, altogether, can earn h$ 1,000,000!) during which tariffs may be suspended or products may be given as bonus, or certain rules of commercial agreements may be relaxed. However, other States generally ask for the massive production of certain products in return, and this requires coordination capacity by the government. The cohesion mechanism is observed not only in the capacity to coordinate actions for the purpose of satisfying the requirements of the international community. The game itself requires high coordination capacity among the agents. For instance, during all the academic periods of this course, it has been necessary for the State to invest some money in education, that is to say, hire someone (sometimes a student, sometimes a teacher) to teach the 'poorest' citizens the rules of the game and how to play it. Likewise, the role of
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the State is indispensable in preventing the saturation of a product in the market. To avert this situation, the State can adopt an incentives policy by means of lowered taxes or bonuses to citizens producing for the first time, among other actions. To conclude, even though the design of the game emphasises that each student must be responsible for his/her own learning process, the effectiveness and efficiency of their performance in the game certainly depend on the coordinated action of all players. This requires a higher level of recursivity to deal with the residual complexity (Espejo, 1989) that they are not capable of managing. Students must learn to deal with the complexity of the Pensajistani environment, which is constituted by the other member States of ICNS and the ICNS itself, and with the internal complexity of the system within which they interact and continuously produce and reproduce.
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Discussion
At this point, it is difficult to assess whether this design is more effective than other designs might be, for teaching or learning. It is not the purpose of this paper, however, to demonstrate a measure of learning. We do not have one. In this sense, we are without the means to show the effectiveness of this course design. None the less, we certainly can show certain indications which suggest that we are pointing in the right direction. The results shown below correspond to the first academic period for 2006, during which 88 students took the course.
•
The demand for the course has increased. In 2004 around 40 students were taking the course. 105 students are now inscribed in the course. Currently, "Introduction to Systems Thinking" is the elective course second-highest in demand in the department of Industrial Engineering. The ECASIS outcomes presented in Section 3.2.3 are an indication of learning in the discursive domain. At the beginning of the course eight students took the level-1 and level-2 exams. On average they answer 51.83% of the 40 questions correctly. Following table summarises the results at the end of the course.
No. of students 17 16 96 41 Average (%) 50.00 57.98 70.55 60.83 63.75 45.00
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Level 1 2 3 4 5 6
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These results are satisfactory for us in the sense that these exams are designed to be more difficult than normal. This is because they are earning per hour more holons than they earn producing essays, models, or experiments. Besides, these exams cover all of the contents of the course.
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N.L. Lammoglia et al. Ten students got a mark of 5.0. The most common strategy among them was: L11, L13, L14, L17, T11, L21, L23, T21, T23, L31, L33, L35, L36, E31, E32, L41, L42, L47, T41, L52 and E52. This strategy uses 13 of the 16 products of the strategy shown in Section 4! On average they exported 20.3 products during 15 weeks. Following unlabelled table shows how much a student with final mark x received for their exported products on average. It also shows the Confidence Interval of these payments.
Average payment 3765.89 3234.41 3097.24 2953.46 2942.19 2837.75 2548.91 2688.88 Confidence interval (? = 0.05) (3462.47, 4069.31) (2953.00, 3515.82) (2753.73, 3440.74) (2701.39, 3205.53) (2751.50, 3132.89) (2434.41, 3241.09) (1969.86, 3127.95) (2060.86, 3316.91)
•
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Final mark 5.0 4.5 4.0 3.5 3.0 2.5 2.0 1.5
We can observe that there is a significant difference between payments received by students whose final mark was 5.0 and payments received by the others. One could suppose that this happens because of the quality of the products exported by this group of students. However, statistically there is no difference between payments for products of the same level received by students whose final mark was greater than 3.0. This might imply that the difference in payments received by the group of students with the highest mark is explained by their strategies and not necessarily because of the quality of their exported products. This may be true only for the group of students whose final mark is greater than 3.0.
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Students covered the whole 'Knowledge Tree'. It means that they exported every single product at least once. Students showed a high level of coordination. They were able to design group strategies and put them into practice. The one with the greatest impact was proposed by a Congressman, which granted certificates to all the students in the course for any product already produced by someone. That is, the State bought a product, hired someone to improve it, and finally exported this improved product in the name of all the interested students. This was a very well designed strategy which proved to be extremely effective.
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Final reflections
In this paper we have shown an application of Organisational Cybernetics to the teaching of Systems Thinking and Organisational Cybernetics. The design showed here views the course not as a group of students but as a system. In this sense, it does not add up the capabilities provided by each single student, but instead relates to them as a totality that is
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capable of using adequate mechanisms for the management of greater complexity. At the same time this goal is achieved in an environment where students develop their own autonomy. Students also experience the need to be able to adapt themselves to dynamic environments. Therefore, autonomy is used as an effective amplifier of complexity by the system. In this way each student is able to couple with the environment in order to be effective in a certain domain of knowledge (Zarama et al., 2004). This individual process of adaptation to the environment triggers a co-evolution process which allows for group learning. Because this dimension became real for students, they were able to grasp most of the contents of the course without experiencing an additional burden. Notwithstanding these benefits, students have also shown that they are not well prepared to be in charge of their own autonomy. Even though we assumed this capacity on their part in the initial design for the course, the fact is that this aspect became one of the most relevant challenges that both the students and we had to overcome. Our experience has taught us that autonomy is not a capacity that we may assume will emerge in any case, but instead is one that requires nurture, requiring that we build spaces in which students can learn how to manage and develop it. Just as we explained in the individual and systemic learning section, students tend to optimise their short-term strategies at the expense of long-term ones. Based on this finding, we believe that the design of the game has been an effective tool in highlighting the consequences of these decisions. This is evidenced in the load of additional work that burdens students who did not plan for the long term. As we mentioned in Section 6, it is difficult to assess whether this design is optimal or defective. We do have, however, certain indications which tell us that we are moving in the right direction. We have observed students beginning to deal with their autonomy, thinking strategies, balancing short-term and long-term strategies, and trying to coordinate each other. We have not yet found the way to measure these results in a way that satisfies us, but we seriously believe that this course changes the way in which students think about and observe the world around them. In conclusion, the Pensajistan game shows that it is possible to design new teaching methods that deal with systemic ways to observe the world. Additionally, the game proves that certain aspects of skill that we consider relevant, such as autonomy and management of complexity, require the design of a specific learning process and the appropriate context for the development of these skills.
Acknowledgements
The latest versions of both the course and this paper have been improved through the participation of Jorge Villalobos, Daniel Garcia, and Samira Haddad. We also want to thank our students, without whom this work would not have been viable.
References
Aristotle (1998) Ética Nicomaquea, Editorial Porrua, Mexico. Beer, S. (1985) Diagnosing the System for Organizations, John Wiley and Sons, Chischester. Beer, S. (1993) Designing Freedom, House of Anansi Press Limited, Concord, Ontario.
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Bermeo, J. (2005) Diseño De Juegos En Las Conversaciones Ciudadanas , Unpublished manuscript, Bogota, Colombia. de Zeeuw, G. (2001) 'Three phases of science: a methodological exploration', Systemica, Vol. 13, pp.433-460. Espejo, R. (1983) 'Information and management: the complementary control-autonomy', Int. J. Cybernetics and Systems, Vol. 14, pp.85-102. Espejo, R. (1989) 'The VSM revisited', in Espejo, R. and Harnden, R. (Eds.): The Viable System Model: Interpretations and Applications of Stafford Beer's VSM , John Wiley & Sons, Chichester, pp.77-100. Giddens, A. (1986) The Constitution of Society, Polity Press, Cambridge, UK. Luhmann, N. (1984) Sistemas Sociales: Lineamientos para una Teoría General , Anthropos Editorial, Universidad Iberoamericana and CEJA, Universidad Javeriana, Barcelona, Spain. Maturana, H. and Varela, F. (1995) De Máquinas y Seres Vivos, Autopoiesis: La Organizacíon de lo Vivo, Santiago, Chile. Reyes, A. and Zarama, R. (1998) 'The process of embodying distinctions - a reconstruction of the process of learning', Cybernetics and Human Knowledge, A Journal of Second Order Cybernetics, Autopoiesis and Cyber-semiotics, Vol. 5, No. 3, pp.19-33. Searle, J. (1992) The Speach Acts, Cambridge University Press, Cambridge, USA. Spencer-Brown, G. (1969) Laws of Form, Allen and Unwin, London, UK. Von Foerster, H. (1998) Sistémica Elemental, Ed, Fondo Editorial, Universidad EAFIT, Medellin, Colombia. Zarama, R., Bermeo, J., Lammoglia, N. and Villamil, J. (2004) 'A Latino American Requiem for Stafford Beer', Kybernetes, Emerald Group Publishing Limited, Special Edition, Northhampton, pp.701-716.
doc_573066763.docx
In general usage, complexity tends to be used to characterize something with many parts in intricate arrangement. The study of these complex linkages is the main goal of complex systems theory.
Case Study on Teaching on Managing Complexity Using Complexity Management Tools
Abstract: This paper explains the design of the course: "Introduction to Systems Thinking". This design uses Complexity Management tools from Organisational Cybernetics in order to teach Systems Thinking in general, and Organisational Cybernetics to Manage Complexity in particular. This design attempts to articulate theories, tools, and practices of systems thinking in a context in which students can develop their autonomy. The implementation of this design is a game, which models a social system. In this way, students learn how to make decisions by themselves in a complex environment. Keywords: organisational cybernetics; education on managing complexity; simulating complex environments. Reference to this paper should be made as follows: Lammoglia, N.L., Bohórquez, J.C. and Zarama, R. (2008) 'Towards teaching on managing complexity using complexity management tools', Int. J. Applied Systemic Studies, Vol. 2, Nos. 1/2, pp.95-108. Biographical notes: Nelson L. Lammoglia is a PhD student in Engineering at the Universidad de los Andes since 2003. His current research interest is in building experimental and computational models of social systems in order to strengthen intuition in observing large-scale social systems. Juan Camilo Bohórquez is a PhD student in Engineering at the Universidad de los Andes since 2005. N.L. Lammoglia and he were teaching assistants in the "Introduction to Systems Thinking" course in the Department of Industrial Engineering at the Universidad de los Andes since 2004 until 2007. Roberto Zarama is an Associate Professor and Director of the Industrial Engineering Department at the Universidad de los Andes, Colombia, SA. He received his Doctorat d'Etat Français from the Ecole des Hautes Etudes en Sciences Sociales. He has pursued Postdoctoral studies at the Ecole des Hautes Etudes en Sciences Sociales and Oxford University. He was Professor for the "Introduction to Systems Thinking" course until 2007.
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1
Introduction
This paper describes an implementation of Organisational Cybernetics in teaching. We have been using this approach while in charge of the course in "Introduction to Systems Thinking" in the Undergraduate Program of Industrial Engineering at the Universidad de los Andes. This tool has been useful in teaching a systems approach to the observation of organisations. Our initial idea was that if we are teaching 'systems thinking', then we are already assessing the fact that there are different ways of 'thinking'. In this perspective, we should design different ways of 'teaching' and select among them. We think that teaching is not simply a process of transmitting information from a source to a target, but rather that it is a process of establishing a context (von Foerster, 1998; Reyes and Zarama, 1998; Zarama et al., 2004). In this way of seeing the process, students should be able to learn by themselves with the guidance of the teacher. Therefore, we understand learning to be an iterative process of structural coupling (Maturana and Varela, 1995) between a system (who learns) and its environment (whom he or she learns with). Bearing this in mind, we needed to align the methodology with the products and conceptual focus of the course. This implied designing an active methodology that employed systems thinking and that would evidence non-systemic approaches in practice. In this sense we wanted that the students, and the course as an autonomous system, would determine, and be responsible, of their own learning process. Here we are not only referring to the autonomy of the individual, but also of the working groups and the course as a whole. Finally, we required that the methodology - as it is indicated later on included activities beyond the time restrictions of the course. Because of the above, we fashioned a design for the course that attempts to:
• • •
articulate theories, tools, and practices (Aristotle, 1998) of systems thinking in a teaching-learning context generate a context where students develop their autonomy set the context in which students learn to use tools to manage complexity.
In order to achieve these goals, we designed the course as a game. This game simulates a social system. Students make their own decisions autonomously, but they are subjected to the rules and purposes of the course. We have implemented this design during each semester since the first semester of 2004. We have observed that we can manage more complexity without losing the cohesion of the course. We have also observed that most of the students learn how to deal with their own autonomy. They also learn how to coevolve with a dynamic environment in order to achieve their own goals. This paper is divided into six sections, which are constructed to show:
• • • •
the introduction of the text the reasons for using a game to teach systems thinking the rules of the game the strategies that students may follow to achieve the objectives of the course throughout the game, and the relationship between these strategies and organisational cybernetics
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• •
2
a brief discussion of certain observed results some closing reflections.
Background
The purpose of the course is to introduce students to the Systems Thinking approach applied to Organisational Management. To that end, we expose them to several topics in order to guarantee that students have the broadest knowledge of these theories and tools. The contents of the course include: systems thinking theories, systems thinking tools, tools for modelling and simulating complexity, and simulation of social systems through the use of games and experiments. We cover all these topics in an introductory way. Oncoming elective courses deal with these aspects in greater depth. To cover all these contents, an average student should work 280 hrs during an academic period. For this calculation we assume that an average student spends four hrs working on an essay, six hrs programming a computational model and eight hours designing and implementing an experiment. However, as regulated by the university, the academic load that this course may demand from a student is 45 h of class attendance, and 90 h of individual work. This was one of the problematic limitations that we recognised when designing the course. Accordingly, we posed to ourselves the following questions:
• • •
How can we enable the group (as a social system) to manage greater complexity than the sum of the efforts made by each isolated student? How can we lead the group to articulate the practices, tools, and theories of systems thinking? What tools can we ourselves use to answer these two questions?
We found the answer to these questions in organisational cybernetics. One way to manage complexity is to use attenuation and amplification mechanisms to effectively master the action in focus. Thus, we had to establish the context in order to guide students in relating to each other and in producing a social system. Therefore, a student does not have to work 280 h, but n students have to. In this way, we have 90?? n students' working hours to satisfy our requirement of 280 h of individual study. However, we had to guarantee the diffusion of this knowledge. For this, it was indispensable that we build an appropriate environment for students to develop their own autonomy.
"In this framework [cohesion] and autonomy are not opposites (Espejo, 1983). Viable subsystems with autonomy are necessary in order to implement the organizational tasks; in other words, it is necessary to have the 'amplification' provided by viable (autonomous) subsystems to make possible to control of the organization's outcomes. The above discussion suggests that in any viable system there is, in one form or another, a complementary between [cohesion] and autonomy. Thus the problem is to find criteria to make the most out of it." (Espejo, 1989, p.91)
According to the above, we can grant more autonomy for the students, all the while maintaining the necessary cohesion of the course. One can maintain it by means of certain rules. Some of these are not negotiable; students must accept the General
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Regulations of the university, the established topics of the course, the members of the teaching staff, and the transformation function of the points earned in the game into marks. Other rules may change, but they must be obeyed by all the participants in the game, including the teacher's staff. On the other hand, autonomy is granted in those aspects of procedure that make students responsible for their own learning process. One of these is the students' management of their own time. Students may also select which topics they want to focus on in their academic production. Although this latitude could generate failures in the learning process for some students, it may be understood as a tradeoff between thediscursive and practical domains (Giddens, 1986). Students may lose capacity in the discursive domain but gain it in the practical one. To implement these ideas, we had to model the course as a social system. We understand social systems as self-constructed objects (de Zeeuw, 2001) which are observable on the basis of differentiation (Luhmann, 1984). Because of this, a social system continuously produces the border between itself and its environment on its own. When an observer draws the boundary of the social system, he or she observes its structuring properties. Chief among the ideas that allow us to distinguish (SpencerBrown, 1969) social systems are their structuring properties, which correspond to their rules and resources (Giddens, 1986). These rules and resources are continuously produced and reproduced by the social systems themselves. For example, any university can be distinguished by the student-professor relationship which is invariant (Beer, 1993). On the other hand, we understand that games are collections of rules and resources, which establish how players are to relate to one another. We distinguish among rules as being constitutive and regulative (Searle, 1992).
"Constitutive rules [...] show the meaning and significance of the recourses required to play a game. There are three types of constitutive rules. [1.] The rules that establish the purpose of the game. [2.] The rules that establish the resources used. These rules establish where, with what, and by whom the game is played. And, [3.] the rules that establish possible action. That is to say, what is permitted and not permitted in the game. Constitutive rules build for a recurrent practice, which generates autonomy to the game and makes it possible for an observer to distinguish the game as well." Regulative rules institutionalize performance. [...] these are divided into two different kinds. [1.] Strategic [which] indicate specific standards for playing the game [...]. And [2.] Arbitration [which] seek to guarantee the game is being played according to what was institutionalized. Arbitration rules are divided into two kinds as well. [i.] Declarative rules, which establish what is true and false within the game. [ii.] Negotiation or assignation rules, which establish how discrepancies and disputes within the game are to be settled. Notice how the resourceful articulation of these rules is what creates cohesion for the resources to give institutionalism to the game, and also these rules provide for a recognizable practice of the same event due to the same institutionalism." (Bermeo, 2005)
Based on the above, it might be possible to model and simulate a social system into a game. This possibility can be assessed, because games and social systems are observable as self-constructed objects which produce rules and resources that allow them to be distinguished by an observer. In this way, simulating a social system as a game is participating in the continuous production, reproduction, and deduction of the same game
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(Zarama et al., 2004). And players, while playing the game, produce the social system they constitute. Summarising these ideas, we took as our starting point the principle that the demands of the course would be greater than the capabilities of the students. To facilitate this principle, we designed the course so that it would guide students to relate one another, while at the same time offering an environment in which students can develop their autonomy. However, to be effective, students must balance this autonomy with cohesion, which means that they have to act as a coherent whole system capable of handling more complexity than the one that the sum of the efforts of its separate parts could. We also expect that, during the implementation of the game, students will become familiar with the theories and tools of systems thinking on the discursive level. And we also assume that they will learn to work effectively within a complex environment by putting these theories and tools into practice. These are the objectives of the course design.
3
The Pensajistan Game
The 'Pensajistan Game' has been implemented during each academic period since 2004. Due to the fact that students may turn in assignments developed during previous periods some, certain variations are necessary to prevent this kind of institutionalisation of the game. The version we are explaining in this paper corresponds to the course designed for the first academic period of the year 2006.
3.1 Context of the game
Pensajistan, Evomod, Pensaquira, URSSA, and Rumanda are States. They constitute the International Community of Nomad States (ICNS). At the beginning of the game, Pensajistan is ruled by the Emperor, who happens to be the professor of the course. The Emperor has signed, along with the other four States (teacher's staff), the 'International Agreement'. This is a series of regulations for international commerce and diplomatic relations among the States. Additionally, he has signed bilateral agreements, subject to the International Agreement. All agreements have rules on how they must be modified. Because of this, ICNS and its constituent States are self-referential systems. The Kingdom of Pensajistan may change its political system if:
• • •
the majority of the people want a democracy or if one of the citizens wants another political regime another State supports the revolution the Emperor's Army is defeated (revolutionaries spend some resources according to the political regime that they want).
In a democratic revolution, the Constitution of the Systemic Republic of Pensajistan comes to power and the citizens (students) govern the State of Pensajistan. That is to say, they may modify all the rules of their own State so long as they do not contradict any international agreement.
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3.2 Constitutive rules 3.2.1 Purpose of the game
We assume that students want to get the highest mark. The university's marking system is numeric, with a discreet rating scale from 1.5 to 5.0 with intervals of 0.5. If a student gets a 3.0 or a superior mark, then he or she passes the course; otherwise, he or she fails. Based on this, Table 1 shows how the mark obtained in the course is related to achievements in the game of Pensajistan.
Table 1 Mark 5.0 4.5 Transformational function Readings achievement h$ 10,000 h$ 10,000 Computational achievement h$ 10,000 h$ 10,000 h$ 10,000 h$ 7500 4.0 h$ 10,000 h$ 10,000 h$ 10,000 h$ 5000 3.5 h$ 10,000 h$ 5000 h$ 5000 5000 3.0 2.5 2.0 h$ 0 h$ 0 h$ 0 h$ 0 h$ 0 h$ 0 Experimental achievement h$ 10,000 h$ 7500 h$ 7500 h$ 10,000 h$ 5000 h$ 5000 h$ 10,000 h$ 5000 h$ 10,000 h$ 5000 H$ 0 h$ 0 h$ 0 Individual achievement h$ 70,000 h$ 60,000 h$ 10,000 h$ 10,000 h$ 50,000 h$ 10,000 h$ 10,000 h$ 40,000 h$ 5000 h$ h$ 10,000 h$ 30,000 h$ 20,000 h$ 0 h$ 60,000 h$ 45,000 h$ 30,000 h$ 70,000 h$ 80,000 Total holons h$ 100,000 h$ 90,000
As Table 1 indicates, students must get five achievements: readings, computational, experiments, individual, and TOTAL holons. The schema implies accumulating as many holons in each cell as indicated in Table 1. The above description suggests that a student must work about one hour to earn h$ 1000. Holons (h$) are the monetary unit within the game of Pensajistan. The holons from readings, computational models, and experiments are earned by doing assignments (products in the game's jargon) corresponding to each one of these types of evaluation. The sum of accumulated holons in these types of evaluation corresponds to the individual achievement. The total holons is the result of adding the individual achievement and the holons earned or lost in the interaction with other students, via commerce mainly, within the framework of the game rules.
3.2.2 Resource rules
The only possibility of economic growth for Pensajistan is to export products (essays from readings, computational models, and experiment results) to the other States of ICNS. Inside Pensajistan it is a zero sum economic game. When a Pensajistan citizen exports a product, the importer pays for it and, besides, according to the product's quality, he or she grants a quality certificate or not.
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3.2.3 Rules of action
The rules of action state how holons can be obtained and accumulated. In this text we will only emphasise the five most important ways to earn and accumulate holons:
•
When the revolution proves victorious in Pensajistan, the citizens take control of the State. Thus, they can collect taxes from the citizenry and the corporations they form. With these taxes they can pay salaries. The game allows up to h$ 20,000 from the salaries earned by public officials of the State to be valid for completing any of the course achievements. PRODUCING. When one or more citizens produce a product and export it, they can earn holons for the corresponding achievement and the quality certificate of the product. If a product is exported by more than one citizen, then all of them get the certificate, and the total payment for the product is divided into the number of exporters. To export, exporters must have received all quality certificates of the products which are prerequisites of the exported product, as indicated in Table 2. PURCHASING. When one or more citizens buy a product, they can improve and export it to earn holons (only 10% of these holons is part of the individual achievement) and the quality certificate of the product. In case it is exported by more than one citizen, they will all get the certificate, and the total payment for the product will be divided into the number of exporters. The purchased product must have been previously exported and paid for. SELLING. Citizens can sell their products to other citizens of Pensajistan. For this, one or more citizens form a corporation. To sell their products, they must previously have produced, exported, and received payment for them. At the end of the game, the stakeholders of the corporations receive the dividends of the corporations they formed. These holons add up to the total holons, but not for the individual achievements. ECASIS. In order to evaluate students, they can pay for exams. In this way they transform total holons into individual achievements. There is an exam for each level. These exams consist of 20 multiple choice questions about certain concepts discussed in the course. They have 30 ms to answer each exam. If a student answers correctly more than 80% of these questions, then he or she gets all the quality certificates of the corresponding level.
'Knowledge tree' Products Introduction Systemic On systems Games Complexity Emergence I SLL Quality requisites None None None None None None None Code L46 L47 L48 L51 L52 L53 L54 Products Fractals Six degrees A N.K. Science Networks VSM Struct. Theory Foucault Quality requisites L34 L36 None L47 L41, and L42 L41, and L42 L43, and L44
•
•
•
•
Table 2 Code L11 L12 L13 L14 L15 L16 L17
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'Knowledge tree' (continued) Quality requisites Code None None L11, and L13 L11 and L12 L13 and L14 None L21 and L23 L21, and L23 T22, and T23 Inf. Theory L23, and T21 L36 Experiments L31 L31, and L35 E31, and L32 E34, and L33 L35, and L34 L55 T11 T21 T22 T23 T41 T51 T52 E31 E32 None Products Models Introduction Segregation Game of life Daisy World Sand model Fractals Learning Justice E33 None L32 L42 L43 L41, and T41 Quality requisites L43, and L44 None L9, L18, and L16 L19, L15 L36 L46, L45, and L48 L45, and L46 L23 L23,
Code Products L18 L19 L21 L22 L23 L24 L31 L32 L33 L34 Digital mantras Mathematica On complexity Emergence II Learning MAS Trust Causality Recursivity Altruism E34 L41 L42 L43 L44 L45 System/Env. Communication SSM Nexus Complexity
Burning forest L19, or L15
On managing complexity L21
and L22 L35
Daisy world T21, and L24 E41 E51 E52 E53 E54 Trust Networks SSM Daisy world
Communication L42
Table 2 shows the products' codes, names, and quality requirements for producing them. The product code has three digits. The first digit corresponds to the type of product: L for readings, T for computational models, and E for experiments. The second digit corresponds to the product level. The third digit is enumeration.
3.3 Regulative rules 3.3.1 Declarative rules
There are many regulative rules, not all of which need be described for the purposes of this paper. Therefore we shall mention only some of these. Each State is in charge of evaluating the quality of the products exported by students. According to this evaluation, the ICNS States fix the price of the products exported to them and decide whether or not to award the corresponding quality certificate. Additionally, the only valid accounting system is carried out by the Central Nomad Bank and the Superintendent of Securities. Such entities are managed by the teacher's course staff.
3.3.2 Negotiation rules
All controversies between any constituents of the State of Pensajistan are dissolved by the following instances: the Supreme Court of Justice of Pensajistan, the International Court of the ICNS, the chamber of commerce of the International Court, and, finally, by the Council of the Faculty of Engineering.
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4
Individual learning
If students want to be effective at the game and get the highest mark, then they must overcome the following two main challenges:
• •
managing their own autonomy performing the functions of politics, intelligence, and cohesion, along with learning the adaptation mechanism of the Viable System Model (VSM).
In this context we define autonomy as "the freedom of an embedded subsystem to act on its own initiative, but only within the framework of action determined by the purpose of the total system" (Beer, 1985, p.105). According to this guideline, whenever we let students decide when and what to produce by themselves, we assume that we are building the context in which students can be autonomous. When we designed the course, we believed that it was going to be relatively easy for students to master. However, this proved not to be the case. Managing their own autonomy turned out to be a heavy load for them; it was also not easy for most of them to start producing. It seemed that they needed somebody else to decide for them when and what to produce. As a matter of fact, the main student criticism of the course design was that there are no precise stipulations either for deadlines or for the work to be done. We have also observed that the sooner a student understands the rules of the game, the richer he or she will be. We also found that students concentrate their efforts in the 'here and now'. This implies that they do not carry out actions related to the intelligence function of the VSM. At the beginning of the game, the products exported by the students have no relation to a long-term strategy. Usually they export either the 'easiest' products or those that have bring the highest price. This strategy minimises costs and maximises returns in the short term, but it is not optimal in the long-term. Students typically do not know the prices of the products being exported, but they do know that there is a strong positive correlation between the level of the product and its price. Thus, a level-1 product pays around h$ 2,000, and in general any given product pays: (level + 1)?? 1,000 holons. In that sense, if they want to comply with the Computational achievement (see Table 1), then they can export at least one type-T product from level 1, and three more from level 2. And if they want to comply with the Experimental achievement, then they can export at least three type-E products from level 3. This means that they must have the quality certificates of L15, L16, L18 and L19 (see Table 2) to get the computational achievements, and must have the certificates of L13, L14 and L23 to get the to the same level. However, the most commonly exportedproducts at the beginning of the game are: L11, L12, L17 and L21. This has two consequences that damage their effectiveness in the game:
• •
this strategy allows one to reach only the achievement of readings, which implies a mark of 3.0 or less in the course the market of these products will be completely saturated, implying that those who produce and sell the products L11, L12 and L17 will only get h$ 500 or less for them because of the over production and the excess of competitors in the national market, while those who produce L15 and L19, for instance, will get profit from a short-term monopoly and may get h$ 1,000 or more at the moment of selling.
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On the other hand, the not-buying-improving-and-exporting strategy is inefficient in the long term. For instance, those who carry out the 'selfish' strategy will have to produce: L13, L14, L15, L16, L18, L19, L23, T11, T21, T23, T22, E31, E32 and E33 in order to reach each one of the achievements by themselves. If they obtain the highest payment for all of these products, they will have accumulated only h$ 40,000 of individual achievement after having produced 14 products! While if, instead of producing level-1 products, they buy them in the national market, improve, and export them, they will be able to accumulate h$ 70,000 of individual achievement, plus some more holons toward the total, after producing only 16 products as follows: L21, L23, L31, L35, L36, L41, L42, L52, L53, T21, T22, T23, T41, E31, E32, E33. This last strategy is clearly better than the first. Nevertheless, during the first half of the first semester of 2006 it was implemented by only five students out of 80! However, this strategy also has a problem. If it were implemented by all students, then it would saturate the market. If that happened, then it would be more difficult to accumulate the total holons. Because of this, it is necessary to implement the coordination function and the cohesion mechanism of the VSM, which will be explained in the following section.
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Systemic learning
Once the citizens of Pensajistan take control of the State, they constitute a higher level of recursivity. Dealing with this factor demands the use of the mechanisms described of viability of the VSM (Espejo, 1989). The members of the State have to deal with two environments: the environment outside Pensajistan (the other member States of ICNS); and the internal environment, that is to say, the citizens and corporations that constitute the State of Pensajistan. Their job in relation to the external environment is carried out through the adaptation mechanism. The main tool which the Pensajistani State can use to manage its external environment is negotiation with other States. During these negotiations, it is possible to lower tariffs, get benefits in products, and arrange fairs, among others. However, all of these negotiations are subject to what Pensajistan can offer. Therefore, the government of Pensajistan has to be capable of:
• •
knowing the main demands of their citizens generating enough cohesion within the system to be able to satisfy these demands.
For example, commercial fairs have proven to be a main mechanism of coordination and economic growth in Pensajistan. These consist in short periods of time (a day or less when they, altogether, can earn h$ 1,000,000!) during which tariffs may be suspended or products may be given as bonus, or certain rules of commercial agreements may be relaxed. However, other States generally ask for the massive production of certain products in return, and this requires coordination capacity by the government. The cohesion mechanism is observed not only in the capacity to coordinate actions for the purpose of satisfying the requirements of the international community. The game itself requires high coordination capacity among the agents. For instance, during all the academic periods of this course, it has been necessary for the State to invest some money in education, that is to say, hire someone (sometimes a student, sometimes a teacher) to teach the 'poorest' citizens the rules of the game and how to play it. Likewise, the role of
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the State is indispensable in preventing the saturation of a product in the market. To avert this situation, the State can adopt an incentives policy by means of lowered taxes or bonuses to citizens producing for the first time, among other actions. To conclude, even though the design of the game emphasises that each student must be responsible for his/her own learning process, the effectiveness and efficiency of their performance in the game certainly depend on the coordinated action of all players. This requires a higher level of recursivity to deal with the residual complexity (Espejo, 1989) that they are not capable of managing. Students must learn to deal with the complexity of the Pensajistani environment, which is constituted by the other member States of ICNS and the ICNS itself, and with the internal complexity of the system within which they interact and continuously produce and reproduce.
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Discussion
At this point, it is difficult to assess whether this design is more effective than other designs might be, for teaching or learning. It is not the purpose of this paper, however, to demonstrate a measure of learning. We do not have one. In this sense, we are without the means to show the effectiveness of this course design. None the less, we certainly can show certain indications which suggest that we are pointing in the right direction. The results shown below correspond to the first academic period for 2006, during which 88 students took the course.
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The demand for the course has increased. In 2004 around 40 students were taking the course. 105 students are now inscribed in the course. Currently, "Introduction to Systems Thinking" is the elective course second-highest in demand in the department of Industrial Engineering. The ECASIS outcomes presented in Section 3.2.3 are an indication of learning in the discursive domain. At the beginning of the course eight students took the level-1 and level-2 exams. On average they answer 51.83% of the 40 questions correctly. Following table summarises the results at the end of the course.
No. of students 17 16 96 41 Average (%) 50.00 57.98 70.55 60.83 63.75 45.00
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Level 1 2 3 4 5 6
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These results are satisfactory for us in the sense that these exams are designed to be more difficult than normal. This is because they are earning per hour more holons than they earn producing essays, models, or experiments. Besides, these exams cover all of the contents of the course.
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N.L. Lammoglia et al. Ten students got a mark of 5.0. The most common strategy among them was: L11, L13, L14, L17, T11, L21, L23, T21, T23, L31, L33, L35, L36, E31, E32, L41, L42, L47, T41, L52 and E52. This strategy uses 13 of the 16 products of the strategy shown in Section 4! On average they exported 20.3 products during 15 weeks. Following unlabelled table shows how much a student with final mark x received for their exported products on average. It also shows the Confidence Interval of these payments.
Average payment 3765.89 3234.41 3097.24 2953.46 2942.19 2837.75 2548.91 2688.88 Confidence interval (? = 0.05) (3462.47, 4069.31) (2953.00, 3515.82) (2753.73, 3440.74) (2701.39, 3205.53) (2751.50, 3132.89) (2434.41, 3241.09) (1969.86, 3127.95) (2060.86, 3316.91)
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Final mark 5.0 4.5 4.0 3.5 3.0 2.5 2.0 1.5
We can observe that there is a significant difference between payments received by students whose final mark was 5.0 and payments received by the others. One could suppose that this happens because of the quality of the products exported by this group of students. However, statistically there is no difference between payments for products of the same level received by students whose final mark was greater than 3.0. This might imply that the difference in payments received by the group of students with the highest mark is explained by their strategies and not necessarily because of the quality of their exported products. This may be true only for the group of students whose final mark is greater than 3.0.
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Students covered the whole 'Knowledge Tree'. It means that they exported every single product at least once. Students showed a high level of coordination. They were able to design group strategies and put them into practice. The one with the greatest impact was proposed by a Congressman, which granted certificates to all the students in the course for any product already produced by someone. That is, the State bought a product, hired someone to improve it, and finally exported this improved product in the name of all the interested students. This was a very well designed strategy which proved to be extremely effective.
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Final reflections
In this paper we have shown an application of Organisational Cybernetics to the teaching of Systems Thinking and Organisational Cybernetics. The design showed here views the course not as a group of students but as a system. In this sense, it does not add up the capabilities provided by each single student, but instead relates to them as a totality that is
Towards teaching on managing complexity using complexity
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capable of using adequate mechanisms for the management of greater complexity. At the same time this goal is achieved in an environment where students develop their own autonomy. Students also experience the need to be able to adapt themselves to dynamic environments. Therefore, autonomy is used as an effective amplifier of complexity by the system. In this way each student is able to couple with the environment in order to be effective in a certain domain of knowledge (Zarama et al., 2004). This individual process of adaptation to the environment triggers a co-evolution process which allows for group learning. Because this dimension became real for students, they were able to grasp most of the contents of the course without experiencing an additional burden. Notwithstanding these benefits, students have also shown that they are not well prepared to be in charge of their own autonomy. Even though we assumed this capacity on their part in the initial design for the course, the fact is that this aspect became one of the most relevant challenges that both the students and we had to overcome. Our experience has taught us that autonomy is not a capacity that we may assume will emerge in any case, but instead is one that requires nurture, requiring that we build spaces in which students can learn how to manage and develop it. Just as we explained in the individual and systemic learning section, students tend to optimise their short-term strategies at the expense of long-term ones. Based on this finding, we believe that the design of the game has been an effective tool in highlighting the consequences of these decisions. This is evidenced in the load of additional work that burdens students who did not plan for the long term. As we mentioned in Section 6, it is difficult to assess whether this design is optimal or defective. We do have, however, certain indications which tell us that we are moving in the right direction. We have observed students beginning to deal with their autonomy, thinking strategies, balancing short-term and long-term strategies, and trying to coordinate each other. We have not yet found the way to measure these results in a way that satisfies us, but we seriously believe that this course changes the way in which students think about and observe the world around them. In conclusion, the Pensajistan game shows that it is possible to design new teaching methods that deal with systemic ways to observe the world. Additionally, the game proves that certain aspects of skill that we consider relevant, such as autonomy and management of complexity, require the design of a specific learning process and the appropriate context for the development of these skills.
Acknowledgements
The latest versions of both the course and this paper have been improved through the participation of Jorge Villalobos, Daniel Garcia, and Samira Haddad. We also want to thank our students, without whom this work would not have been viable.
References
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