The complexity paradox: An analysis of modeling education through the lens of complexity science

Modern software is inherently complex: it typically needs to address a huge variety of interactions with users, hardware devices, physical application contexts, and other software systems, typically in highly dynamic and continuously changing real-world environments. As a tool to deal with complexity during software development, companies rely on modeling. Brook’s famous essay on essential and accidental complexity [1] offers a framework for motivating the use of models, as a tool that abstracts from the accidental complexity involved in low-level programming, and allows developers to focus on the unavoidable, essential complexity of the problem at hand.

Paradoxically, experiences in software engineering education indicate that students often perceive modeling as adding, instead of removing, complexity during software development, and struggle with the associated challenges [2]. Modeling is usually taught in undergraduate courses, either in dedicated courses on software design, or as a section in broader introductory courses on software engineering. In these courses, students typically engage with small modeling tasks. In such contexts, explicitly designing software systems in a new language presents a radical departure from the programming activities that students are familiar with, and students often struggle with using dedicated tools that they perceive as complex and not particularly user-friendly.

In this position paper, I analyse modeling education from the lens of the theoretical framework of complexity science [3, 4]. Complexity science is involved with the study of systems that are highly dynamic, uncertain and non-linear in nature. It has previously been used as a framework to problematize and suggest improvements to educational practice, both in general [3, 4] and subject-specific education [5, 6, 7]. As such, complexity science provides a vocabulary that allows exploring connections between challenges in modeling education and the previous pedagogical literature, and drawing inspiration from other disciplines’ ways of dealing with complexity. I provide an overview of background in this direction in Sect. II.

To analyse complexity-related challenges in modeling education, I apply a lens of interpretation based on the distinction of two mindsets—an analytical one and a complexivist one–, lifted from educational literature. I motivate and explain this approach in Sect. III. Through this lens of interpretation, in Sect. IV, I revisit recurring challenges reported in modeling education literature and discuss them in the light of complexity science, with a focus on misalignments between analytical-mindset teaching practices and the complex situations that students will encounter in practice, which require a complexitivist mindset. To address the identified challenges, in Sect. V, I present recommendations for addressing complexity.

I now revisit complexity science and its use as a framework for discussing education. In particular, I describe how complexity science has previously been employed as a framework for problematizing aspects of higher education.

From their theoretical framework, Davis and Sumara derive consequences for teaching methods. A key distinction is between two mindsets, the analytical and the complexivist one [11]. The analytical mindset, which is advocated by traditional teaching methods, is focused on linear, analytical knowledge, teaching students skills that are suited for systems of limited complexity. A key tenet of the analytical mindset is reductionism, which seeks to remove complications from the analysis of situations to reduce them to the essential elements. A criticism is that this mindset might not be adequate to prepare students to real-world situations, in which they are faced with the complications inherent to complex systems. To foster the capacity for dealing with complexity, they propose to engage with learning activities that are conducive to a mindset that embraces complexity, a so-called complexivist mindset.

In computing education, Fabricatore et al. [12] adopted a complexity-science-based teaching strategy in a game design course. Towards the course goal of developing a game for a museum, the course included three project milestones, project workshops, lectures, and formative tasks. The course was designed in an adaptive way, by considering the emerging evidence as the course was given. Applied complexity principles included decentralised control and self-organisation within teams, frequent and unexpected perturbations (in the form of consultant feedback) triggering adaptive dynamics, selection of course contents based on external, contextual factors, and iterative, incremental teaching applying concepts at increasing levels of depth and complexity.

In medical education, educators need to prepare students for multi-faceted clinical situations with complicating factors such as time pressure, sensitive human aspects, and ethical dilemmas. Gormley and Fenwick present a ward-based simulation exercise [5], in which students interact with actors during a realistic ward situation. The situation is made increasingly more complex, to include aspects of inappropriate patient and colleague behavior, and life-and-death-related decision making. Data collected during a run of the simulation allowed the uncovering of complexity-related patterns. They derive a set of strategies for managing complexity, namely: taking time to size up the system; attuning to what emerges; reducing complexity; boundary practices; and working with uncertainty.

Project management education has traditionally been informed by professional standards such as PMBOK and APM, describing formalized, context-independent processes [6]. To better prepare project managers for complex projects with sudden changes, disruptions and interpersonal challenges, Thomas and Mengel propose a re-shift of project manager education towards the development of “emotionally and spiritually intelligent” project leaders, who comfortably navigate complex systems in the transition between a stable and a perturbed state [6]. They suggest project-based learning modes that take complexity science seriously, fostering an ability to adapt to change and to develop new approaches on the fly.

In sustainability education, it has been long recognized that sustainability problems are wicked problems [7] that cannot be addressed in terms of isolated factors, as they typically involve an interplay of complex societal and ecological circumstances. Complexity science offers mathematical methods for describing complex phenomena that can be used to support an explicit analysis of such factors in educational activities. Weber et al. [7] report on a workshop in which participants from diverse backgrounds were prompted to prepare graph-based system representations of a selected sustainability problem, which were then discussed in-plenum. Feedback indicates that the activity furthered the participants’ interdisciplinary thinking.

In this paper, I apply a complexity-science-based lens of interpretation to discuss and inform the design of learning activities in modeling education. This lens comprises two basic tenets that build on the conception of analytical and complexitivist mindsets [11], as introduced earlier: Methodologically, this approach is inspired by model papers [13], a type of conceptual article that summarizes arguments about a focal construct as a set of logical statements, in this case, the tenets.

Before taking a modeling course, students have typically participated in first-year programming courses, potentially in addition to high-school courses and hobby projects, where they dealt with problems that were linear in nature, facilitating the adoption of an analytical mindset. Such problems have several key commonalities: First, they can be solved entirely by an reductionist approach, in which the overall problem is reduced to several smaller, sub-problems (the “divide and conquer” paradigm; see the standard examples in programming courses, such as searching and sorting). Second, these problems grow linearly in size, in terms of the number of entities in the system. For example, adding a filter in a “pipes and filter” architecture requires adding code at one specific location in the overall codebase, instead of modifications at many places. Third, problems are specified in a clearly delineated “box” (input and output specifications of an algorithm), abstracting away from real-world intricacies, and their inherent uncertainty. For such basic problems, students are well-prepared with the contents of first-year programming courses.

In contrast, the nature of complex real-world problems that software deals with, in which modeling unfolds its potential, require a complexivist mindset [11] to cope with complexity. Complexity arises because software systems are deployed to the real world, and as such, are prone to changes, require to make decisions in a certain context, might be affected by uncertainty, and involve people in various roles, who may or may not have shared understandings, perspectives, and interests. Drawing a parallel to recent developments in other disciplines affected by such factors (discussed in Sect. II), I make a case that modeling education could greatly benefit from a mindset shift: To support the development of a mindset that prepares students for complexity, we need learning activities that explicitly take aspects of complex systems into account.

I now revisit recurring reported challenges retrieved from field-specific literature and discuss them from the chosen lens of interpretation. The focus of this section is on a problem analysis, before describing solutions in the next section.

Students often question the added value of models [16] as an additional artifact that takes effort to be created and maintained. We can apply our interpretative lens to analyse this concern, which seems particularly justified in an analytical mindset: There is no essential reason why models are required for building a software system. The system itself consists of code that provides the required functionality. A complexivist mindset acknowledges the effort invested into modeling, but, in turn, draws attention to the effort that is saved from the use of models, in the context of realistic development settings: Communication problems, misunderstandings and design flaws can be discovered early, before the system is built, which can help avoid significantly greater effort and time for fixing problems after the system has been built. To support development of this mindset, educational activities should be designed in a way that makes it likely for students to encounter situations that allow them to appreciate the advantages of modeling, e.g., in terms of saved effort.

Students regularly struggle with abstraction, and, consequently, deem modeling as too far away from programming [2, 15]. These observations can be explained with the analytical-mindset-oriented tasks and problems that students consider in their pre-modeling education: small-scale programming problems do not evoke a need for abstraction; it is sufficient to have a fully-worked out solution with all details in one place. In fairness, such problems and the associated mindsets are adequate for their educational purpose: for the “first steps” into computing, it is effective to deal with simple problems, which encourage a mindset focused on solving such problems. Yet, at some point, students need to deal with the complexity of real-world software. In a complevixist mindset, abstraction is a necessary means to that end: The behavior of a system arises from the interaction of its components. In the crucial notion of levels of emergence [3], phenomena need to be understood at the level of their emergence, and cannot be understood in terms of lower-level, more detailed activities. For modeling education, this implies that, for students to understand the need for abstraction, we need to expose them to problems that cannot be solved without it.

With the focus on modeling languages, there is a tendency in courses to lack guidance regarding the context in which modeling is performed, specifically: the problems that modeling tries to solve, the scope within the real world in which these problems occur, and the positioning of modeling in the development process [16]. In an analytical mindset, it is tempting to view this as a non-issue. Following the reductionist approach, problems are given in the form of an exact specification and problem solving entails splitting the problem in smaller sub-problems, solving each sub-problem independently, by using available problem-solving tools. A complexivist mindset acknowledges the importance of learning in context. Software addresses particular problems whose exact formulation my not be clear to begin with, and different involved actors, including the potential users, could have disagreeing views and interests in the solution. Solving it might require deep understanding of the application domain, which might not necessary be one in which the developer has expertise in. A complexivist mindset naturally encourages the use of project-based learning [18], which provides opportunities to understand a phenomenon in a rich, realistic context.

However, students struggle with available modeling tools [15, 19, 16]. Their learning experience is affected by the perceived complexity and lack of user-friendliness in these tools, leading to decreased motivation. From an analytical mindset, it is tempting to discourage the use of realistic tools in the first place: as a problem-solving device, it would be equally valid to create models using PowerPoint or on paper; factors that add accidental complexity [1] could be seen as noise and should be discouraged in education. From a complexitivist mindset, using authentic tools seems generally welcome, as it allows students to explore modeling in a realistic context, with all of the associated benefits and drawbacks. However, the degree of realism needs to be managed, mirroring some concerns that the influence of allowing unrestricted complexity in education might not necessarily be positive [20]. It is the teacher’s responsibility to ensure that accidental tool issues do not get in the way with learning and forming a deeper understanding. This theme bears a connection to the issue of facilitating independent problem solving when learning under guidance, which is explored in Vygotsky’s idea of the Zone of Proximal Development, and the notion of scaffolding [21].

I now present recommendations to address complexity in modeling education. As put forward in Section III, their underlying principle is to facilitate the adoption of a complexivist mindset, preparing the students for complex problems they will encounter in the real world, and explaining the role of modeling as a tool in this context. Where I draw from cases from other disciplines, I reference them accordingly.

Studying the educational practice from other disciplines can be insightful to inform the teaching of modeling. The most important direction for future work is to study the impact of complexity in modeling education empirically.

I revisited recurring challenges in modeling education from the lens of complexity science, and offered recommendations for improved teaching practices. Drawing from complexity-science-inspired strategies in the educational practice of four other disciplines, I presented five recommendations with the common goal of supporting the adoption of a complexivist mindsets by students.

A future work, first, I envision an a empirical study of the usefulness of the proposed recommendations, studying short-term implications on course outcomes, and long-term effects based on feedback from students who moved on to developer roles. Second, a more comprehensive study of complexity-science-based teaching practices in various disciplines and their potential impact to modeling education.

The author wishes to thank the teachers and participants from Gothenburg University’s course Teaching and Learning in Higher Education 3: Applied Analysis (PIL103), especially Janna Meyer-Beining, for high-quality feedback and insightful discussions on previous versions of this article.