Complexity Thinking

Derived from Doll’s (1993) seminal conceptualization of a post-modern curriculum with the criteria of 4Rs (i.e., richness, relations, recursion and rigor), the present research continues the effort to complexify and theorize recursion and recursive curriculum. This study re-conceptualizes mathematics curriculum as recursive through the lens of complexity thinking (Davis & Sumara, 2006), which studies complex systems that are adaptive, such as cognition and knowledge. A mathematics curriculum often seems be designed or delivered as linear: a sequence of predetermined, sometimes unrelated, topics with few chances for learners to revisit them from different perspectives. This suggests learning as accumulation with predictable outcomes. Learning, observed through a complexified world view, is neither linear nor predictable. Learning is a self-organizing process through which a learner and her environment co-evolve, and a recursive elaboration through which a learner transforms her previous understanding (Davis & Sumara, 2002; Davis, Sumara, & Luce-Kapler, 2008). Both learners and school subjects are complex systems with a biological structure (Davis & Sumara, 2002) that emerges. This view demands a recursive curriculum that centers on reviewing previously encountered ideas with an orientation towards newness and changes along its formation. What might such mathematics curriculum be like, particularly at high school level, in theory and practice is my research focus.
The research methodology follows the tradition of hermeneutics (Gadamer, 1989/2013) that attends to language and emphasizes emerging understanding through iterative loops of interpretations. The interpretations in this research are informed by three kinds of entry texts, my personal reflections about recursive curriculum, teaching documents (i.e., programs of studies and textbooks), and conversations with teachers, serving to provoke my thinking and generate further reflection subjected to new rounds of interpretations. Several high school mathematics teaching documents from Canada and China were examined to see in what ways a planned curriculum might afford recursion. Conversations with experienced high school mathematics teachers were conducted in professional development workshops and/or individual meetings. Teachers were invited to reflect on their learning and teaching experiences and comment on several teaching and learning practices (e.g., reviewing), and work with me to revise or generate curriculum materials to promote such practices orientated towards helping students to learn something new from what they have encountered before.
This study aims to make a contribution in the field of mathematics education by addressing the gap between the perceived importance of recursive mathematics curricula and the insufficiency of research about them. I expect that this study speaks to a reinterpretation of reviewing, and potentially provokes learners (both teachers and students) to interpret mathematics and curriculum differently and inspires learners to (re)embark a complexified hermeneutic inquiry on recursive mathematics curricula for the purpose of both learning and teaching. This study has led to a metaphorical and iconic image of recursive curricula that represents abundant curriculum possibilities rather than a fixed one. Such visualization can provide theoretical and practical references for mathematics educators and education researchers to draw inspirations from when designing towards recursive mathematics curricula.

Sosiaali- ja terveydenhuoltojärjestelmän uudistamisen (myöh. sote-uudistus) tavoitteita ovat alueellisten hyvinvointi-ja terveyserojen kaventaminen, laadukkaiden ja helposti saavutettavien palvelujen turvaaminen, tuottavuuden kehittäminen ja kustannusten hillintä, ammattimaisen henkilöstön saatavuuden varmistaminen sekä väestön ikääntymisen ja syntyvyyden laskun aiheuttamiin haasteisiin vastaaminen. Tavoitteista ei ole erimielisyyttä, mutta niiden toteuttaminen jakaa mielipiteitä. Joidenkin mukaan tuottavuus ja laatu paranevat, mitä enemmän palvelutuotantoa annetaan yritysten hoidettavaksi, kun taas toiset mielellään varoittavat yksityistämisen vaaroista, kuten eriarvoisuuden kasvamisesta ja veroeurojen siirtymisestä pääomasijoittajille. Sote-uudistuksella on myös poliittinen ulottuvuutensa. Poliittista vääntöä on aiheuttanut erityisesti se, että uudistus vaikuttaa kuntien, alueiden ja valtion suhteisiin pitkälle tulevaisuuteen. Sote-uudistusta on syystäkin luonnehdittu pirulliseksi (esim. Erhola ym. 2019). Tämän narratiivisena kirjallisuuskatsauksena toteutetun katsauksen tavoitteena on muodostaa tutkimuskirjallisuuteen ja sote-uudistusta käsitteleviin ohjelma-asiakirjoihin, selvityksiin ja raportteihin pohjautuva tulkinta sote-järjestelmän kompleksisuudesta ja sen uudistamisen pirullisuudesta. Tavoitteena on vastata kysymykseen: Millainen kuva sote-järjestelmästä ja sen uudistamisesta piirtyy, kun sitä tarkastellaan kompleksisuuslinssin läpi?

The focus of this book leans us toward the future of Coaching Supervision1. What is happening now that offers insights into what might become? Throughout this book, we are invited into little-explored avenues. Here, we found ourselves inspired to examine the generative nature of Coaching Supervision as it is emerging and manifesting in these, its embryonic years. Why? Because of a bigger question: How can we (collectively as agents in the system with myriad roles) understand, and more importantly, influence developments in a way that upholds and enhances ourselves, our practice and our field, and those engaged and impacted, locally and globally - now and in the future?

Research on the theoretical conceptualisations and research methods informing current change agency theory and practice in the field of Organisation Theory (OT) in general, and Organisational Change and Development (OCD) in particular, are deficient to engage with the inherently complex nature of business organisations. The dominant paradigm applied in organisational change interventions assumes that change happens through linear cause and effect approaches, which can be enhanced by technical skills, with the aim of maximising optimisation strategies. The theoretical and practical contributions by organisational scholars to important mainstream debates on alternative conceptualisations and methods to explore and re-think change agency have been limited.

The purpose of this dissertation is to cultivate and foster a re-think of the role of change agents in OCD interventions by employing a critical complexity lens to shift their current spiritual identity praxis towards co-creating alternative complexity-informed change agency praxis. The following framings are explored: new avenues for providing complexity-informed interpretations of change, organisational structure and function in general, but more specifically alternative change agency as informed by identity and spirituality in OCD interventions. 

A critical complexity lens is adopted for exploring and re-thinking the interactional nature of both identity and spirituality of change agents. The study highlights these notions as possible entry points for reflecting on novel change agency praxis. It is argued that the notion of ‘spiritual identity praxis’ (ways of being-becoming) enables the co-exploration and co-creation of complexity-informed theoretical and methodological contributions to organisational change agency and mainstream debates on OCD.

The study explored whether OCD practitioners could reflect on their current spiritual identity praxis and what the implications were of re-thinking their current roles as change agents when employing critical complexity as a lens. Co-operative Inquiry (CI) was used, which is ideally suited to explore a participatory worldview for co-creating propositional, experiential, practical and presentational knowledge. With the aid of multiple qualitative methods, CI enabled the co-creation of a re-imagined spiritual identity praxis heuristics framework.  Collaborating with six OCD practitioners, a co-created community of practice was established which reflected over a period of eighteen months, on processes of: (i) engagement with ideas of complexity thinking and its influence on change agents; (ii) spiritual identity and the co-operative inquiry process in contributing to a deeper reflection on their perspectives as change agents; (iii) spiritual identity praxis in framing the roles of change agents in change interventions; and (iv) authentic co-operation and collaboration during the co-operative inquiry process.

The research findings confirm the importance of: (i) embracing complexity thinking as change agents; (ii) navigating ambiguity and incongruence of spiritual identity; (iii) becoming aware of the relational constitutedness of spiritual identity praxis; and (iv) the utility of critical complexity integrated with CI in co-creating resilient heuristics through authentic collaboration and co-operation, which fosters complexity-informed spiritual identity praxis heuristics. The study contributes to an extended understanding of change agency praxis, provides a framework for re-imagined complexity-informed being-becoming praxis in change agency, and offers non-linear pathways to distil iterative principles and reflective signposts for complexity-informed OCD praxis.

From 2012 until today, I have given several seminars on metadesign, strategic design and collaborative design in Brazil (Unisinos), Mexico (Universidad Iberoamericana and Tecnológico de Monterrey), Italy (Università di Bologna), Guatemala (Universidad Rafael Landivar) and Colombia (Universidad de Caldas).
I collected the various contents in a single presentation that I am making available to my students and to the design scientific community.
The presentation does not consider the practical activities, due to its great diversity.

The aim of this contribution is to reflect on a complex translation theory as a theory of possibility (Görnitz and Görnitz 2008). The starting point is Edgar Morin’s concept of homo complexus (1999), which by analogy suggests the idea of homo interpres complexus. The communication process as a series of interacts (speech acts) is characterized by uncertainty. Furthermore, the homo interpres complexus is a self-organizing living machine that shares the content of its thoughts (relevant properties) through such interacts with a specific intention. We will attempt to show that, in contrast to monolingual communication, trans-semiotic communication is a dual process of distancing and approaching and functional and cultural adjusting. A translation theory should include uncertainty and unpredictability as relevant principles, thus resembling a theory of possibility (Görnitz and Görnitz 2008). Based on this theoretical model, I present a complex methodology and its first application to students in the MA in Interpreting programme at Heidelberg in 2012.

Slow translation refers to translation practices that allow reflexivity and debate by people who translate, publish, read, comment on, or republish translations. Slow collaborative activist translation (SCAT) is an example of slow translation that occurs in the midst of social movements, challenging governments and societies from north to south. SCAT takes place mostly in the virtual world of Web 2.0 where consumers are also producers of content, creating influential sociodigital networks (Bissière et al. 2015). How could such kinds of translation be approached? What methodological framework is best? Possible answers to these questions will be examined.
As the epistemological vision of complexity theory is central here to analyze relevant SCAT properties as reticularity, recursiveness, and dialogism, a transdisciplinary analysis is necessary. Inspired by the open methods of the social network analysis, including the concept of “sociogram” (Mercklé 2004; Hanneman and Riddle 2005), I graphically show the social network of selected translations, done and published by translating the printemps érable, a Canadian SCAT initiative related to the Quebec student movement (2012). The resulting translation-centred sociograms will include not only the traditional binary relations author-original text/translator-translated text, but also the interactions triggered by published and republished translations, namely readers’ recommendations and republications and most importantly their commentaries or modifications to the original translation.
This first transdisciplinary effort should allow a theoretical and pragmatic rebinding, in simple terms a process of distinction and conjunction of the emergent properties of new phenomena (Bolle de Bal 1996; Morin 1996, 2008), which constitutes a main methodological proposition by these two complexity thinkers. Analyzing the dynamic and multidimensional network of texts and people weaved by the Canadian initiative, through the lens of the aforementioned sociological theories, should contribute to a better understanding of SCAT as a new and complex translational phenomenon. In addition, it enables us to consider other possible rebindings with pertinent social sciences disciplines which have been applying complexity thinking in their respective fields of research.

In the novel San Manuel Bueno, mártir (1933), Unamuno's existential contradiction is expressed through the intra-history of the characters, the cultural landscape and the village of Valverde de Lucerna. How does the translator-reader identify and reproduce the symbolic value of nature at different moments in history? What kind of historical and cultural connotations do elements like a lake or a mountain have in Spanish and German culture? This novel reflects the human paradox of believing or not, the consciousness of the unamunian historical " self " that emerges throughout an indirect narrative in which the symbolism of nature and the constraints of the civilized world are in constant opposition. Thus, the novel gains a symbolic value due to the scenery suggested by the lake of Sanabria (in the village of San Martín de Castañeda), the ruins of convent of Bernardos and the mountain (Peña del Buitre). They represent the most intimate and deep aspect of unamunian consciousness, typical of the Generación del 98's Spain. After describing the symbolic value of these natural elements, three translations into German of San Manuel Bueno, mártir shall be analyzed focusing on the interpretation of nature in an existential and cultural sense.

The complexity of teacher education is fascinating, illusive, and creative. While it is simultaneously difficult to grasp and conceptualize, complexity has real presence and effects, and needs to be managed and simplified for meanings to emerge. Given this, interest in complexity, and its value to education more broadly, has grown rapidly over the past two decades (Davis & Sumara, 2006; Osberg, Biesta & Cilliers, 2008). This turn to complexity is linked to three intertwined ideas. The first, which is ontological, involves viewing the world as organized relationally through highly connected and interdependent elements so that the focus becomes not about understanding what something is (an emphasis on the individual, essence, and being), but how it comes into being (a focus on becoming, emergence and affect) (Deleuze & Guatarri, 1987; Richardson & Cilliers, 2001). The second, which is conceptual, involves drawing on a renewed vocabulary and conceptual toolbox that enables generative w...

La constante búsqueda de una teoría de la traducción que fuera científica ha llevado a los distintos investigadores a ampliar cada vez más el campo de estudio, hasta tal punto que se ha llegado a hablar de multidisciplinariedad, interdisciplinariedad o transdisciplinariedad (Kalverkamper 2004; Santana 2010). Esto muestra lo complejo del asunto: la traslación. El problema que plantean algunas teorías son los modelos mecanicistas-funcionalistas, que parten de una concepción simplista y lineal del proceso traslativo que no responde a su complejidad real. Es en este contexto donde, inspirándome en la fisica cuántica y el principio de incertidumbre (Heisenberg 1927) y tomando como ejemplo el valor comunicativo de la Escuela Traductológica de Leipzig, propongo un cambio paradigmático sobre ·la base de la teoría de la información, la teoría cibernética y la teoría de sistemas (Morin 1991) que nos dan acceso al paradigma del pensamiento complejo. Partiré de la hipótesis de que todo conocimiento debe considerar la incertidumbre y concluiré que una teoría (general) de la traslación basada en este tipo de concepción debe indefectiblemente aproximarse a una teoría de la posibilidad (Gornitz & Gornitz 2008).

Interdisciplinary or trans-disciplinary research is becoming more common and their importance is increasingly being recognized. However, in practice many of these efforts tend to end up in more or less isolated activities around a common theme. Successful forms of cross-domain interactions may be feasible as long as the stakeholders that team up around a certain research theme share a common vocabulary. However, the risk of fragmentation becomes greater when they have little in common and so cross-domain research that involves contributions from the hard sciences and the humanities are relatively rare.
Besides a willingness to be open for each other’s contributions, one of the biggest challenges for the success of such efforts is to find a common vocabulary that can be recognized and shared by all the parties involved. Such a vocabulary could contribute to a lingua democratica, a consensual and cooperative means of sharing knowledge amongst domains.
This paper aims to draw attention to the concept of patterns and pattern libraries as means to create such shared vocabularies. A number of patterns, based on the concept of feedback, will be introduced from the often very abstract research area of computational intelligence and related areas. These patterns aim to transform and condense some essential characteristics of feedback in such a way that, hopefully, they may become more or less accessible for other scientific disciplines. The resulting ‘pattern-oriented approach to complexity’ (PAC) aims to address the necessarily interdisciplinary nature of complexity, not by cross-domain criticism, but rather by attempting to achieve certain synthesis.

Although the term 'pattern' is often used in science, it is an elusive term and can have different dialectic meanings in various disciplines. Yet, the 'feel' for this term is fairly consistent; it usually requires little explanation to understand what a pattern is,
and therefore it usually tends to be used informally. Perhaps only in building architecture and software design, patterns are used in a more rigid fashion, as a methodological construct to solve recurring problems.
This paper aims to argue that patterns, used in a slightly different way, can provide the same strength in order to improve communication amongst scientific disciplines. It is claimed that this advantage is more than a linguistic trick, but rather is based on the notion that discovery of patterns is in fact the essence of most scientific endeavours, especially in complex systems theory.

The Flow System shows how to generate and nurture self-organizing teams that mobilize the full talents of those doing the work to cope with dizzying change and complexity, while also drawing on the contributions of those for whom the work is being done–the customers.
—Steve Denning, author of The Age of Agile

Organizations that pull off this triple helix trick of thinking about the complexity of their systems and the environment in which they’re operating, distributed leadership to engage the collective intelligence and creativity of the organization, and building teams of teams so the whole is greater than the sum of the parts have good chance of keeping up and staying ahead.
—Steve Spear, MIT Sloan School senior lecturer, author of The High Velocity Edge

The Flow System’s Triple Helix provides many of the tools and ways of thinking we will need to do that; it is agile without being doctrinaire about Agile.
—David Snowden, creator of the Cynefin Framework, Chief Scientific Officer of Cognitive Edge

Complexity concepts help to open the black box of social innovation for public sector managers and policy-makers and to understand why social innovation can simultaneously be both a solution and problem. Complexity thinking guides formulating essential questions and helps to imagine the desired future and, in so doing, it also provides heuristic tools to address the paradox of social innovation.

Interdisciplinary or trans-disciplinary research is becoming more common and their importance is increasingly being recognized. However, in practice many of these efforts tend to end up in more or less isolated activities around a common theme. In many areas where it is becoming more recognized that collaboration around certain research themes is essential to understand certain phenomena, it becomes important to develop a vocabulary that all parties involved can share, and which reflects the essential concepts that are needed to grasp subject matter. This could contribute to a ‘lingua democratica’, a cooperative and deliberative means of cross-scientific research.
Within limits, many research disciplines can easily adapt their regular ‘dialects’. For instance, biology and informatics share a common framing in mathematics and systems approaches. Likewise, some disciplines within the social sciences and humanities can find each other in certain schools of thought or theoretical frameworks. However, the gap between the natural sciences on one hand and the social sciences and humanities on the other, is quite problematic, and in part, this is due to mathematical and graphical orientation of the former, as opposed to the linguistic orientation of the latter. This article explores the notion of patterns as means to develop a graphical vocabulary that may assist in cross- domain research that includes contributions from both the natural sciences as social sciences and the humanities. It will be clear that this is targeted for research themes that take place at the boundaries of the traditional disciplinary focus. In this article a number of patterns will be discussed and used to model a discourse on the theme of ‘mental health’, which is currently being recognized as being a concept at the interface of biological, psychological and social interactions.