Method 101: Diagramming as Theorizing

Yrjö Engeström is a Professor of Adult Education and Director of the Center for Research on Activity, Development, and Learning (CRADLE) at the University of Helsinki and Professor Emeritus of Communication at the University of California, San Diego.

Yrjö Engeström was attracted by the Soviet-Russian tradition of cultural-historical activity theory when he was a university student and activist and started his first activity-theoretical study in 1982. In order to avoid the curricular constraints in school settings, he chose the world of work and organizations as the field of study in which he encountered a more open attitude toward novel ideas and practices. (Engeström & Glaveanu, 2012, p.515).

This start point anchored his research trajectory and led to a series of great innovations such as Activity System, Expansive Learning, and Developmental Work Research. In 1987, he published his keystone work titled Learning by Expanding (1987/2014) in which he developed the now-famous Activity System triangle, the concept and model of Expansive Learning, and the early version of the methodology of development work research. Since then, his research has significantly advanced our understanding of development and learning in different work settings and made significant contributions to cultural-historical activity theory.

One major outcome of Learning by Expanding is a diagram that aims for picturing Leontiev’s activity system. Now the diagram has a nickname called “Engeström’s Triangle”.

Engeström’s triangle is based on the cultural-historical psychologists’ notions of mediation as individual action (subject — instruments — object) at the top of the diagram. Engeström (1987) considered “a human activity system always contains the subsystems of production, distribution, exchange, and consumption.”(p.67), thus, he added the bottom of the triangle to the original individual triangle in order to include other people (community), social rules (rules), and the division of labor between the subject and others.

Some authors see this diagram as a graphical heuristic. For example, Geri Gay and Helene Hembrooke said, “…Building on these principles, Alexei N. Leont’ev (1981) created a formal structure for operationalizing the activity system as a complex, multilayered unit of analysis (figure 1.1). His model is less a representation of reality than a heuristic aid for identifying and exploring the multiple contextual factors that shape or mediate any goal-directed, tool-mediated human activity.” (2004, p.2).

Clay Spinuzzi (2020) also used “graphic heuristic” to review this model, “…Engeström provided a graphical heuristic (the now-famous triangle) for picturing Leontiev’s activity system. This heuristic, which has been derided by some critics (e.g., Miller, 2011)…”. However, Spinuzzi pointed out the positive value of the diagram, “This heuristic…was meant not only as an analytical device for researchers but (critically) also as a way to communicate with — and codesign work with — research participants (e.g., Engeström, 1999; Engeström & Sannino 2010). That is, it served as an interventionist “language game” (Ehn 1989) similar to the prototypes and organizational games that Bødker and other participatory designers used to leverage the tacit expertise of participants. This point has been overlooked by those who have critiqued the triangle heuristic as an oversimplified theoretical tool.”

Engeström considered the use of graphic models as an important part of his method of theory building. He said, “There are further two specific features of presenting and processing data in this book. The first one is the extensive use of quotations from the theoretical sources discussed and analyzed. The second one is the almost equally extensive use of graphic models.”

He sees graphic models as both representations and instruments which invite readers to build their own version of the diagram. He said, “My extensive use of graphic models serves a twofold purpose. For the first thing, it aims at making the central categories found transparent and compact. This is the representation function of the models. But I use the graphic models in a series of successive variations, not just as singular representations. The series of successive variations serve the instrumental or processual function of the models. With the help of such variations, I try to demonstrate how the models can depict movement and change. The reader is invited to formulate and test his own variations.” (1987, p.47)

How many diagrams did he use for chapter 2? The answer is not 1, it is 12.

Engeström really understood the power of the diagram and diagramming. I use the noun “diagram” to refer to what Engeström called “representation function of the models” and the gerund “diagramming” to refer to what Engeström called “instrumental or processual function of the models.”

The representation is static, permanent, and bounded while the instrument is dynamic, temporary, and boundaryless. From the perspective of activity theory, a diagram is an instrument of our knowing and understanding. Vygotsky, distinguished between two types of instruments in human activity: tools and signs which also means “psychological tools”. According to Vygotsky, “The following can serve as examples of psychological tools and their complex systems: language; various systems for counting; mnemonic techniques; algebraic symbol systems; works of art; writing; schemes, diagrams, maps, and mechanical drawings; all sorts of conventional signs; etc.” (Vygotsky 1981, 137. cited in Engeström, 1987)

Clay Spinuzzi (2020) reviewed some criticisms of Engeström’s triangle and gave a fair assessment as a response. He said, “Engeström provided a graphical heuristic (the now-famous triangle) for picturing Leontiev’s activity system. This heuristic, which has been derided by some critics (e.g., Miller, 2011), was meant not only as an analytical device for researchers but (critically) also as a way to communicate with — and codesign work with — research participants (e.g., Engeström, 1999; Engeström & Sannino 2010). That is, it served as an interventionist “language game” (Ehn 1989) similar to the prototypes and organizational games that Bødker and other participatory designers used to leverage the tacit expertise of participants. This point has been overlooked by those who have critiqued the triangle heuristic as an oversimplified theoretical tool. (See Sannino 2011 for further elaboration of this point, and see Engeström 2018, pp.23 and 78 for other representations Engeström has developed for local stakeholders.)”

As Engeström mentioned, “I use the graphic models in series of successive variations, not just as singular representations…With the help of such variations, I try to demonstrate how the models can depict movement and change. The reader is invited to formulate and test his own variations.” (1987, p.47) We should remember that the diagram is not a dogma but a guide to action.

When we think about thinking, we usually think we are thinking in words. However, linguistic thought is not the only way of the human mind. Cognitive scientist and psychologist Barbara Tversky argued that spatial thought is the foundation of our abstract thinking in her 2019 book Mind in Motion: How action shapes thought.

I want to highlight three ideas I learned from Barbara Tversky. The first is about taxonomy and partonomy, the second is about individual differences in mental rotation, and the third is a story about the Feynman diagram. First, Tversky said, “Spatial hierarchies are partonomies, not taxonomies like the categories of objects, events, and scenes…Partonomies are hierarchies of parts; taxonomies are hierarchies of kinds…categories allow reducing the amount of information in the world…Like taxonomies, partonomies allow inferences, but inferences of containment, not of properties…(p.77–78)”

According to Tversky, “Mental rotation is a distinctly visual-spatial transformation. It has been likened to watching something actually rotate in space…mental rotation task has become one of the major measures of spatial ability.” (p.89–90) She also pointed out the individual differences in mental rotation, “Surgeons, plumbers, electricians, football coaches, mathematicians, fashion designers, urban planners, gardeners, physicists, fire fighters, architects, basketball players, interior designers, dentists, and so many more use mental rotation and other forms of spatial reasoning regularly in their work…lawyers and journalists and historians and accountants and executives and philosophers and poets and translators don’t seem to need mental rotation in their work.” (p.91)

Tversky also directly talked about the diagram in chapter eight of Mind in Action. The title of the chapter is Spaces We Create: Maps, Diagrams, Sketches, Explanations, Comics. She said, “The ease of reasoning from well-designed diagrams has encouraged new fields to blossom, endeavors to make mathematics, logic, physics, and computer science diagrammatic, yet rigorous, in order to capitalize on our extraordinary abilities to see spatial relations and to reason about them. The rationale is the same, that diagrams use the power of spatial-motor reasoning for abstract reasoning.” (2019, p.210)

Tversky shared a story about the Feynman diagram with us, “Mark Wexler, now a cognitive scientist working on perception and mental imagery, used to be a physicist. When he was a physicist, he was working with the Feynman diagram in Figure 8.8. Each gray blob represents a separate universe. For the universe to be coordinated, the twist in the lower blob had to be undone. He imagined grabbing each of the lower ellipses with his thumb and index finger and twisting them in opposite directions, a bit like Cat’s Cradle. Doing that made him realize that untwisting the lower one twists the upper. The only way to remove the twist is to cut one of the attachments. This conclusion has implications for spacetime and quantum gravity, but that’s beyond me and thankfully beyond the scope of the book. His intuition turned out to be right, as he later showed in a rigorous line-by-line proof. Feynman diagrams are admittedly abstrute, as is the physics they represent, but once they are learned, like all effective visual spatial representations, they become a powerful thinking tool.” (p.211)

The goal of activity theory is for understanding various types of human activities in the real world. Engeström also targeted his audience as both researchers and practitioners. The value of learning activity theory is not only knowing some concepts and ideas but the real transformation in real life with the help of concepts and methods of activity theory. I want to claim that Engeström’s triangle and his graphical approach to theory building is a great case of “diagramming as theorizing”.

Since Barbara Tversky claimed the sixth law of cognition as “Spatial thinking is the foundation of abstract thought” (p.72), we should change our minds on theory development and knowledge building. It is time to switch from “language-based theorizing” to “spatial thinking-based theorizing”. Diagrams and Diagramming are great approaches for visualizing complex structural relationships such as “activity” and other social phenomena.