Thinking through Drawing 2014 DRAWING EXPLANATIONS: ABSTRACTION IN ART MEETS ABSTRACTION IN THOUGHT Barbara Tversky a Eliza Bobek b a Columbia University b Stanford University
Drawing to Explain Just as most of us cannot speak without gesturing, artists, designers, scientists, engineers, and mathematicians don t seem to be able to speak without drawing. What does drawing allow them to say that words and gestures do not? Drawing to explain is ancient. Maps are a paradigmatic example. Relics of maps, which are in essence explanations of places, go back at least 6000 years (Brown, 1979; Noble, 1981). Maps were surely created earlier, but didn t survive. Maps are a remarkable feat of the mind. Unlike the even older cave paintings of animals and hands that have been found on every continent, maps are not drawings of what can be seen. Maps typically portray large spaces when small spaces are those that are viewed, so to make a map requires piecing together many different views. Maps typically portray overviews of spaces, when embedded views are those that are seen, so maps portray imagined views, not seen ones. Maps typically portray spaces schematically, lines for paths, boxes for places, when what are viewed are ground and sky, rocks, structures, and vegetation. Maps portray only the important elements of a space, their spatial array and their connections, typically simplifying and even distorting the elements and their structure (e.g., Tversky, 1993; 2000). Sketches Abstract and Organise the Essentials. Those qualities of a drawing, extracting and representing the essential elements and their structure, are among the reasons that designers, architects, engineers, mathematicians, and scientists grab napkins and draw as they think and explain. Words bear only an arbitrary, symbolic relationship to the ideas they express. Sketches map the elements and spatial (or metaphorically spatial) relations of ideas to elements and spatial relations on the page, the way they are arrayed in the world, or the way they are arrayed in our mental representations (Tversky, 2011). Natural spatial correspondences allow readily understood mappings of value, power, strength, happiness, and more to the space of the page (Tversky, 2011). Words come one after another, one replacing another, in a disappearing sequence. Gestures can also map elements to spatial arrays, but gestures, like words, are fleeting. Sketches remain in front of the eyes where they can be scrutinised, analysed, reorganised, and revised. Sketches expand the mind, which can quickly get overwhelmed by ideas that are large or complex. 1
Insights from Sketching. Scrutinising sketches or drawings or diagrams is a way to generate new knowledge. With maps, it is commonly used for finding the best route. But maps are also used for a broad range of inferences and discoveries, for predicting traffic, for understanding the spread of pollen or disease or populations, for redesign. Designers, architects, and artists actively engage cycles of looking and seeing in their practice (e. g., Goldschmidt, 1994; Kantrowitz, in progress; Tversky and Suwa, 2008). As noted by Schon (1983), they often describe this process of drawing new insights from their own sketches as having a conversation with their sketches. Getting new ideas from sketches, making inferences from drawings and diagrams can be challenging. Experts are better than novices (Suwa and Tversky, 1997), so, as for so many skills, practice is productive. Ambiguity helps (Tversky and Suwa, 2008). Perceptual reorganisation, reconfiguring the elements on the page, is especially effective, and among the skills that effective designers foster (Tversky and Suwa, 2008). Hints help, both concrete and abstract (Tversky and Chou, manuscript), as do analogies (Smith and Linsey, 2011), almost any way of changing perspective, bottom- up or top- down. As practitioners know from experience, distributing practice helps, get some coffee, take a walk, take a nap (Tversky and Chou, 2010). New associations, new ideas come forth unsolicited. Bridging the Divide: Abstraction in Art and Abstraction in Thought. If drawing can map ideas directly to the page, if scrutinising sketches promotes understanding and discovery, why are these practices limited to working artists, designers, scientists, and engineers, who embrace them? There appear to be barriers on both sides, both art and education. Drawing is common in early childhood education, but used primarily for drawing things, not ideas. This should change as the art world comes to embrace the beauty of drawings of ideas, a cause celebrated in this volume. But drawing has to be taken from the domain of art to the domains of teaching and understanding science, math, engineering, and even history, politics, economics, law, and literature. Books, websites, journals, and instruction in math, science, and increasingly in the humanities rely on diagrams that map ideas to space. Think of the simplest diagram, a network. A network consists of nodes and links among them. The nodes can represent any idea, intersections in maps, landmark dates in time, particles in physics, movements in history. Links represent the connections between nodes, spatial in maps, temporal in time, abstract in history. Networks are the backbones of visualisations of thought, and can be enriched to capture more aspects 2
of ideas. Despite the prevalence of visualisations of thought, students are typically asked to convey their knowledge in words. Creating Visual Explanations It is known that students benefit from explaining material they are learning to themselves or others (e. g., Fonseca and Chi, 2011). Intriguingly, self- explanations are even more effective from diagrams than from text (Ainsworth and Loizou 2003). Apparently, diagrams depicting phenomena evoke more thought than text describing the same phenomena. In most of those demonstrations, the explanations were verbal. Given that sketches and diagrams promote thought and inferences, would drawing visual explanations of science and engineering processes bring more benefits to learners than crafting verbal explanations? As noted, creating a visual explanation entails extracting the essential elements and relations and arranging them in the proper spatial array. Expressing processes entails extra effort because, for processes, there are at least three layers of structure, spatial, temporal, and causal. Conveying spatial structure, as in maps, architectural plans, or diagrams of the body or machines, is relatively easy even for novices, but conveying change over time, temporal and causal structure, presents challenges (e. g., Tversky, 2011; 2013). One of the advantages of visualisations is that they are static, allowing scrutiny and analysis. Visual explanations can be and often are animated to show changes in time. However, despite the conceptual correspondence of using change in time to convey change in time, explanatory animations have met with limited, if any, success, simply because of the difficulties of perceiving and comprehending changing displays (e.g, Tversky, Morrison, and Betrancourt, 2002). Although conveying change, process, or causality is difficult in visualisations, conveying change, process, and causality is relatively easy in words. Creating Visual Explanations Improves Learning. Because there are good reasons to think that visual explanations might surpass verbal ones and other good reasons to think that verbal explanations might surpass visual ones, an experiment was in order. Or two experiments, a task that we (Bobek, 2011) took on. In favor of visual explanations are the direct mapping of thought to marks on a page and the evidence that visual representations stimulate more reflective thought than verbal ones. In favor of verbal explanations are the ease of expressing change, behavior, process, and causality in language, and the difficulty of expressing those ideas visually. Bobek was teaching junior high science, and her classrooms and students served as our participants (with their approval and 3
the approval of the IRB). To one set of students, she taught an engineering unit, how a bicycle pump works, using a real bicycle pump in her lesson. To another set, she taught a science unit in chemical bonding, using a range of multi- media. Importantly, for both units, change over time, process, causality, are central. In case of chemical bonding, students knowledge was tested immediately after learning. Then each set of students was divided into two groups. One group was asked to create a verbal explanation and the other group was asked to create a visual explanation. Both groups were asked to create explanations sufficient for a complete novice to understand. After completing the explanations, students were retested. One remarkable finding was that in the case of chemical bonding, students did better on the second test of knowledge than the first test; that is, they increased their knowledge simply by creating explanations, in the absence of new information (students learning the bicycle pump were only tested once, after completing their explanations). The second remarkable finding was that creating visual explanations was more beneficial than creating verbal explanations for students with low spatial ability for the bicycle pump and for students with both high and low spatial ability for chemical bonding. Visual Explanations Contain More Information. To provide insight into the superiority of visual explanations, Bobek analysed both kinds of explanations and post- test performance in detail. For the explanations, information was separated into structural and functional. Structural information was primarily information about the parts and their configuration, information that is relatively easy to depict; functional information was primarily information about behavior, process, or cause, the information that is harder to depict and easier to describe. However, the visual explanations used both depiction and description to explain the processes, whereas the verbal explanations almost never added depictions. As a consequence, for both the bicycle pump and chemical bonding, visual explanations included more structural information than verbal explanations and equal amounts of functional information. See one (good) example of each below: 4
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Why Creating Visual Explanations is Better There appear to be several reasons for the superiority of creating visual explanations to creating verbal ones for learning. First, there is a natural mapping from meaning to space, from the elements and relations of ideas to the visual elements and spatial relations on the page. In particular, it is easier to show what elements look like and to show spatial and other relations than to explain them in words. Next, the diagrammatic nature of visual explanations provides checks for completeness are all the parts there? and for coherence are the parts assembled in the right configuration? It is far easier to overlook both in verbal explanations. Finally, the diagrammatic nature of visual explanations provides a platform for inference from structure to function. What behavior is enabled by the structures depicted? In many cases, diagrams and sketches can suggest behavior, process, and causality by using arrows (Heiser and Tversky, 2006) or sequences of sketches, as in the previous examples. Drawing Things Together Perhaps it is not megalomaniac to suggest that drawing is the bridge between abstraction in art and abstraction in STEM. We have seen that those in both the arts and in STEM draw to explore ideas and to express ideas. Putting thought on a page demands abstracting and organising the essentials. Inspecting what s on the page allows consideration of the ideas, and 6
then reconsideration, revision, and inference, processes that are fundamental to thinking and creating. For art, it appears as though drawings are goals in and of themselves, and for STEM, drawings serve the ideas, but as the papers in this volume make clear, visualisations of ideas can be beautiful, and drawings can evoke beautiful ideas. Acknowledgments. The authors are indebted a number of colleagues or collaborators excited about drawing, especially Andrea Kantrowitz, Juliet Chou, and Masaki Suwa. The authors are also grateful to NSF grants HHC 0905417, IIS- 0725223, IIS- 0855995 for facilitating the research and or preparing the manuscript. 7
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