The Seven Trans-Disciplinary Habits of Mind - Punya Mishra's Web

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and transformative- teaching. The article introducesthe Technological Pedagogical Content Knowledge(TPACK) framework as a way to develop the specializedknowledge, skills, and understanding that teachersmust have to become effective classroom constructorsof transformative learning experiences. The authorsnote seven cognitive tools needed for success in thenew millennium, within this TPACK framework. Toillustrate and describe these skills, they offer examplesof how teachers can repurpose digital technologiesto use these thinking skills toward building excitingtransformative learning experiences, across a variety ofsubject matters. The authors explore the implicationsfor research and practice.Today, the defining skills of the previous era-the "leftbrain" capabilities that powered the Information Agearenecessary but no longer sufficient. And the capa~bilities we once disdained or thought frivolousthe"right brain" qualities of inventiveness, empathy,joyfulness, and meaning-increasingly will determinewho flourishes and who flounders. (Pink, 2005, p. 3)The Role ofTechnology in learningWe live in exponential times-digital technologieshaye already transformed the way we work and play. Fromcell phones to Websites, from YouTube videos to multiplayergames like World of War craft, technology is fundamentallychanging how we interact with information andwith each other. The future promises more of the same,given the increasing pace of technological innovation.This rapid rate of change is a challenge for educators,as technologies become obsolete as quickly as theyarrive. There is increased pressure on teachers to learnnew ways to incorporate technology into their teaching.Technology integration, however, still finds disappointinglevels of penetration and success (Barron, Kemker,Harmes, & Kalaydjian, 2003; Bauer & Kenton, 2005;Cuban; Kirkpatrick, & Peck, 2001; Ertmer, 2005; Frank,Zhao, & Boreman, 2004; Gulbahar, 2007; Keengwe,Onchwari, & Wachira, 2008). For effective integration,teachers must know more than the technical aspects oftechnology, and must understand its affordances andconstraints both for representing content and identifyingpertinent teaching approaches (Harris, Mishra, &Koehler, 2009). Recently, the Technological PedagogicalContent Knowledge (TPACK) framework (Koeh ler &Mishra, 2008; Mishra & Koehler, 2006) has been offeredas an integrated framework for teacher knowledge foreffective technology integration.The TPACK framework acknowledges that teachingis a highly complicated practice using flexible and integratedknowledge (Shulman, 1986, 1987). Teacherspractice in a complex, dynamic environment (Leinhardt& Greeno, 1986; Spiro, Coulson, Feltovich, & Anderson,1988; Spiro, Feltovich, Jacobson, & Coulson, 1991) andmust integrate knowledge of student learning, knowledgeof the subject matter, and increasingly, knowledge---Technological ......'-/'''' -Pedagogical Content " \./KnowledgeI (TPACK) \I \ContentIKnowledgeTechnological \{ (TCK) J\ I\ I\ /'" ' Pedagogical /" Content'- ' Knowledge /" .... '- ",--­...... Contexts _,Figure 1. The TPACK' Framework (source: www.tpack. org). 'of technology. At the intersection of pedagogy, content,and technology is the specialized brand of teacherknowledge represented by TPACK.The TPACK framework (see Figure 1) describes thesecomponents as being a critical synthesis of knowledgeused by the most effective teachers. Content Knowledge(CK) refers to the knowledge about the subject matter, suchas eighth-grade mathematics, or fifth.grade science(though we shall complicate this straightforward conceptualizationlater in this article). Pedagogical Knowledge(PK) refers to knowledge about the processes and practicesor methods of teaching. It includes classroom managementskills, teaching strategies, evaluation techniques,and the nature of the target audience. TechnologyKnowledge (TK) refers to knowledge about both the standardtechnologies and more advanced technologies(Harris, Mishra, & Koehler, 2009; Koehler & Mishra, 2008;Koehler & Mishra, 2009; Mishra & Koehler, 2006; Mishra& Koehler, 2008; Mishra & Koehler, 2009).These three core constructs (diagrammed in Figure 1)interact in important ways. At their heart is TechnologicalPedagogical Content Knowledge (TPACK),which emerges from the interaction of content, pedagogy,and technology knowledge. The TPACK frameworksuggests that quality teaching requires a nuancedunderstanding of the complex interplays between threekey sources of knowledge: technology, pedagogy, andcontent, and addresses how they play out in specificcontexts (Koehler & Mishra, 2008, 2009; Mishra &Koehler, 2006). It is also important to note that theTPACK framework offers no specific directives aboutwhat content to teach (science or music), whichEDUCATIONAL TECHNOLOGY IMarch-April 201123

pedagogical approaches are useful (didactic or constructivist),and what kinds of technologies to use inteaching (digital or analog). Thus, given the changingworld we live it, it becomes critical for us to ask ourselveswhat it is that today's students need to know inorder to succeed (i.e., understand the "C" in the TPACKframework). Once we identify these larger purposes andgoals, the TPACK framework helps us consider how toachieve them via technological/pedagogical solutions.Living and Learning in a Changing World:An Overview and a CritiqueThe rapid evolution of technology in the 21st centurycalls for '! new form of learning, one that is receptiveto our continually changing world (Florida, 2002).Recently there have been a spate of books and reports thatcriticize the current goals and practices of schooling(Keengwe, Onchwari & Wachira, 2008; Kozma, 2003,2009; Zhao, 2009). These authors argue that schoolingneeds to be fundamentally reconfigured to emphasizehigher-order cognitive processes, such as critical thinking,creative problem solving, curiosity, and adaptability.Most of these recommendations, however, do noteven mention content, and in the rare cases that theydo, it is only in terms of traditional disciplinary contentareas, such as language arts, mathematics, and science.Standard disciplinary structures, , around which schoolcurriculahave been constructed, may not be as useful asthey once were. Disciplinary knowledge is shiftingbeneath our feet (Koehler & Mishra, 2008). Recommendationsfor the future of learning emphasize the importanceof being able to creatively move across multipledisciplines, to cross-pollinate ideas between domains.Furthermore, current research and theory on creativitysuggests that creativity is both domain-general anddomain-specific. As Plucker and Zabel ina (2009) write:A person who deals with domain general techniquesand approaches to creativity will never scratch thesurface of a problem, yet someone who focuses tootightly for long periods of time on a particular task islikely to experience functional fixedness ... [Thel optimalcondition for creative production is a flexible positionsomewhere between generality and specificity ... withthe individual moving between positions as the task orproblem of the moment dictates. (p. 9)This means that creativity is intimately tied "tocultures of disciplines, ways of knowing and being thatare constrained by specific fields of study as well asbroader ways of thinking that cut across differentdisciplinary frameworks.Transformative Learning andTrans-Disciplinary LearningAs must be obvious, preparing students for 21 stcentury learning presents a challenge to educators, andrequires us· to rethink the goals of education.Transformative Learning Theory (Mezirow, 1991, 1995,2000) addresses this challenge by requiring learners torethink prior knowledge, or even drastically transformtheir approach to an idea. Transformative LearningTheory expresses the universal challenge of teachingand learning as a critical kind of knowledge transformation,a "paradigm shift" or a perspective transformation,in which a renovation of existing knowledge structuresoccurs (McGonigal, 2005).We suggest that trans-disciplinary knowledge whichemerges from disciplinary practices, and also transcendsthem, is critical. Trans-disciplinary knowledge helpsstudents move beyond looking for one "correct" solution,towards an approach that integrates differentsolutions, viewpoints, or perspectives.Trans-disciplinary approaches eschew traditional distinctionsbetween art and science, applied and pureknowledge. This approach seeks to find commonalitiesbetween strategies and habits of thought used by creativeindividuals in any discipline. Our work in this areabuilds on prior conceptual work done in this area byRoot-Bernstein (1996) and Root-Bernstein and Root­Bernstein (1999), which studied the value of trans-disciplinarylearning through both historical and empiricalresearch. Th is led to thei r assertion that creative scientistsand artists generally use a key set of cognitive skillsthat cut across disciplinary boundaries. As the Root­Bernsteins (1999) note:... at the level of the creative process, scientists, artists,mathematicians, composers, writers, and sculptorsuse ... what we? call -"tools for thinking," includingemotional feelings, visual images, bodily sensations,reproducible patterns, and analogies. And all imaginativethinkers learn to translate ideas generated by thesesubjective thinking tools into public languages to expresstheir insights, which can then give rise to new ideas inothers' minds. (p. 11)Based on their key "thinking tools" we proposeseven key trans,disciplinary tools (or cognitive skills),which encapsulate how creative minds think effectivelyacross a range of domains.* These seven cognitive toolsare: perceiving, patterning, abstracting, embodied thinking,modeling, play, and synthesizing. Each of these isdescribed in greater detail below. We assert that these"tools," or habits of mind, comprise a frarnework fortrans-disciplinary creativity and can serve as the basisfor the kinds of curricula that are essential for the "conceptualage" (Gardner, 2007; Pink, 2005).• The Root-Bernsteins list 13 cognitive tools in their book. We have modifiedthis list to come up with seven that we consider to be particularlysignificant.24EDUCATIONAL TECHNOLOGY IMarch-Aprii 2011

Connecting TPACK toTrans-Disciplinary Cognitive ToolsWe began this article with a description of the TPACK. framework and noted that it did not specify explicit pedagogica[and content goals. The preceding sectionsdeveloped an argument for transformational [earning ofa specific kind-moving from standard disciplinarystructures to those which are trans-disciplinary.Consistent with the TPACK framework, this change inhow we conceptualize content has implications forboth pedagogy and technology. Here we describe eachcognitive tool and offer examples of how each can beinstantiated in a classroom context through appropriate,TPACK driven uses of technology.Perceiving'The cognitive tool of perception is critical to both thearts and the sciences. This is a two-layered process,requiring both observing and imaging. Observing is afinely tuned skil[ based on focus on, attention to, andcuriosity about information gathered through the fivesenses. For example, bacteriologists use their sense ofsmell to observe bacteria, or an ornithologist mightidentify bird species by sound. Imaging calls for theability to evoke or bring to mind the impressions/sensations we observe, without the presence of externalstimuli. Artists, scientists, mathematicians, and engineersall have well-developed imaging skills andfi nd them essential for the work they do.Both observation and imaging can be honed withpractice to improve the skill of perceiving, and teacherscan design opportunities for students to develop theseskills. The Website Found Functions, for example, combinesphotographs of curves found in nature with thegraphs and functions associated with them. This sitecan push students to go beyond the "abstract" curves intheir textbooks, and observe the "underlying mathematica[rea[ity" of objects in the world. This type of exerciseutilizes knowledge highlighted in the TPACK frameworkwhere the use of technology is inextricably [inked tothe needs of pedagogy and content.PatterningCreative practitioners are always involved in recognizingand creating patterns. Recognizing patterns involvesidentifying a repeating form or a plan in a seemingly arbitraryarrangement of things or processes. Recognizing isthe analytical part of patterning, while forming is basicallya creative act of constructing new patterns. For example,when architects study a landscape and then utilize thepatterns they see to design a building, they are both recognizingand creating patterns. Innovative writers andpoets also do this, relying on their knowledge of linguisticpatterns and structures, with their own innovations, inorder to dream up a new story, poem, or other formof writing (Gardner, 1983; Root-Bernstein, 2003).Teachers can help students develop patterning skil[swithin and across domains. One example demonstrateshow the TPACK framework might be used to developpatterns in math and/or music, using freely availableDJ software called trakAxPC. This software lets usersdownload music samples and copy and paste them intoa mixer. Students can cut the samples into smallerunits of sound and rearrange them. What makes thiscompelling, from a TPACK standpoint, is that studentscan manipulate the software to help them describe andexplain fractions, ratios, and percentages. By connectingmusical concepts such as rhythm and tempo to mathematica[concepts (ratios and percentages, etc.), studentscan creatively find and build patterns. The elementsof TPACK in this lesson are just one example of themyriad possibilities of how technology, pedagogy, andcontent can seam[ess[y combine to design [earningenvironments that promote students' patterning skills.AbstractingCreative people use Abstracting in order to concentrateon one feature of a thing or process, in order to boilit down to basics and grasp its essence. Scientists, forexample, eliminate superfluous traits from a physicalsituation (i.e., shape, size, co [or, texture, etc.) to key inon features of interest such as boiling point or mass.Another aspect of abstracting is the finding of analogiesbetween seemingly disparate things. We may be morefamiliar with poets using analogical thinking, butscientists do it as wei!. Newton's comparison of themoon to a ball thrown so hard that its descent missesthe earth and passes intoorbit is an analogy as well, andone that led to the theory of universal gravitation.A creative example of abstracting is given by a professorof mathematics to her students, to write mathematicalpoetry and share it on the Web. Writing creatively anddel iberate[y about mathematical topics necessitates adeep understanding of both poetry and mathematics. Inorder for students to retell a mathematical proof or ideain a new an~ different way, they must fully understandthe main idea (to abstract) and then "trans[ate" thisthrough analogies and rhetorical moves into rhymingverse. Sean Nash, a high school biology teacher at St.Joseph Missouri, has extended this to the domain ofscience as well and has written extensively (on his b[og)about its pedagogical value. His students have writtendozens of poems that they share with the world on theirclass site. This lesson shows us how technology, pedagogy,and content.are bound together towards a commongoal of transformative [earning, and to facilitating thetrans-disciplinary skills of abstracting and analogizing.Embodied ThinkingEmbodied thinking involves two skills which generallyfeed into each other-Kinesthetic Thinking andEDUCATIONAL TECH NOLOGY/March-Aprii 201125

Empathizing. Kinesthetic Thinking means thinkingwith the body, including the sensations of muscle, skinand sinew; and the feelings in the body of movement,balance, and tensions. For example, in his thoughtexperiments, Einstein imagined himself as a photon, anddescribed not only what he saw, but what he felt in hisbody (Root-Bernstein, 2003). Besides this trait of bodilythinking, an important element of embodied thinking isempathizing, or imagining oneself in another's pOSition,or thinking and feeling as they would. Actors, poets, andnovelists, for example, frequently empathize withcharacters in order to portray them in interesting ways.Individuals in the sciences must also sometimes applyempathetic thinking to understand other organisms,even non-living things and processes.Technology can easily engage embodied thinking toillustrate a number of concepts. For example, by using atilted and time-infused version of the Cartesian coordinatesystem (a dynagraph) in a math applet createdwith Geometer's Sketchpad, teachers can demonstrate theproperties of a mathematical function. In such an applet,students drag the input point A along a horizontal axis,and the output responds by moving appropriately accordingto a certain rule or function. Students can see the functiontraced over time, and feel the tempo of it as the inputis pulled along the axis. Students can watch the motionsof such functions with the same curiosity they might directtoward human behavior, asking,1uWhat will they do next?Why are they moving like that?" From a TPACK standpoint,this is a simple but powerful way to fuse technology,pedagogy, and content in a kinesthetic manner. Thelearning experience is transformed from static to tactile.ModelingModeling is to represent something in real ortheoretical terms in order to study its nature, composition,or purpose. Artists create and draw on models,often by preparing smaller views of a piece of art inadvance of creating it. Scientists also employ basicmodels of things and processes. Modeling requires thatwe employ abstractions or analogies, and more importantly,that we use the facility of dimensional thinking,that is, our thinking with respect to space and time.Creative people think dimensionally when they changethe scale of things, when they take two-dimensionalinformation on blueprints and construct them in threedimensions, or vice versa. Dimensional thinking, pairedwith abstractions and analogies, helps create models ofthings or processes that explain the real world.As a part of the 8its to Atoms project at the Universityof Virginia, teachers use cheap, portable, and lightweightdie-cutting machines to teach mathematics andvisualization to children as young as second-graders.Students can develop their three-dimensional visualizationskills by designing 2-D cutouts that are then diecutand constructed into 3-D shapes. Examples thathave been used include models that depict the Earth'smajor tectonic plates that are designed to be cut out andassembled with the aid of a used tennis ball. These areexplorations that combine the power of manipulatingdigital bits and bytes with the physicality of atoms.Deep Play or Transformational PlayPlaying is something that we do just "for the fun of it."When innovative people play with things, or concepts, orprocesses, they may open doors to new ways of thinkingvia unexpected breakthroughs. Creative people in differentdisciplines all play with distinctions, boundaries,unassailable truths, and the limits of utility, and it isthrough this play that they also transform. We call thisdeep play to distinguish it from everyday play, which canbe superficial. Deep play in contrast is creative, seekingto construct new ways of being in the world. In this, ourapproach is consistent with current research on educationalgames and learning, particularly the idea of epistemicgames (Gee, 2003; Prensky, 2001; Shafer, 2005).Mathematicians often describe their work as beingakin to play. Through video games, simulations, puzzles,and interactive software, students can engage and playwith ideas, propose solutions, and test them. In someway, many of the examples already provided above canbe seen as examples of play. The crucial difference isthat the essence of play is its open-ended ness and thatneeds to be considered when thinking of including playin the classroom.SynthesizingThe final cognitive tool ties together all the toolsdiscussed above. Synthesizing requires that we put multipleways-of-knowing together. When we fully understandsomething, our feelings, senses, knowledge, andexperiences come together in a multifaceted and cohesJvekind of knowing. A person feels what they knowand they know what they feel. For example, Einsteinnoted that when he sai led he felt and experienced mathematicalequations occurring via the boat interactingwith the wind and the water. The creative process isoften described by artists, writers, and scientists as acoming together of the five senses and their emotions, inan aesthetic and intellectual experience which is difficultto dissect. When feeling and thinking work together,creative and intellectual processes are far more powerfuland have been described as being "synesthetic."The act of synthesizing is difficult to describe. It is similarto Dewey's idea of an educative experience, wherecontinuity of an individual's past interacts with the presentsituation to open up a person's access to futuregrowth experiences. By bringing together the previoussix habits of mind, synthesis allows for the developmentof deeper connections between subject matters. Thus,these ways of thinking, and the examples that go witheach, are not completely independent of each other.26EDUCATIONAL TECH NOLOGY/March-April 2011

Figuring out the mathematical equations underlyingshapes in nature is as much' a process of perception as itis one of construction. Writing a poem is as much aboutpattern forming as it is about abstraction. In this these sixprevious tools work together to develop a synthesisgreater than the sum of its parts.ConclusionThese seven cognitive tools, which emerge out ofdisciplinary practices and are yet universal in theirapplication, are key aspects of the kinds of transformativelearning we seek to achieve.Please note that most of the examples we've providedrequire educators to repurpose existing tools for pedagogical.purposes.For instance, using the die-cut printerfor teaching solid geometry was not something the toolwas designed for-but it is an extremely powerful toolfor doing so. We have described this idea of "creativerepurposing" in greater detail in other. publications(Koehler & Mishra, 2005; Mishra & Koehler, 2003).Also, the reader may have noted that all the examplesprovided are connected to mathematics. This choiceshould not in any way suggest that these seven cognitivetools are applicable just for this domain. Quite the contrary,as trans-disciplinary skills they can, and should, beapplied across other domains. One of the reasons forchoosing mathematics is that mathematics is often seenas a dry subject, restricted to1formulaic (pun intended)problem-solving strategies. What few students realize isthat this dull conceptualization of mathematics is verydifferent from how practicing mathematicians see it.Mathematics can be (and has been) the basis of manyartistic endeavors: from the tessellations of M.e. Escherto the songs of Tom Lehrer; from the Op art of BridgetRiley to the impossible structures of Roger Penrose; fromthe geometric patterns of Islamic architecture to thethree-dimensional geodesics of 60-atom carbon molecules.All of these go to show that mathematical sophisticationand artistic representation, far from beingdivorced from each other, actually do go hand in hand.To realize that many students do not get to explorethis rich conceptualization of mathematical thinking istragic, denying them access to some of mankind's greatestachievements. One could easily replace mathematicswith writing, or music, or science, or political science, andthe argument would still hold true, though the exampleswould change. 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Catching up or leading the way: Americaneducation in the age of globalization. Alexandria, VA:ASCD.Virtual Worldsas a Triggerfor TransformativeLearningStephen W. HarmonThis article examines the affordances of virtual worldsfor initiating a transformative learning experience foradults. In particular, it addresses the capacity of virtualworlds to allow creation of an alternate self whichrequires some level of personal self-reflection; provideatypical experiences that can initiate reflection; allowexperience of typical situations from alternate viewpoints;and enable shared professional expertise of acomplex domain.Alison Elliott is a priestess who enjoys collecting wildflowers and herbs. Recently she was out looking for asomewhat rare wildflower in a beautiful meadow notfar from her home, when she realized she was notalone. This was clearfy going to be trouble. Her heartbegan racing as she turned and fled. A pair of miscreantscame after her. She knew her only hope was to try andfight them off. She spotted a large tree and decided itwould have to do. She planted her back against it andraised her walking stick to defend herself. Before shecould even utter a cry a rogue appeared from out ofnowhere and drove his dagger into her back. In a secondit was over and Alison Elliot was dead. As her spirit roseinto the air she heard one of her assailants say, //That'sthe third zombie priestess I've killed in this valley tonight.What is this place coming to?"IntroductionAlison (a pseudonym) is not really an undead priestess,of course, at least not most of the time. In reality she isa 45-year-old school media specialist who was playingWorld of Wareraft as an assignment for a class inonline learning. I have given this assignment to stu-Stephen W. Harmon is Associate Professor and Director ofLearning Technologies at the College of Education at GeorgiaState University in Atlanta. His research focuses on new andemerging technologies for learning and performance. He alsoconducts research on instructional technology in developingcountries and has worked on projects throughout the world,including ventures in Botswana, South Africa, and Egypt (e-mail:swharmon@gsu.edu).28EDUCATIONAL TECHNOLOGY/March-April2011