CEP 957 Notes

Possible article title: Learning and Teaching in Complex Domains

! We want to give specific advice to teachers about low-threshold opportunities to deal with complexity in their teaching more appropriately/effectively

Boxes (examples of complexity? sample cases?)

Part of the paper structured like Wittgenstein's choose-your-own-adventure?

Irrationally held truths may be more harmful than reasoned errors. -Thomas H. Huxley

Goal of paper: an umbrella/synoptic view of learning and teaching in complex domains, from whence readers can depart to other texts, return to from other texts, and put other texts in context

20-30 page manuscript

Introduction: Maps and Labyrinths

Nature of Complex Domains

• What is complexity?
• Why should we care?
• Complex vs. ill-structured

Strategies for Exploring Complex Domains

• Cognitive and affective disposition
• Criss-crossing, revisiting, and iterative knowledge
• Analogies, models, and the trap of tools

Teaching Complexity and Complex Things

• A sample model/game: Complexity Bingo
• Principles and cases

Conclusion: Why Should We Care (Revisited)?

Nature of Complex Domains

What is complexity?

• Looking at a thesaurus or synonym finder to get a sense of what we already know (or think we know) about complexity
• Consider the appealing or unappealing connotations of synonyms of complex
• undecipherable, enigmatic, cryptic, puzzling, perplexing, bewildering - games as enigmatic texts to non-gamers (the literacy Gee speaks of); players (esp. adolscents) using games to create and defend private subculture(s)
• tortuous, sinuous, meandering, anfractuous, flexious - the challenge and anxiety of games as desirable to players
• obsession, fixation, mania - gaming as healthy or unhealthy, the need for moderation
• Wittgenstein: "meaning is use" (e.g., what is a game?) (people can use "game" in a sentence, but can't define it) (e.g., what is constructivism?)
  • Parallel to the spirit v. the letter of the law (and connect that to cases, case precedent, casuistry)
  • Rather than Platonic forms, embrace Wittgenstein's family resemblances (which may be the same as intuition)
• Great successes in all four boxes of "Types of world's hypotheses"
• Complex domains
  • Total Cost of Ownership
  • infinite diversity in infinite combinations (Star Trek)
  • Genre?
  • Equilibrium (can be dynamic but appear static)
  • Expert admissions officers vs. simple linear regression (high school GPA and composite SAT score): regression outperformed as a predictor for success in college

Why should we care?

• Big goals in education: metacognition and transfer
  • Bad: oversimplified, overgeneralized
  • Good: constructivism, discovery learning
  • Understanding and accelerating expertise, esp. in professions (e.g., medicine)
  • Getting it right, using it, power and efficiency
• New tools for writing, reading, learning, teaching (knowing?)
  • Hypermedia; Readerly texts vs. writerly texts (Barthes)
  • Compare to Wittgenstein's index cards, allowing many possible books by re-ordering the numbered passages
• Well-structured domains may seem ill-structured to novices (and ill-structured domains may seem well-structured)
• Opposing a conspiracy of certainty
  • Closure science vs. frontier science
  • "Need" for certainty vs. need to be adaptive and flexible to survive and thrive (hence real need is for uncertainty)
  • Robot using simple algorithms to navigate a maze, doesn't need to know about mazes or maze-ness
  • Tangent to whether our civilization of certainty and control is leading us toward doom (e.g., creating self-perpetuating dangers like super diseases)
  • Bob Dole, universal health care, and a complex chart (1994 State of the Union?) (Ross Perot mocked for his charts?)
• Motivation = Expectancy x Value. Honoring complexity should help raise the value side, thus raising expectancy
  • Answering: When we will ever use this? don't wait for field experience for the "real" learning

Complex vs. ill-structured

• Rand distinguishes complexity from ill-structured
  • Complex != Ill-structured (at least not necessarily; plenty of correlational cases)
  • Babies babbling, only the parents understanding, multidirectional, baby learning from parents, parents learning from babies
• Rand says ill-structured domains are non-essentialist
  • Ill-structured domains tend to be more ambiguous
• Need to determine what's truly new, and what can be understood through older contexts and models; Rand thinks a totally novel context is a rarity
• Aristotle, organic unity: specialized, focused organs working in concert in a larger organism
• Rand distinguishes difficult from deep
• Well-structured knowledge may be ill-structured with regard to access (schema selection)
• Ill-structured domains as just out of reach of understanding. If defined then seldom ill-structured in the grand sense, anymore. So CFT etc. is a lens for viewing the frontier. Different lenses once explored

Strategies for Exploring Complex Domains

• Theories of learning in ill-structured domains don't need to be ill-structured themselves (e.g., CFT).
• Figurative language can be valuable in studying complexity and complex domains (but don't be bounded by models and metaphors).

Cognitive and affective disposition

• being aware of your lenses, your habits of mind
• Focusing on entaglements, don't try to vaporize them
• The skills and mindsets for studying complexity (e.g., not being bounded by models and metaphors) are useful in other pursuits
• Not weird when teaching to read chapters out of order, but heavily hypertext text is worrisome to some readers; is it that kids are more comfortable (generation/technology issues)? learners are more comfortable? both? (intersection with game studies)
• Sometimes we like complexity (composite materials in a ski, a sophisticated recipe/flavors), sometimes we don't
• Parallels between conspiracy of convenience and educational technology: people don't want to be confronted with the reality/complexity of instruction (and the need for innovation in ed tech integration) because it's simpler to stick with the familiar. Similar parallel to innovative instruction (constructivism, group work, activities vs. lecture)
• Ignorance is bliss. People don't want to know that something is complex. e.g., 10 Commandments or literal Bible as a necessary and sufficient system of ethics
  • Recall my presentation to the THS English department on my classroom technology, and colleague's luddite response ("so what?")
  • The desirability of diversity in dialog. The tangled oars analogy in heart failure depends on a sense of rowing, which is probably true for white boys from prep school, but not so much for other backgrounds
• Irregularity or variability of application suggests that certain personalities/dispositions are better predisposed to dealing with complexity: nuance, improvisation, extrapolation, multitasking
• Some desirable traits
  • Thinking in continuums rather than dichotomies
  • Becoming comfortable with uncertainty. Being comfortable as an instructor not having all the answers
  • Learning symptoms, but not forgetting the associated condition(s)/disorder(s)
• The (non)orthodoxy(?) of our examples
  • Using con artists to analyze teaching is even more risky/unorthodox than using stage magicians to analyze teaching
  • Role-playing
  • Geometric proofs
  • Faculty professional development
  • Classroom discipline
  • Learning about complexity
  • Subtraction ("borrowing")
  • Critical thinking
  • Foreign language
  • Holding an online discussion (CEP 817)

Criss-crossing, revisiting, and iterative knowledge

• can only explore possibility space by design, need that context sensitivity before further work can be done; non-linear thinking in problem solving, parallel to iterative design, parallel to systems thinking and the use of simulations in problem solving, playing with simulations
• When fragmenting, can reach a point of diminishing returns when atomising is too confusing to justify advantages of nonlinearity/non-directive; need the unifying landscape, the greater context
• TE classes as LEGO blocks, as a swirl
• Rand recommends alternating between standing on a hill looking over the terrain, and criss-crossing the terrain up close
• An interplay between local features and totalities/ensembles

Analogies, models, and the trap of tools

• Finding ways to represent complexity in a way that is cognitively manageable. One possibility is visual, to leverage the power of gestalt visual processing (e.g., faces)
  • Chernoff faces - uses faces to describe rocks (e.g., big rock, big face; rough rock, rough nose). Subjects could sort and aggregate
• Remember Accentus (sound datafeeds for investment bankers)
• data vs. process solutions (esp. in simulation, game design)
• Science is somewhat about identifying and modeling key data and processes, but some data and processes can't be simplified, their complexity must be preserved
• Tools, of course, can be the subtlest of traps. -Neil Gaiman (Sandman: The Wake, p. 141)
  • When your only tool is a hammer...
  • e.g., PPT and Tufte
  • Metaphors we live by
• Con artists understand the thinking traps that people can fall into
  • Playing 8 ball pool with James, him setting up his friend to scratch on the 8 ball

Teaching Complexity and Complex Things

• Teaching complexity, complexity in teaching, complexity in teaching teachers
• Teachers can forget what it is not to know. They become familiar with content, and have trouble seeing it through students' eyes
• Teaching as a science, art, craft
• !!! Much work to create hypermedia and similar instructional tools, so not surprising that complexity is usually mis-taught
  • Connect that to iterative model of game design, of research. The challenges of qualitative research. Mixed methods take more work (conceptual and mechanical).
  • Connect that to Elbow's Belief Game, Shulman's Disciplined Inquiry. Also, the energy of activation, learning the skills to create/use the tools. Challenges of integration. Hypocritical to not echo the labor of practitioners
• Illustrate how the backgrounded/implicit elements are shaping indirectly the foregrounded elements
• Confront students misconceptions, jar them (cognitive dissonance, but watch out for students' tendancy to discredit jarring new info) (girl in the dark, Private Universe)
• Abstractions need to be tailored to their contexts
• Fighting students' pressure to simplify, accept simple answers Disposition (habits of minds, epistemic beliefs, openness, tolerance of ambiguity/uncertainty) Intellectual faculties (wholistic evaluation, intuition, metacognition) Nature of teaching, nature of teaching teachers
• If wear glasses all the time, you forget that you're wearing glasses Make sure people know what they're doing Help them see how what they're doing is causing problems, doesn't work, causing them to fall short Offer a replacement with something that works and that they can learn

A sample model/game: Complexity Bingo

• More Bingo terms: multiple representations, family resemblance, templates, rigid/brittle, simplification, static/dynamic, scripts
• Ontology games, philosophical games, essentialist games, Plato's Republic as a game
• Candidates for center square: CFT, uncertainty, or nothing? Don't want to have a seductive, misleading, axial central premise. Don't want to simplify complexity. Need to honor the essence/spirit/nature

Principles and cases

• Sykes and Bird, cases trump principles, principles trump cases
• Rand takes least interpreted meaning of cases (examples, events, instances, etc.)
• Some epistemological/pedagogical points of view
  • 1. Principles/concepts/categories/themes/prototypes made primary (abstract entities) ("traditional knowledge view") (tendancy toward to over-generalization, over-regulation, over-extension) ("we feeded the deers")
  • 2. Traditional case view - case books (Rand cautions that this view has a tendancy to devolve back into 1, especially when cases are categorized or nested under abstractions) (false sense of completeness? thoroughness? necessary and sufficient?)
  • (3.) Spurious distinction - both matter, etc.
  • 4. Cases truly primary, abstractions secondary (opposite of 1)
• 1 ideal for well-structured domains, 4 ideal for ill-structured domains
• So one definition of well- vs. ill-structured is the suitability of 1 vs. 4 for mastering the domain
• Suggested experiment: find real-world cases and examples, sort them into conventional headers, then try to find an alternative sorting system(s) based on organizing using other case characteristics) (control group studies categorized cases, experimental group studies randomized cases; Rand believes better cross-chapter connetions in experimental group)
• Goal is to be prepared for new cases in inquiry and actual practice
• Consider cases vs. principles in ed tech, unique affordances and constraints

• New professionals feel like they got a lot method 1 instead of 4, and would have benefitted from 4
• Bruner's paradigmatic vs. narrative ways of knowing don't map cleanly to 1 vs. 4. Narrative has much to do with how to present a case
• Method 4 is an ecological combination of abstractions (a virtue)
• Another virtue: Contextualization of contexts
• When you map a new case to an existing case, you're right and wrong. Need to pull out the elements of the prior cases that are applicable. Rand talks about the Cuban Missile Crisis, and applying and mis-applying the prior cases of Munich and Korean War. (cf. Pinker, Violence, avoiding the Hobbesian trap)

Conclusion: Why Should We Care (Revisited)?

• Resonance between actively assembling understanding as a learner, and actively assembling working plans in teaching. A schema of the moment
• Studying complexity as a approach to reform ("conspiracy of convenience")
• Institutions need to be comfortable as havens for inquiry, not bastions of truths (Sykes and Bird; Erickson; Greeno, Collins, Resnick)
• Training students to be the kind of teachers we think they should be, vs. can be, vs. will see in real schools
• Don't worry that it seems too hard. Everything is changing, including educational teachnology

Unsorted

Themes

• Individual differences, domain differences, task differences, cultural differences
• Discreteness v. continuity
• Interference with perception (remembering interferes with perceptions)
• Interplay between local complexity and global totality
  • Organic unity (e.g., face) done well, rather than reducing, enhances

Polya, How to Solve It, problem-solving heuristics

Klein, Intuition at Work

Gladwell, Hunch

See Types of world's hypotheses handout

The true affordances and constraints

Visualizations of complexity: the Klein bottle (http://www.math.rochester.edu/misc/klein-bottle.html)

==

__ Are there other courses in learning and teaching complexity?

__ Table, with each group a header, look for overlap among columns

Rand is vexed by critical analysis of film, art, history, etc. when it offers "the" answer/theme

Rand says 4-7 core themes / representations tends to be optimal

• Themes don't have to be mutually exclusive / independent
• Watch for outliers in cases/contexts under scrutiny

Cooking French toast, scorch butter, smoky, fanning door, "ESP" (Klein), glasses

Triangle Poems

Schemas of the whole

Schemas vs. improvision in cooking

Practitioner knowledge vs. pedagogical content knowledge (PCK)

2-3 examples

Revisiting is not repeating

Picking cases

• Representative (not radically anamolous)
• Amenable to revisiting (e.g., rich, multiple interpretations)
• Ecological interconnectedness
• Address the recurring theme of balancing

Studying complexity (e.g., the experience of taking Rand's course and juxtaposing it with individual background domains (e.g., teaching using games))

03/29

erleibness - lived experience

How much of your processing do you need to be aware of? (not ESP, the power of intuition, tacit knowledge, the firefighter example with the living room floor collapsing)

synecdoche

changing the underlying habit of mind; if each case is the best, can't fixate on a super-prototype

Rand showed Reciprocal Teaching / Questioning the Author CFT evironment

Rand says CFT is anti-exemplary, anti-best practices. It doesn't matter whether the cases are the best examples; what matters is whether the learner constructs functional, transferable understanding through interaction with the cases/mini-cases/environment

Kuleshov Effect, film context/montage effect: http://www.ambiguous.org/robin/word/kuleshov.html

2005/04/05

Meeting in groups to discuss individual papers

Aroutis: design (habits of mind): iteration, subjectivity/ambiguity, research, communication, context; fun vs. learning, process vs. simplicity

application of understanding complexity (e.g., design as finding knobs, Klein's leverage points, Spiro's multiple representations)

self-communication, self talk, learning the talk of experts, Vygotsky

Vanida: teaching medicine and nursing in higher ed: everything at the same time, can't artificially sequence, teaching using cases is good (esp. with discussion), technology/representation, compressing/accelerating experience, differentiated learning (not assuming everyone is coming from the same place) (especially in complex domains), autonomy, self-directed, technology allows for many layers

scaffolding of the moment?

Mike: forum theater as a form of teacher preparation: so how does this model support CFT recommendations for teacher preparation; take responsibility (personalized; connection to Vanida's differentiated learning, connection to Kym's risk-taking); communal; multiple possible perspectives; role-taking and role-playing (creates safe distance); unhiding assumptions

connecting to the forum piece, communal, co-construction of knowledge, co-construction of "the real," absolute vs. subjective truths in teaching; context dependency, schemas of the moment, not pre-packaged; responsibility and authority

Back together

• multiple notions of expertise
• philosophical roots
• hypertext
• language learning
• design
• consent in multiplayer games
• forum theater
• teaching medicine and nursing

much discussion

decision to blog: capturing dialog and disagreement, not losing good ideas, no categories so structure emerges organically, don't need to be in class, students traveling, collaborative tech, Wittgenstein cachet

• April 5 today; start blogging
• April 12 roles set; start synthesizing
• April 19 report back on roles and syntheses
• April 26 content all in place
• May 3 polished; review you section and the rest of the paper for May 5 clas
• May 5 final changes

2005/04/19

prefigurative schemas

Changing perception:

1. Make people aware of the lenses they're using (habits of mind, epistemic beliefs) (cf. distinction between "knowing" and "knowing with," "thinking about" and "thinking in terms of," foreground and background, seeing as) (blind person probing with a pen)
2. Show them the flaws of the lens affects
3. Provide an alternative lens; show a plurality of "best" lenses
4. Help them learn to use the lens

one important part of helping people learn complex things: help them practice knowledge assembly

new areas seem ill-structured to a learner; learner has an attitude choice about whether to believe that there is structure and/or strategies to be discovered (e.g., math, interpersonal intelligence)

2005/04/26

Normative / Evaluative

• Positive
• Negative

Inquiry strategies

• What?
• Where did it come from? (etiology)
• Multiple representations
• Technology

Participants in the educational process

• Learner
• Teacher
• Ed. materials/tools builders/designers (including texts, tests, software)

Theoretical perspectives

• Constructivist
• Behaviorist / Didactic / Direct Instruction

Core themes / lenses / schemas of the whole / owned perspectives / 9-word basic vocabulary for talking about L in CD (syntax from how they combine in actual cases)

1. Habits of Mind / Epistemic Beliefs [Lana]
2. Habits of Mind / Action [Nick] [Wei]
   • (e.g., negotiating pressures on teacher identity) (what people do do)
   • Ways people "smooth out," over-simplify, over-generalize, over-regularize, etc.
   • Local / Global
   • Grand narratives, totalities
   • Ill-structured / Well-structured
   • Turning rough shapes into circles
3. Creativity (vs. Prescriptiveness) [Danah]
• Multiplicity, pluralism [Aroutis]
• same as Danah's?
• Design
4. Interconnected / Compartmentalized [Leigh]
   • Dependent / Independent
   • Continuous / Discrete
5. Immersion & Receptivity [Kym]
   • Engagement
   • Principles & cases
   • Criss-crossing, revisiting is not repeating
   • Constructivism, constructionism, in the world and of the world (cf. John 18:36)
   • Overlap with iteration & improvisation
   • Overlap with epistemic beliefs, but greater emphasis on affective dispositions & experience
6. Holistic learning environment (ecosystem) [Vanida]
7. Discourse, dialog, & improvisation, & performance [Mike]
8. Modes of presenting complexity, modes of representing complexity, visualization [Rand?]

2005/05/03

CFT: AKA for ISD (Advanced Knowledge Acquisition for Ill-Structured Domains)

Metacognition, John Flavel and Anne Brown

• two essential sets of strategies: self-monitoring & repair

Rand emphasizes raising consciousness when teaching for schema-use, including schema accessbility, schema recombination (issues of metacognition, metaknowledge, prior cognition)

Broudy's distinction between knowing that and knowing with

Some ppl argue we always/only think about things in terms of something else

__ Consider how Ink is a tool for thinking about other things

Cognitive distinctions: intellect vs. intuition, convergent vs. divergent thinking, intellectual vs. sensuous, deductive vs. imaginative, rational vs. metaphoric, discrete vs. continuous, abstract vs. concrete, directed vs. free, propositional vs. imaginative, differential vs. existential, analytic vs. relantional, lineal vs. non-lineal, positive (via logical positivism) vs. mythic (Levi-Strauss), analytic vs. Gestalt, rational vs. intuitive, relations vs. correlates, sequential vs. multiple, analytic vs. holistic, explicit vs. implicit, reductionist vs. compositionist, rational vs. integral, objective vs. subjective, atomistic vs. gross, hierarchal vs. heteroarchal, sequential vs. simultaneous, light vs. dark, time vs. space, heaven vs. earth

Creativity

! Donald Campbell, evolutionary epistemology (in Philosophy of Karl Popper)

Note the incubation stage, which the Gestalt model of creativity also touts

Consider Punya's course, seeing the knobs

! Creativity sometimes depend on connecting distant or disparate fields/ideas/models/etc., so well-served by semi- or complete randomness. Need receptivity to observe those connections when they're possible, rather than only seeing what you're looking for

Two modes of creative exploration. Iteration, exploration, recombination are critical. The first mode is sensual: finding the right probability space, the possible criteria. The second mode/second stage, which is easier, is exploring that local space with those criteria in mind. Consider what a lateral move means: it's more first mode than second mode

2005/05/05

9 perspectives on 1 case

• Preparing to teach first course in high school biology, specifically the unit on the body
• As part of preparation, reading a book about biology (Bernard)
• From the perspective of immersion & receptivity
• Knowing the chemistry & physics, be sensitive to whether you've got a complete picture
• Try to disprove your certainty (as Popper would suggest)
• Idea of harmony - look for the harmony in situ, not with a preconceived harmony
• Practice levels of immersion: ecosystem, species, organism, system, organ, cell, cell parts, biochemistry
• Be sensitive to how the level of immersion illuminates and hides various features
• Experiment with different metaphors and representations for the exchange: systems, organisms, minds, teams, schools
• Play roles within those metaphors (e.g., buyers and sellers)
• Respect the effectiveness and efficiency of the whole: audit simple explanations
• Consider a variety of instruments, to find an instrument that is properly sensitive to the feature of interest; finding compelling but contrasting cases, e.g., maggots for cleaning wounds, petroleum-eating bacteria, organic acidity indicators, equilibrium is best understood through simulation. Beware of compartmentalising (e.g., Klein, molds and penicilin)
• "mutually generative"
• The best map is the reality itself
• Leigh/connectedness, restructuring around a textbook, the engagement of reading out of order, foregrounding a different schema for learning the domain, knowing where we've been, are, going; perhaps having students make up their own tables of contents; Rand/Mike/improv emphasizes how hypermedia can serve the goal of students makign up their own, even multiple, tables of contents
• Nick/habits of action, filtering, not so much what he said but what I heard, immersed in context, filters/templates as part of that context, where you're coming from and where you're going, there is no objective scientist, author, reader
• This whole activity is role-play
• Rand/Mike/improv : not approaching biology case with pre-conceived schemas/templates, need to develop in the moment to respect organicism
• Immersion as danger and advantage
• The infinite creativity of language. Much of that infinity depends on the power of allusion and figurative language, which is a weak form of immersion: calling up the "feel" of a dissimiliar thing
• An effective approach is dissection or vivisection: the best map is reality, messy, imperfect, interactive, not at all perfect; expensive, messy, ethics; simulation, hypermedia; can't give up because its expensive, messy; want deep, flexible learning, have to create contexts that compell and challenge
• "A classroom is like a body, and teaching is like an organistic process." From the perspective of immersion, teaching can only be learned through interaction, trial-and-error, planning, feedback, and reflection. This is why field experience and student teaching are a critical part of effective teacher preparation programs.

Back to creativity

An effect on emotional sensibility as an indicator in creative efforts

Rand considers CFT to a theory of everyday necessary creativity

Mixed bag

Order at the edge of chaos; complexity is not chaos

Possible starts in Phil. Investigations: 65 (games)

Intertextuality as an antidote to compartmentalization