7/23/2019 Teaching Learning and Thinking in Fractel Patterns

1/1

DESIGNED&PRINTEDBY:

www.POSTERPRESENTATIONS.com

Teaching, Learning, and Thinking in Fractal PatternsDr. Edward Nuhfer, Director of Faculty Development, California State University at Channel Islands ed.nuhfer@csuci.edu

Fractal Challenges to Educators Applications - Knowledge Surveys

Applications - Teaching Philosophies as Action Plans

Why fractals?

The Importance of GeneratorsABSTRACT: A group of faculty and faculty developers havebeen working since 1993 on developing better instruction through

a week-long development retreat called "Boot Camp for Profs."Benefits of this camp have spread to other communities too.

The program derives from a m odel that uses awareness of fractal

properties of neural networks in the brain to aid development of

successful college instructors. (See

http://profcamp.tripod.com/bootcamp08.htm.) Emphases include

(1) understanding the process of improving education by reflecting

on the educational process through different scales, (2) recognizing

paramount importance of the affective domain on successful

learning and teaching, (3) realizing that assessment and evaluation

are attempts to measure fractal systems, (4) recognizing that

students learn better when they understand the process of brain

development and what is happening to them as they learn, and (5)

developing and maintaining sophisticated teaching philosophies as

blueprints for action. Employment of knowledge surveys, learning

documents, student management teams, and learning design

exercises, which incorporate both individual reflection time and

cooperative interactive engagements, further aid success for

students and instructors.

In the brain, all cognitive

knowledge and learning is

connected inextricably with the

affectivedomain, much like two

clouds of colored smoke blown

together. All action involves aprior affective feeling. We "feel"

a decision before we can

articulate it or act on it.

Power of the Affective Domain

The sheer power of the affective domain m akes it the principal

influence on the life decisions and satisfaction of instructors and

students. Students choose colleges, classes, major, and careerslargely from feelings that become action choices. Math anxiety

and writer's block can change aspirations of students while

morale, campus atmosphere, and quality of life trigger life-

changing decisions by faculty. It seems impossible to divorce a

single cognitive thought or decision completely from the affective

domain. Faculty development and education of students require

working with the affective domain. The critical first moments of

courses, classes and introduction of new topics can produce better

learning by engaging the affective domains of students in positive

ways. Wanting to learn is an affective decision. The neural

networks that involve affective domains are likewise fractal. They

can learn and develop, just as can our cognitive domains.

Create self-assessment rubrics; use often! Have students enter their

reflections and score their own confidence in reflective journals such as dou ble

entry journals. The highest levels of thinking (Perry, and others-see below)

involve a meld of content and skill expertise with awareness of the influence of

one's own affective mind. This state is not one of irrelevant emotion andinsignificant feeling but rather is the integration of the affective domain on a

conscious level with high levels of cognitive development. Alverno College's

curricula use self assessment as a primary vehicle to high level thinking.

E mp ha se s- -> c on te nt -i nt en si ve e mp ha si s + p ro ce ss -i nt en si ve e mp ha si s + s el f- re fl ec ti on + j ud gm en t fr om e xp er ie nc e

Perry,1968;

1999 2nd ed.

1.BasicDuality

2.

Multiplicity

Pre-legitimate

3.

Multiplicity

Subordinate

4.

Relativism

Subordinate

5.

Contextual

Relataivism

6.

Commitment

Foreseen

7.

Initial

Commitment

8.Multiple

Commitments

9.Resolve

King &Kitchener,

1994

1.Knowledge

experienced

2.

Experienceandauthority

assource

3.

Unclear

distinctionofevidencefrom

belief

4.

Evidenceacceptedthat

fitsestablished

belief

5.

Beliefsjustified

withincontext

6.

Beliefsjustifiedby

comparingevidenceand

opinion

7.

Beliefsjustifiedbased

onrelativevalue ofcompetingevidence

Thisareaisnota

productof cognitive

developmentalone.Thisis largely

therealmdescribed

under"EmotionalIntelligence"

byGoleman,1995.Actions&decisions are

made

withsophisticated

frameworksofreasoning

plusa recognized

influence ofan ethicalframework,emotions

andotheraffectivefactors

Blosser,

1973;1991

1.

CognitiveMemory

2.

Convergent

Thinking

3.DivergentThinking

&

4.EvaluativeThinking(crude withpoorjustifications)

4.

EvaluativeThinking

(withbetterjustifications)

4

EvaluativeThinking

(withincreasingly

sophisticatedjustification)

Bloom,1956

1.

Knowledge

2.

Comprehension

3.Application4. Analysis

5.Synthesisand6. Evaluation(5 &6 done crudely)

5.Synthesis(done better)

6.Evaluation(done better)

6.Evaluation(donewith

sophistication)

Biggs&

Collis,1982

"SOLO"

1.

Pre-structural2.

Unistructural

3.

Multistructural

4.

Relational

5.

ExtendedAbstract

DeBono,

1985W h it e H a t ( f a c tu a l) + B l a ck H a t, Ye l lo w H a t (a d vo c ac y b as e d o n fa c ts &e v i de n ce ) +GreenHat

(creativethinking)

+Red Hat(emotional)

+BlueHat(conscioussynthesis

ofal lhats)

General Equivalence of Some Models of Adult Thinking E.B.Nuhfer

All learning, skill development, and progression toward higher

levels of thinking involves building a neural network through

establishing and stabilizing synaptic connections. These synaptic

connections are fractal. Fractal forms develop by a recursive

operation on a basic "seed" called a generator. In the figure below,

the generator is a simple Y and the recursive operation is a

replacement of each branch of the Y with another Y generator. As

we learn, we literally "grow a brain." This brain is marvelous and is

truly capable of infinite thought. Not only are no two people alike,

no two thoughts are even exactly alike. Because our brain is fractal,

many of our actions and traits have fractal qualities.

Good beginnings are essential. Complex fractal forms exhibit

qualities of the generators that form them. Below is the generatormodel that developed through the experiences with Boot Camp for

Profs. We found that faculty development is healthy when it

provides attention to all six colored components. All are

assessable. Whatever generator an instructor possesses will

ultimately determine her/his operational teaching philosophy, the

course documents such as syllabi, and the quality of lessons

enacted in class.

Where faculty cooperate to plan outcomes thoughtfully, they

can work together as "one large brain" to develop courses that

contribute to a larger vision of students' growth through curricula

and degrees. Because the neural networks required for high level

thinking (Perry model and others' derivatives) cannot develop in a

semester, planned curricula are essential. Great courses taught by

great teachers working alone are surely insufficient. We find most

curricula are not really planned; most are simply assemblages of

courses. Current evaluative practices and less attention to the

scholarship of teaching and learning keep faculty attention focused

only at the scale of courses and there, most often, just on content.

The actions and traits often translate into fractal patterns in time.

Becoming educated results from a series of events in time. Like

rainfall patterns, "aha moments" typified by changes in thinking are

punctuated events in a fractal pattern interspersed with many

common events and even dry spells, when it seems like not much

change is happening. The complex form of experts' neuralnetworks can do many things that the simpler form of novices

cannot do. Fractal awareness helps us to realize that we need to be

patient with students. Most are developing, not being intransigent.

Let length of coastline be L. Let divider width used to measure L be r.

How long is a coastline?

The length of a coastline is one of the earliest

examples to show that the dimensions of a

fractal form change depending on the tool of

measure. A one-dimensional line is the

simplest fractal form. Brain neurology

consists of three dimensional networks

folded upon one another. Fractals don't have

absolute dimensions, but they have order.

Lessons: We can't measure a fractal form with a number that is

uniquely correct, but we can understand fractal forms, if we use

multiple measures. There will never be a perfect test or survey that,

when used by itself, will ever allow us to understand a learner.

Some Euclidean Misconceptions of Education

1. How many letters are in the English

alphabet?

2. How many words can those letters

produce?

3. How many ideas can be expressed by

those words?

4. How many stories are possible?5. Might these be infinite in a single

discipline?

6. Might these be infinite in a single

discipline described in a single

language?

7. Can all human knowledge/experience

be accurately described by words?

The above quiz juxtaposed to the positron emission image from Petersen et al.

(1989) shows the problem of trying to assess a network capable of infinite

thought. The complex fractal neural network is just the wiring. When live with

neurochemicals and electrical signals, there are infinite combinations of form,

sequence, and intensitiesinfinite fractal patterns in space and time. This

explains why tests and test questions fail to achieve reliability, why multiple

choice results don't correlate with essays, and why different tests shouldn't beexpected to correlate so perfectly with one another or with alternate measures.

They are measures of separate transects across different fractal neural networks

and are not really measures of the same thing.

How do we diagnose MBTI

or Multiple Intelligences?

Content alone is

roughly finite and

quantifiable.

Once in the brain,

learned content

becomes part of a

network of thought

and feeling that is

infinite.

Confusing content with learned

content makes us think we can

use single measures.

"The harder I study it, the less I understand it!" "The more I learn, the b igger

this problem seems to get!" are both exclamations noted when dealing with

phenomena that have fractal qualities. Fractal thinkers realize they are not

performing measures on absolute quantities of skills and knowledge. Instead,

they know they are seeking un derstanding of fractal neural networks with noabsolute dimensions. This introduces a different awareness about how to

understand learning, evaluation, and assessment. It's obvious why MBTI and

intelligence types require more than a few survey items.

Fractal thinkers appreciate multiple measures, and knowledge surveys are a

fractal thinker's tool. Most yield well over a hundred measurements-per-studentdirected at specific details of content learning. The survey shown below yields

200 measurements per student both pre- and post- course, which translates into

about 8000 bits of information for assessment of a class of twenty. Unlike tests,

knowledge surveys address a strong affective component in their item

responses. A test item might read: "Describe the scientific method and provide

an example of its application," whereas the knowledge survey item might state:

"I candescribe the scientific method and provide an example of its

application." These are two measures of different neural networks that involve

understanding about what science is and how it operates. The "I can..." is a

probe of the affective domain. Knowledge surveys prov ide samples of

cognitive and affective domains operating together. They provide reliable

information that taps neural networks not sampled by tests and grades.

Concept of a Knowledge Survey

1. = I have insufficient knowledge to answer this question.

2. = I have partial knowledge or know where to quickly (20

minutes or less) obtain a complete answer to this question.

3. = I can fully answer this question with my present

knowledge.

Those unfamiliar with test reliability presume their tests and grades are

measures of "actual knowledge." In fact, most faculty-made tests and grades

have reliability of only about R=0.2 to 0.6. In contrast, knowledge surveys

have reliabilities of R > 0.9. This observation doesn't mean that we shou ld

give up tests. Rather it means we must take multiple measures in order to

obtain multiple perspectives of fractal phenomena too complex to understand

through information yielded by single tools.

Applications - Reflection Journals/Self Assessments

Operating without a sophisticated teaching philosophy is like trying to nail

together a house without blueprints. The six component colored generator n ear

the top of Column 2 is really a graphic teaching philosophy. The root, self

introspection, is largely affective in that it confirms what we most want to do as

professionals in our teaching. We need to be versed in the other components tothe extent that we can articulate their use in our philosophies. An individual

who picks up a course document such as a syllabus, a learning assignment or

an exam should be able to see critical parts of its creator's teaching philosophy.