Delphian The Role of Frame Analysis in Enhancing the Transfer of *) Knowledge Minstrel Barry Krusch UltraShadow Internet Press CasqueOpenFace *( Knowledge at the blink of an eye Bookman Electronic Copyright Times 1994 by Barry Krusch ^PThis document may be (re-transmitted) by (any person, group, or organization) to K(any other person, group, or organization) in (DP ELECTRONIC form only) via K(any electronic mode or media, including modem, storage on a BBS server, CD ^NROM distribution, DAT, Syquest, E-Mail, LocalTalk, Ethernet, FTP, ISDN, floppy Fdisc, or any other electronic mode of transmission) without (financial Pcompensation to Internet Press), provided that (no words are added, substituted, Rrearranged, omitted or otherwise altered, other than for exclusively personal use) Qand (that no hard copies are made, other than for exclusively personal use, or to Rgive to a friend, or for not-for-profit educational purposes). This right does not Dextend to documents saved in a format other than DP ELECTRONIC form. INOTE TO USER: The purpose of retaining copyright is to insure the textual $integrity of the following document. Avant Garde LAST UPDATED: October 26, 1994 7The latest version of this document may be obtained at ftp.netcom.com /pub/krusch Times lGDoes previous experience transfer to new situations, and if so, in what H0circumstances? To educators, this phenomenon of transfer is key. Without transfer, HQone has educated or been educated only in the rather limited domain of that which Lhas immediately occurred in the classroom: a contrived situation that seldom Joccurs twice. As transfer increases, so does the value of education. In an FInformation Age, where the amount of knowledge that can be known grows Jexponentially (and with it the amount of knowledge that has to be taught), Kincreasing the efficiency of education is an issue of paramount importance. EConcern with this issue is not new, however. Prior to experiments by HPThorndike and Woodworth in the early part of this century, a theory known as the doctrine of formal discipline / was widely accepted. According to this theory, general )+G principles of formal reasoning could be taught implicitly by selecting HSmaterial for learning which subjected the mind to these principles. Latin and Math Pwere widely considered to be useful in this regard. Students would take courses Onot for content, but because they exercised the mind. These habits would then transfer ),M at a later time to other disciplines, such as science. The clear implication HTof this hypothesis that transfer was readily obtainable was that education should be global )$3 to achieve maximum efficiency. (Detterman, 1993). GBut this optimistic theory was challenged by Thorndike and Woodworth in HA1901. The psychologists trained subjects to estimate the area of rectangles H%Subsequent tests involving different polygons )3( (triangles and circles) revealed errors HW90% as large as the errors before training. On this task, it appeared that transfer of the general skill of estimating the area of polygons was very difficult to obtain. HEAfter analyzing their results, Thorndike and Woodworth concluded that Nimprovements in a single mental function rarely brought about an equal improve ment in another function. 3Surprisingly, Thorndike and Woodworth reached this general conclusion H5even though 1) the nature of the task given was very specific [estimating the area HQof geometrical shapes], and 2) subjects required between 1,000 and 2,000 practice Jtrials to achieve improvement on rectangle area estimation [introducing a fatigue HOsource of error]. Still, many subsequent studies seemed to confirm Thorndike's Jfindings. According to Detterman (1993), since the Thorndike and Woodworth Nexperiment there have been hundreds of experiments reaffirming the same point. 'Transfer is very difficult to obtain. ( See also )5 Singley and Anderson (1989), who reached a similar conclusion). But even though the theory of general )+( transfer was discredited, the notion of H transfer in any form )H5 was not, not even by Thorndike, who introduced as an H3alternative to the theory of formal discipline the theory of identical elements. Times H9According to this theory, transfer would occur only when specific component skills in the target area ( to be )%3learned) were isomorphic with those present in the that which was )ZAlearned). Learning Latin would perhaps not help a student learn HOChemistry, but it might help her learn Spanish (a language with elements common Wto Latin): [o]ne mental function or activity improves others . . . because it contains elements [in] common )~> to them . . . [K]nowledge of Latin gives increased ability to HPlearn French because many of the facts learned in the one case are needed in the other. (Thorndike, 1906, pp. 243, emphasis supplied). lAHowever, elements in common is a vague expression. As Gick and HIHolyoak (1987) perceptively noted, an escape clause was implicit in the Klinguistic formulation of this hypothesis, since common elements could be /construed in a general way to include not only perceptual features )q but also H$categories, procedures, principles, and even emotional attitudes ; in other words, HQcommonality existed at not just the level of immediate sensation, but at a deeper Slevel, that of cognitive processing (where the meaning perceived is in large part a function of the processing )=( through which the meaning was derived). Commonality HRcould exist at low, middle, and high levels, depths as well as surfaces, depending 7on the minds and approaches of the student and teacher. QThis was a different angle: identity does not exist in and of itself, but only as a function of the frame )!9 of reference through which the information is perceived. HQThe common element restriction fails because, at some level of abstraction, and "through some frame of perception, everything has ) something in common with HIevery other thing. For example, learning Math and Latin share the common Melement of having to study. Biology and Chemistry share the common element scientific method. And so forth. From this angle, the view was completely Ndifferent, and from this perspective, many psychologists saw the potential for Qtransfer where others saw none. Thus, Cormier and Hagman (1987, at p. xi), after Qciting several reviews of the topic, stated that "[t]ransfer of learning . . . is Spervasive in everyday life, in the developing child and in the adult." According to Othese authors, the magnitude and generality of the effects produced by previous Glearning upon performance in new learning tasks suggested that transfer Jphenomena should assume a critical importance in psychology. The theory of transfer had come full circle. KOnce the dust created by term-mongering ( general vs. specific transfer, vs. transfer, etc.) settles, it is clear that transfer must take place H at least F time. Take the words on this page as an example: even if we were all trained to read Courier )Z*in the mono-spaced Courier font, like this , it is HMreasonable to expect from everyday experience that when we are presented with Times material Garamond Narrow 3in the proportional-spaced Garamond font, like this we can still HNcomprehend the text. We can even read text presented in other styles, such as italic , or shadow 4This means that the learning and recognition of text H@elements such as lettershapes does not take place merely at the local level of lettershape-as -(FONT: Times )$ )-(SIZE: 14 point )-(STYLE: Plain ), but, more importantly, at the global level of lettershape, a more )* schematic level which can be HPexemplified by any example which follows the form. This ability to see patterns T(via the perception of similarities through the filters of differences) allows us to Rmake sense of the world, and explains why certain experiences in our lives quickly Pgrow familiar. To use a mundane example, we learn where to shop for food, how to Vget to the store, and how to pay for the groceries, and don t worry that the available Tparking spaces have changed each trip, nor that new items are on the shelf, nor that Hfamiliar cashiers greet us at the check-out counter. The accumulation of knowledge acquired from , shopping experiences is transferred without HFdifficulty to present shopping experiences (Gick and Holyoak, 1987), a phenomenon which cuts across experience in general. lGIndeed, observation of the world around us shows us that the ability to HOrecognize patterns and form generalizations leads to a practice makes perfect Ophenomenon: because of this phenomenon, pilots are trained on flight simulators L(Rose, Evans & Wheaton, 1987), soldiers fight in war games, actors rehearse, Mprospective surgeons experiment on cadavers, architects work from models, pro Jfootball teams draft from colleges, prospective employees are filtered for Jconsideration based on their prior experience, and college courses require Xprerequisites. In fact, one entire educational domain, law school, has as its explicit Taim not to teach the law, but teach the student how to find the law, an ability Tderived from past experiences. Transfer exists, so much so that when it exceeds its )legitimate boundaries, we refer to it as negative transfer, the well-known psychological phenomenon of overgeneralization: the young boy who calls every HRadult daddy ; the young girl who is given night, light, and right to spell, Uand then spells hight ; or the nationalist who believes that all Japanese people are ruthless. In point of fact, there / to be some degree of transfer, if only because HNrecognizable and predictable patterns exist in the scientific and mathematical Rdomains of reality. A ball released from the hand will fall to the ground whether Mone is in Paris or Rome, and a one in a million chance is not a good chance Uwhether one is afraid of being hit by lightning or anxious to win the lottery. 2 + 2 U= 4 whether the quantity is apples or dollars, and being an historian as opposed to a Times HNbiologist does not shield one from the difficulty of formulating well-reasoned hypotheses. KThe scientific and mathematical disciplines frequently show us that reality HQhas a structure which, skeleton-like, is then filled out by particular phenomena. SWhen we recognize the similarities which cut across differing surfaces (i.e. seeing Sthe phenomenon of gravity in a dropping ball or orbiting planet), we can be said to have seen the deep structure )Q9 of reality, a concept that over the years has cut across sciences like physics and into softer sciences such as the field of Epsycholinguistics, where it was made famous by linguist Noam Chomsky. CChomsky s theory held that, like physical laws, all languages have structures, H9which are instantiated through transformation rules into surface structures. As the HKdropping ball reveals gravity, so does the sentence reveal grammatical deep Mstructure. For example, the deep structure John hit ball converted by the passive HQtransformation results in the surface structure The ball was hit by John, while conversion by the active )!9 transformation will produce John hit the ball. (Mayer, HN1992). As Chomskian psycholinguists noted, transformation rules should be seen universal , transcending all cultures. l9Thus, the rationale for the existence of transfer at the physical and linguistic H3levels. But transfer needs to be understood at the psychological )M level of information processing 9, because any transfer of knowledge will occur only after HRthe processing of information has taken place. Along with the critical concept of Ndeep structure popularized by Chomsky are at least three other key concepts in Qunderstanding how people think from the (respective) fields of cognitive science, +artificial intelligence, and cryptography: schemas frames , and encoding l.Schemas, Frames, and the Encoding of Knowledge *"KTransfer is not the only issue in educational psychology which rests on the HMpremise that reality has a deep structure. In fact, a more well-known area of educational psychology, schema )*4 theory, is also predicated on the existence of this H6concept. (Reed, 1993, at p. 42) described a schema as +$"E[A] cluster of knowledge representing a particular generic procedure, Eobject, percept, event, sequence of events, or social situation. This cluster provides a skeleton structure for a concept that can be instantiated :filled out, with the detailed properties of the particular instance being repre )s.sented. For example, a schema for the American l;Psychological Association annual meetings would contain the Times lJstandard properties of a scientific conference such as its location, date, Eattenders, session types, and the length of presentations. . . . (1st emphasis supplied) *"DSchemas select and organize incoming information into an integrated, HMmeaningful framework. People change new information to fit existing concepts, Oand in the process, knowledge becomes more coherent to the individual. Schema 5theory explains an important aspect of thinking: its organization lKThat schemas are used to organize thinking is not mysterious. Consider the HNworld, and its multifaceted, vast store of information contained in libraries, Iorganized with schematic classification schemes such as the Dewey Decimal Nsystem. Now imagine the Library of Congress and its millions of books, journal Narticles, and newspapers, etc., and simultaneously imagine that its cataloging Usystem is not only entirely destroyed, but that, in addition, all the books within it Lare randomly reshelved. Now how does one find the information one requires? MThe chaff has hidden the wheat. While in reality the information may be only Ftwenty yards away, it is, functionally speaking, unavailable. The same Gphenomenon obtains in the filing systems of our minds, which ordered by 8schematic structures, enable semantic perception itself. JSchema theory now plays a prominent role in the field of education, second HGperhaps only to behaviorism as a structuring paradigm upon which entire Mapproaches of education (e.g.. whole language) have been built. For example, teachers schooled in the whole language )Y+ approach understand that a student will be HPable to fill in (instantiate) the blanks in the words contained in the following Lsentences due to the student s preexisting schemas which are keyed in by the Cknown words in the sentence, and the sentences which surround them: +$")Ed took his daugh____ to the super_____ . He bou___ her some foo_ to ea_ . CThey ate hamb____s and fr___ fr___ , with bak___ bea__ on the side. *"I Schema theorists maintain that whether or not we understand something is HPin large part due to our existing background knowledge; that for which we have a Pschema (cooking), we understand. That for which we do not (nuclear physics), we Tdo not. For this reason, transfer is more likely when we learn material in a domain Rwith which we are already familiar, base learning being rooted in prior knowledge. CSchema theory is closely related to a second information processing HKconstruct which has an impact on the issue of transfer, the concept of the frame Times IBateson, 1972: Goffman, 1974; Minsky, 1975), a cognitive filtering system HSthat can key in items of a text or a situation as meaning while simultaneously +excluding other interpretations. There are interpretive frames (the way we see things [decoding]), and exemplifying )S!frames (the way we present things [encoding]). two parallel vertical lines of equivalent length X intersected H7midway by a perpendicular, horizontal line of length X* , [where is a value typically between .33 and .85] 6, produces something that looks a lot like an , but HSthe only gets to us after it has passed through many different stylistic frames Q(such as FONT, SIZE, STYLE, etc.), as the preceding table clearly shows. But the Pdistinction between schemas and frames is not hard and fast, since the schematic *structures we perceive through frames are themselves created by the frames we use H/when we decode reality, thus affecting what we perceive as the deep structure, and HDthus potentially producing pseudo-deep structures: for example, too specific H+frame decoding the letter produces the rigid ! structure two parallel one-inch HNlines intersected midway by a 1/4 inch perpendicular line 1/2 inch up from the Pbase from a particular example of an which possesses these properties (thus Lexcluding legitimate s which do not fit this rigid description), and too shallow H frame decoding produces the floppy )/ structure two lines and a third, HOformulation which calls up many non-H geometrical forms). The only structure worthy of being called the & structure is that which captures the essence of that HNwhich cuts across all instantiated forms, the structure which accounts for all Olegitimate s, and excludes all those which are not Needless to say, the Mcreation of a deep structure is made far more probable when we see through a decoding frame lGAs we see through frames, so do we communicate with them. Understanding HHthe significance of these interpretive, decoding frames is essential for Funderstanding how human beings see the world. It is also essential for Kunderstanding why communication breakdowns are so pervasive. We see what we @send as A, while the person who gets what we send sees it as B. Merely HGestablishing a similar type of encoding does not insure communication. Frequently HKmiscommunication results when different keys are used in the production and Sreception of information, a fact vividly displayed with analogies from the field of Ncryptography. Just agreeing on a dot and dash system of communication is not Penough; our maps of what the dots and dashes refer to have to correspond, and we Phave to insure this correspondence before we communicate. When calibration does Mnot proceed communication, we can not be assured that we are referring to the same reality. AThis can be illustrated by the following example. Suppose you are H0confronted with the following string of letters: Times lPAt first glance, you may see this particular string of letters as nonsense, HQfunction of your use of an interpretive LITERAL frame to decode this string. But Psuppose you are subsequently told that this string is a coded message and that ?you are to use one of the following keys to decode the message: Helvetica Black STRING KEY A KEY B lMNow you see that to properly interpret this meaningless string, you need to HCshift from a LITERAL interpretive frame to an interpretive frame of KCRYPTOGRAPHY, the critical change (because the key for unlocking meaning is Qprovided). Once this major frame shift is made, the only question that remains is which )!I key to apply. We note that the application of Key A gives us HNKey B gives us Here we can see vividly that sometimes meaning does not 0reside in the reality itself, but rather in the used to encode and decode the HRreality! (To take another example, attorneys, applying their own, private, frame, #will have seen the initials to the merican ssociation ). The reality can HBproduce several widely differing meanings with differing keys, or frames, )) as shown by the following examples: O DECODINGS REALITY (Input) OBJECTIVE Reading (frame of observable phenomena) SUBJECTIVE Reading (frame of internal reaction ) She is wearing a watch. She is wearing jewelry. She is wearing a status symbol. A car has been behind you for five minutes. The car is behind me. The car is following me. A woman smiles at a man. She smiled at me. She is available. U The price of Apple stock is $37. The price of Apple is $37. Apple went up $4 today. Lakers: 110 Clippers: 90 The Lakers won. Magic won in his coaching debut. lKHere we see how different frames of mind produce different interpretations. HKIn a social setting, the problem of frame conflicts becomes acute. Note how Rdiffering frames can produce differing messages in the minds of listeners, and how &communication can silently break down: Times Helvetica Black MESSAGE INTENDED BY MR. Y ENCODING FRAME BY MR. Y MESSAGE SENT TO MR. X BY MR. Y AFTER ENCODING DECODING FRAME USED BY MR. X INCORRECT MESSAGE RECEIVED BY MR. X AS A RESULT OF IMPROPER DECODING FRAME Jim wants LSD. SLANG Get Jim some Vitamin A. LITERAL Jim wants Vitamin A. I ll pick some up at the supermarket. The lab results show I have no trace of cancer. MEDICAL The results were negative, Mr. X SOCIO LINGUISTIC I have cancer. I will give him what he is owed. PROMISE I will give you what you deserve. THREAT He is going to do something bad to me. ll play a joke. APRIL FOOL re fired. LITERAL m fired. s not going to work here anymore. LITERAL re fired. HUMOR s just kidding. Inconsistent ideas clash in subconscious. METAPHORICAL Colorless green ideas sleep furiously. LITERAL s nonsense. I escorted her home. COLLOQUIAL I saw her home. LITERAL He saw her house. I hated the movie. )Z SARCASTIC Best movie I ever seen . LITERAL He loved it. The girl is not beautiful. SARCASTIC s a beauty. METAPHORICAL His car is a beauty. There is a deep meaning contained in this title, probably having to do with the Latin root ) and the Irish term . (a what you get at the of your life). LITERARY CRITICISM Finnegans Wake is an interesting title. GRAMMATICAL s interesting because someone considered a great writer left off the possessive apostrophe. Times lIAs the preceding table shows, the same language can produce two different HImeanings depending on which of many possible decoding processes are used. ONote that one can correctly decipher a message only when applying the same code Oboth ways. Vocal string elp-hay ee-may sends help me! to the person who Qspeaks Pig Latin, blah-blah-blah to the person who does not. Tone string HNdot-dot/dash-dash-dash/dot-dot-dot sends to the person who speaks Morse Qcode, meaningless tones to the person who does not. And a raised dot string sends Hey there! to A, a speaker of Braille; B, not a speaker of Braille, comprehends Praised dots on a page. Frame analysis reveals that we are in distinct cognitive Jvirtual worlds without even realizing it [since the processes which affect Mcomprehension are invisible, and are only made visible when we act on what we Rthink], and most of the time we are tragically unaware that the person across from Nus that we are speaking to may be misunderstanding much of what we are talking about! AThe above analysis focuses on what is perhaps the key problem for H>communicators (and thus educators); communication/learning is encoded with frames, communicated with frames, and comprehended with frames, and not only HPsingle frames, but sub-frames and sub-sub frames as well, all layered one on the other. Hidden references and allusions, differing modes of speaking such as literal, HNmetaphorical, hyperbolic, humorous, ironic, academic, and sarcastic, differing words such as slang, differing meanings for words, vague terms due to abstraction schemas )/* necessary for comprehension, the role of context , and perhaps most importantly, and surface ))4 structures, all play a mutually interactive role in HQenhancing and interfering with comprehension, and thus can have a profound effect Pon the subsequent transfer (or lack thereof) of that which has (or has not) been learned. KThe great power of frames leads to many different comprehension results, by effecting how we perceive reality, categorize reality, and )G evaluate reality. The HPoutputs in our mind of and different and alien familiar all take Pplace within the context of how we take in information, a fact which has obvious Kimplications for the theory of common elements in transfer. For example, consider the items Dolly Parton Mozart , and Babe Ruth viewed through the H frame of Times Dolly Parton Mozart )f Babe Ruth FEMALE lCWithin this frame we see Mozart and Babe Ruth as (male), and HVDolly Parton as different (a female is not a male). In this situation, within this Lframe, Mozart and Babe Ruth are in the majority. But Dolly is only in the minority because we have chosen to view reality through that framework. Note (the re-ordering when we view through an OCCUPATIONAL frame: Dolly Parton Mozart )q Babe Ruth MUSICIAN ATHLETE lFNow Dolly is in the majority. Are we to conclude from the above that HTMozart is always fated to be in the majority? No, since a third result obtains when the items are viewed through a NATIONALIST framework: Dolly Parton Mozart )v Babe Ruth AMERICAN AUSTRIAN lIHere we can see vividly that what counts as common is a function of the HPencoding and decoding framing processes used. The question that remains is, how Ncan these processes be used to facilitate transfer based on a theory of common Kelements? The answer is to utilize framing techniques to pitch educational Iconcepts at the level that gives the greatest degree of transfer: at the level. Times l5The Impact of Frame Analysis on the Issue of Transfer *"JUsage of frame techniques in education is not new: teachers, perhaps since HTthe beginning of civilization, have intuitively used framing techniques for years as Sa way of achieving educational objectives. Often changing the frame of a situation Tis just what it takes to do X, whether X is getting a class to be silent, work on an Massignment, or become motivated. For example, Teacher A cannot get her first Rgrade children to be silent, until she plays Simon Says with the children: it is only when Simon Says )D< be quiet that the children comply. Teacher B knows that HRher junior high school students hate math, so she sets up a mock stock market game Rplayed with pseudo-dollars; the concepts are paired with money, which the kids are Rinterested in, and they cooperate. Teacher C knows that chess is seen as a Ogame in certain subcultures, so when he teaches it he makes sure to use phrases Srooted in violence (a concept seen in the subculture as ), to wit, get him! capture him! t let him run away! , etc. Teacher D forms part of his class Pinto teams and sets up a competition where there are winners and losers. RIn fact, even when the teacher makes no explicit effort to use framing techniques, Tframing is nonetheless part and parcel of the daily rituals in educational life; the school itself activates the THIS IS SCHOOL frame by displaying flags in HIclassrooms, hanging blackboards on walls, ringing bells every 45 minutes, Tarranging desks in rows, and by implementing all the other signifiers of the typical educational environment. FA less obvious use of framing, however, is the enhancement of positive HUtransfer. In this regard, the primary use of framing is to get educators to focus in terms of , as opposed to surface )*., structures. Since transfer occurs only when HUthere are common elements in place, it is the role of the teacher to make sure that Ma) the deep structure of a conceptual subsystem is the target lesson (because Tsignificant commonality is at the deep level, not the surface level) and that b) the Pstudent is given enough disparate examples to create a deep concept. To take an Jelementary example of this approach, a teacher should teach the concept of alliteration )?E using not only examples from poetry (as is typically done), but also HTfrom prose, fiction, and drama. After this initial presentation within the frame of ENGLISH )@G, the teacher leaves this primary frame, and gives examples from other, H!widely disparate frames, such as MUSIC (aural), (visual), and HISTORY (social). So, in MUSIC alliteration might be )8%the repetition of a two-note sequence H at the beginning of every phrase ; in alliteration might be the initial H*presentation of image A from shot to shot ((e.g., beginning every shot with a close up of the star); in HISTORY alliteration might be the framing of every different Times H%year by beginning with a single event (, such as the dropping of a Big Apple in HMTimes Square. The teacher finds these examples, and then teaches them to the Tstudents. Taught from so many widely differing areas, the student begins to see the deep structure of the concept of alliteration , which is [string1] [string2] H [string3] )3O. In this situation, positive transfer (the ability to discern an alliterative situation in # domain) is made far more probable. lEThe use of many examples from a variety of different domains has been HDreferred to by Butterfield, Slocum, and Nelson (1993) as the use of generative frames Hpitching the level of learning at the conceptual level. According to the HTauthors, all deep conceptual learning is generative because it allows the learner to 4correctly classify examples never seen before, from simple (e.g., a person seeing a H6new tree could nevertheless identify it as a tree) to complex (e.g. the generative HLframe "when you know what to do with one example of a concept, you can do it Lwith other examples" can be applied by a person to many different examples). 6Properly used, examples can exemplify deep structures. GAs Haring (1985) found, the teaching of even simple concepts requires a HRminimum of several examples, and thus it is not surprising that studies attempting Rto promote the use of generative frames by providing only a single example usually Nfail (e.g., Gick & Holyoak, 1980; Reed, Ernst, & Banerji, 1974) since a single Qexample can be seen in terms of any one of hundreds of concepts (e.g., Mozart of the applicability of critical thinking (its application to domain) will be lost. HMTo see the notion of domain specificity, note that the previously referred-to 7Joe/Tom math problems are typically discussed within a frame: ADD TO TOGETHER RELATE lLThus, if the student is in math class, and is given the Joe/Tom problems, at HOleast one of the above procedures will occur to the student ( Okay, I m in math 7class now. Solving these problems will involve either add to, add together, relate, and not )54 make past tense, interpret metaphorical as literal, etc. ). The H4surface features of math problems typically call up frames, but critical HQthinking transfer will only be taught when these features call up problem-solving HEURISTIC frames ).4 created by an education system which has previously HQsubcategorized declarative knowledge under procedural (as opposed to the reverse, the status quo), as follows: Times ENGLISH eJWpeJWp ENGLISH ENGLISH CHUNK WORK BACKWARDS ELIMINATE IRRELEVANCIES PROBLEM-SOLVING (HEURISTICS) lEWhen declarative knowledge is subsumed under the rubric of procedural H:knowledge, problem-solving (heuristic) techniques will be taught across declarative knowledge domains , such as and ENGLISH . Unfortunately, HQcurrent education parcels out the day in terms of declarative knowledge units ( Qnoun is a person, place or thing Albany is the capital of New York ) typically Massociated with their subject fields, thus permanently anchoring knowledge in Qterms of local solutions (problem-solving modes confined to the specific field of Qinquiry), and reducing the probability of positive transfer. Unfortunately, local 'framing teaches local processes: thus, addition is a process to be applied in , and make past tense is a process to be applied in ENGLISH . Since make past tense )YC may not properly be applied to numbers, which exist in ideological and not temporal spheres, the ENGLISH algorithm make past tense is domain HMspecific and non-transferable, and the teaching of a number of these kinds of Salgorithms can lead a student (and teacher) to the conclusion that transfer is not Times H+possible. Yet heuristic processes such as eliminate irrelevancies do not labor H*under this handicap. For example, one can eliminate irrelevant data in paragraphs ENGLISH ), and one can eliminate irrelevant data in word problems ( Eliminate irrelevancies + is a global skill that, when practiced in , will H1enhance the ability to solve the same problem in ENGLISH . Consider the Socks H Problem (Sternberg, 1987 at p. 207): l>Suppose you have brown socks and blue socks in a drawer, mixed >in a ratio of 4 to 5. What is the maximum number of socks you @have to take out of the drawer to be assured of having a pair of socks of the same color? *"HThose able to solve this problem know that the 4-to-5 ratio given in the problem is irrelevant. Solving this problem in by finding an irrelevancy H9will strengthen the ability to solve the same problem in ENGLISH (finding an HOirrelevancy), because the concept has been strengthened by yet another example. DSeeing irrelevance at the deep level will strengthen the concept of irrelevance , and HRthus aid in the solution of those other problems in life whose resolution requires finding the signal in the noise. Similarly, working backwards )o/ is a valuable problem-solving skill. Seeing a HIsituation in terms of BEGINNING and ENDING by starting from a known helps Vthe student find the syntax of a situation (which aids in the situation s resolution). ),3, for example, the solution of the addition problem equals lHrequires a reversal of typical math syntax, since one must work from the only known )$F, which is that the M in money must be the number (since HQthe only possible answer); thus, the problem has to be worked from left-to-right, backwards )=D, as opposed to the typical right-to-left syntax schema called up in solving math problems. ( 5 Bartlett, 1958). When this process is also taught in ENGLISH )@> (e.g., one can make writing easier by using the heuristic of working H backwards )=C by figuring out the end of a story first and then figuring out the HVcharacters, plot and setting required to get to the ending), the student has begun to 0see the abstract, deep side of backwards motion. Times Chunk )%B is another useful heuristic that easily transfers across domains. HFDifferent ways of chunking produce different outputs: for example, in ENGLISH HNthe output can be and different (which affects the way we categorize, &organize, think, and write), while in ), the output can be two different arithmetic results. Thus in ENGLISH chunk )"! will allow us to see that Dolly HMParton and Mozart are similar to each other and different from Babe Ruth 1only with reference to a certain category frame ( OCCUPATION ), while in we find that we only get from )# 4 * 3 + 2 when we chunk as (3 + 2) and not (4 + 3) which produces (. Different chunking leads to different outputs, in and ENGLISH lJBut the above heuristics are only a small set of the hundreds of essential HUproblem-solving skills people need to resolve difficult situations. The following is Fbrief list of heuristics that can cut across widely different domains: WORK BACKWARDS CHUNK )u ELIMINATE IRRELEVANCIES DELETE COMBINE )u DECREMENT FIND EXAMPLES FOCUS GO BACK SCHEMATIZE DEFINE TERMS GATHER SCAFFOLD PRIORITIZE OVERSAMPLE REDUCE TEMPO )u INCREMENT MODULARIZE MEASURE PROGRESS INCREASE SORT BINARY SEARCH FIND AN ANALOGOUS SOLVED PROBLEM ISOLATE PARAMETERS FIND THE SYNTAX OF THE SITUATION SEEK EFFICIENCY COUNTERFACTUALS SHIFT THE REFERENCE FRAME MAKE VARIABLES SOLVE A SIMPLER PROBLEM Times lKEducation organized in terms of global heuristic skills can transfer across HNwhat are on the surface very dissimilar declarative knowledge domains, because Nidentity will exist in the deep structure of the frames used to transmit these heuristic skills. IIf a school is organized in terms of heuristics, courses will change from HMthose conveying declarative knowledge to those involving knowledge of problem H4solving processes. Here is a sample course content: Critical Thinking Heuristics English Science General Semantics Frame Analysis Interpretation Subroutinization of Thought Chess Programming Scientific Method Statistics Hypothesis testing lLA student graduated from this school, a school which has radically re-framed HSthe educational day so as to greatly increase the probability of positive transfer, Owould be a student who would see every problematic situation as one which could .be dealt with by applying the proper approach. NThe ability to see in terms of deep structures, an artifact of an educational HTapproach rooted in deep-structure analysis, will enable the student to be the master Qof his or her own perception. No longer the captive of whatever local frames are ?called up by surface features, the student will be able to get kinds of HLinformation from the same text (seeing all the inherent possibilities), and kind HLof information from many different texts (seeing the forest, not the trees). LEducation will be efficient because each problem-solving situation will be a Prehearsal for the next problem-solving situation. The liberation from old tricks Otaught by old dogs within old frames will help all of us trying to cope with an +endlessly morphing, Third Millennium world. Times REFERENCES BARTLETT, F.C. (1958). Thinking. London: Allen & Unwin. BATESON, G. (1972). Steps to an Ecology of Mind. ( New York, NY: Ballantine Books, 1972. HTBUTTERFIELD, E.C. & DICKERSON, D.J. (1991). Promoting Postive Transfer of Different Types. Cognition and Instruction, 8 , 69-102. HOBUTTERFIELD, E.C., SLOCUM, T.A. & NELSON, G.D. (1993). Cognitive and Behavioral VAnalyses of Teaching and Transfer: Are They Different? In Sternberg, R.J. & Detterman, D.K. (Eds.), )@=Transfer on Trial: Intelligence, Cognition, and Instruction (pp. 192-257). l#Norwood, NJ: Ablex Publishing Corp. HRCORMIER, S.M. & HAGMAN, J.D. (1987). Introduction. In Cormier, S.M. & Hagman, J.D. (Eds.), )$>Transfer of Learning: Contemporary Research and Applications (pp. 1-8). New York, NY: Academic Press. HVDETTERMAN, D.K. (1993). The Case for the Prosecution: Transfer as an Epiphenomenon. In *Sternberg, R.J. & Detterman, D.K. (Eds.), /Transfer on Trial: Intelligence, Cognition, and Instruction );0(pp. 1-24). Norwood, NJ: Ablex Publishing Corp. H?GICK, M.L. & HOLYOAK, K.J. (1980). Analogical Problem Solving. Cognitive Psychology, 306-355. HMGICK, M.L. & HOLYOAK, K.J. (1983). Schema Induction and Analogical Transfer. Cognitive Psychology, 15, 1-38. HPGICK, M.L. & HOLYOAK, K.J. (1987). The Cognitive Basis of Knowledge Transfer. In %Cormier, S.M. & Hagman, J.D. (Eds.), +Transfer of Learning: Contemporary Research and Applications )X*(pp. 9-46). New York, NY: Academic Press. GOFFMAN, E. (1974). )x:Frame Analysis: An Essay on the Organization of Experience . New York, NY: Harper and Row. HQHARING, T.G. (1985) Teaching Between-Class Generalization of Toy Play Behavior to Handicapped Children. )r,Journal of Applied Behavioral Analysis, 18, 127-139. KEANE, M.T. (1988). Analogical Problem Solving $. New York, NY: John Wiley and Sons. MAYER, R.E (1992). )q$Thinking, Problem Solving, Cognition . (2d Ed.). New York, NY: W.H. Freeman & Co. HSMINSKY, M. (1975). A Framework for Representing Knowledge. In Winston, P.H. (Ed.), Psychology of Computer Vision . New York, NY: McGraw-Hill. HZREED, S.K. (1993). A Schema-Based Theory of Transfer. In Sternberg, R.J. & Detterman, D.K. (Eds.), )#=Transfer on Trial: Intelligence, Cognition, and Instruction (pp. 1-24). Norwood, NJ: Ablex Publishing Corp. HUREED, S.K., ERNST, G.W. & BANERJI, R. (1974). The Role of Analogy in Transfer Between Similar Problem States. Cognitive Psychology, 6, 436-450. Times HQROSE, A., EVANS, R. & WHEATON, G. (1993). Methodological Approaches for Simulator 5Evaluations. In Cormier, S.M. & Hagman, J.D. (Eds.), Transfer of Learning: l(Contemporary Research and Applications *(pp. 9-46). New York, NY: Academic Press. H(SINGLEY, M.K. & ANDERSON, J.R. (1989). The Transfer of Cognitive Skill , Cambridge, MA.: Harvard University Press. HYSTERNBERG, R.J. (1987). Teaching Intelligence: The Application of Cognitive Psychology to Qthe Improvement of Intellectual Skills. In Sternberg, R.J. & Baron, J.B. (Eds.), Teaching l&Thinking Skills: Theory and Practice .(pp. 182-218). New York, NY: W.H. Freeman and Company. HMTHORNDIKE, E.L. & WOODWORTH, R.S. (1901) The Influence of Improvement in One 8Mental Function Upon the Efficiency of Other Functions. Psychological Review, 8 , 247 THORNDIKE, E.L. (1906) Principles of Teaching )m!. New York, NY: Lemke & Buechner. HVWINSTON, P.H. (1975). Learning Structural Descriptions from Examples. In Winston, P.H. (Ed.), "The Psychology of Computer Vision . New York, NY: McGraw-Hill. @8 p? #+&%" 3K:#$VM T1-9/?O>B;. G=A@!L<()E4& p(0@ A6<84 @` -.,$/& ;-%$1 xTp0` <*`@ 0f6 xT@ |Jx(` <(3=A*:2+). xTp0` xTp0` xTp0` #+&%" 3K:#$VM T1-9/?O>B;. G=A@!L<()E4& A6<84 -.,$/& ;-%$1 '@O@@ r <(3=A*:2+). Zssential problem-solving skills temp.0001 euristics that can cut across widely different domains: WORK BACKWARDS CHUNK ELIMINATE IRRELEVANCIES DELETE COMBINE DECREM Barry Krusch Barry Krusch Microsoft Word Bookman Times Courier Avant Garde Minstrel UltraShadow Garamond Narrow Delphian CasqueOpenFace:~ Helvetica Black K(C8K(C8 K(C8K(C8 K_b^K_b^ rPREC ~PRVS &FNMS