Sameness and Difference in Transfer Ference Marton03

Historical examples of the systematic use of variation.

Although the studies in this section are not transfer studies,they are relevant to the discussion because they demonstrate the historical roots of the systematic use of variation and invariance in instruction.In China there is a well-known approach to teaching math ematics called teaching with variation (Gu,Huang ＆ Marton,2005).Kangshen,Crossley,and Lun (1999) documented the use of this method dating back nearly 2000 years.Gu (1991) nicely captured its appearance in modern practice by demonstrating that more successful mathematics teachers use the teaching with variation approach more often than do less successful teachers.One example of the systematic use of variation can be found in the use of nonstandard figures in order to investigate aspects of geometric figures that students falsely assume to be critical.Polygons are,for instance,always drawn in textbooks with a horizontal baseline.Rotating them can help students realize that angular orientation is not a critical feature of polygons.Additionally,presenting noninstances of a concept can help students become aware of a critical feature.For instance,by presenting a line perpendicular to a radius and intersecting the circle in two points,the students' attention is drawn to the fact that a tangent of the circle has only one point in common with the circle.

Mason and Watson (2005) analyzed textbooks in mathematics used in England from the 16th century on.They demonstrated that in many cases the authors made systematic use of variation and invariance by building sequences of tasks that bring out critical differences between them.

A final example of the systematic use of variation and invariance can be seen in Maria Montessori's pedagogy.She was inspired by two French physicians,Jean Marc Gaspard Itard (1775-1838) and Eduard Seguin (1812-1880).The former became famous for his treatment of the Wild Boy from Aveyron,an 11—or 12-year-old boy who had grown up in the forest without any contact with human beings.An important principle used by Itard was to try to teach the boy to make distinctions by means of contrasts (e.g.,learning to tell apart a round figure from a flat figure by touch,red paper from blue paper by vision,and bitter from sweet by taste).Itard also tried to link the distinctions between sensory impressions to distinctions between corresponding words by means of simultaneous variation in sensory impressions and words (see,for example,Itard,1801/1962;Lane,1977).I can compare Itard's approach with the more common approach of introducing one concept or word at a time and pointing to different instances of that concept (e.g.,looking at a red rose and saying “red”, followed by pointing to a red apple and saying “red”, and so on).The difference between Itard's approach and the more common approach is the difference between the use of contrasts and generalization.

Seguin,who was Itard's follower,worked with retarded children.A central element in his work was the training of the senses by means of the physiological method.Seguin wanted to help children develop finer and finer discriminations with all their senses.He did so by producing sensations that were at first far apart (e.g.,quiet sound/loud sound;light touch/heavy touch;dim light/bright light;and so on),and then later producing sensations that were closer and closer to each other (Seguin,1907).Seguin was considered to be uniquely successful in developing the retarded children's capabilities to deal with the world around them (Marton ＆ Signert,2005).

The training of the senses was a central element in the pedagogy that Montessori developed for children without specific handicaps (as described by Signert,2005).Montessori believed that it was very important to isolate different sense dimensions and to let the children focus all of their attention on one specific dimension at a time.Consider the following example,aimed at letting children discern different dimensions of geometric figures.Four sets of materials are utilized:

Set 1.Cylinders varying both in diameter and height.The tallest cylinder has the largest diameter and the shortest cylinder has the smallest diameter.

Set 2.Cylinders varying both in diameter and height,as in Set 1,but the tallest cylinder has the smallest diameter and the shortest cylinder has the largest diameter.

Set 3.Cylinders varying in diameter only.They all have the same height.Each cylinder is 0.5 cm larger or smaller than the next one.

Set 4.Cylinders varying in height by 0.5 cm per step,all having the same diameter.

Noticing systematic differences of this kind and solving problems by noticing such differences frequently captures young children's intense and uncharacteristically sustained attention,as illustrated by Montessori's own examples (see,for instance,Montessori,1917/1965).

IMPLICATIONS

Transfer as a Function of Differences (and Sameness)

The point of departure for this article is the view that what the learner learns to do in a certain situation may enable her to do the same thing in another situation to the extent that the second situation resembles (or is perceived to resemble) the first situation.I set out to challenge this view,arguing that not only sameness,similarity,or identity might connect situations to each other,but small differences between them might connect them as well.My interest has been how what the learner learns in some situations might enable her to do something different in other situations thanks to perceived differences (and similarities) between situations.I agree with the abovementioned four points made by Lave (1988) in her critique of the culture of transfer experiments,that (a) answers to the question “what is learned?” should not be taken for granted;(b) any generalizations made by the learner contribute to connecting situations;(c) we should focus on relations between sets of situations rather than on only two situations at a time;and (d) connecting situations is done in all of the situations involved as opposed to “what is learned” being applied more or less automatically to a single situation.The main focus of this article is,however,a point not raised by Lave,namely the role of differences in connecting situations.

In the first example in the section on motor learning,we considered a study in which children hit a target with a shuttlecock from different angles.In order for children to become aware of the dimension of angle variation,children must be able to discern it in the very throwing in order to be able to adjust to changes in it.It is only by encountering differences,changes,variation,that they become able to discern it in the throwing.So in order to be able to handle a new angle in Situation B without starting from scratch,they must have encountered throwing from another angle before,in Situation A,or they must have encountered throwing from different angles before.In order to be able to discern a certain dimension of variation,however,not only must the learner experience variation in that dimension,but she must also experience invariance in other dimensions.Nothing can be discerned when everything varies,just as nothing can be discerned when nothing varies.In many of the examples presented in this article,it is by enabling the learner to discern a critical dimension of variation that one situation is linked to another.This was certainly the case in Schwartz and Martin's (2004) study,in which learners in one condition became better than learners in the other condition at discerning the dimension of central tendency and the dimension of variability.

There are values in the dimensions of variation.For example,every specific angle is a value in the dimension of angles,and every mean for every specific distribution is a value in the dimension of central tendency.Contrasts between values enable learners to discern values.One can never discern just one value.It is the difference that is discerned,and to experience a difference takes at least two values.Through contrast,the learner can discern values as well as the dimension of variation in which they are values.This is what Watson and Mason (2005) referred to as the range of permissible change in a dimension of possible variation.

Let us take another look at the Cantonese tone example.As a foreigner in China,when I hear a word (“A”),I cannot discern its two vocal aspects—the sound and the tone—unless the tone differs markedly from the intonation pattern that I am used to.This is Situation A in the traditional transfer perspective,and it is followed by another word (“B”),which has the same sound as A but a different tone (Situation B).Then all of a sudden I can hear the tone in B and retrospectively also in A (thanks to the contrast).Without having heard A,I would not have been able to discern the tone in B.We could thus call it transfer (according to the above definition of transfer as the effect of what someone learns in one situation on what she can do in another situation).But I am not doing the same thing when hearing B as I did when hearing A (cf.,the definition of transfer as the extent to which someone can do the same thing that she learned to do in one situation,also in another situation).When hearing A,I could not differentiate its tone from its sound;yet I can discern the tone in B after hearing A.Although the sameness of the sounds across the two words was a necessary condition for discerning the tone,it was the difference—and not the sameness—that was attended to,discerned,and transferred.Neither repeating Word A nor repeating Word B would have allowed for that.

We find the same phenomenon in the other examples presented in this article.The students in Schwartz and Martin's (2004) study benefited from the learning resource and succeeded in the invention activity because the two arrangements for learning were different (but similar in terms of content).Students may have grasped some of Newton's ideas thanks to having read about Aristotle's different ideas (about the same thing).The form of an egg is discerned because it differs from the previously encountered ball (with which it shares the color),according to Martineau's observation of the differentiating force of contrasts (as cited in E.J.Gibson,1969).In each of these cases,discernment is made possible because some things are the same whereas others are different.

Furthermore,in order to discern a dimension of variation,it must also vary,while other dimensions remain invariant.In the Cantonese tone example,we might not only discern two different tones,but we might also become aware of the fact that there is such a thing in Cantonese words as tones.That is,we might be able to discover tones as a dimension of variation.As a result,we could then distinguish that dimension from other dimensions,such as sound.In order to be able to speak and understand Cantonese,we must be able to discern the different aspects of words when they all vary.After all,this is what Cantonese speakers unconsciously do.

So far I have only dealt with the simplest relationships between discernment and differences or variation in this section.I have talked about the discernment of dimensions of variation or separation,and I have talked about the discernment of values,thanks to contrasts (Marton ＆ Tsui,2004).Perception of one thing affects the perception of another thing.But even these simple relationships are sufficient,I believe,to illustrate that what people learn to do in one situation might enable them to do something different in another situation,thanks to differences (and similarities) they perceive between or within the two situations.

In the description of Itard's (1801/1962) approach to teaching the Wild Boy from Aveyron color names,I mentioned an example of the most common use of variation in educational contexts,namely generalization (Marton ＆ Tsui,2004).It refers to the introduction of a concept or principle followed by a great number of examples of the concept or principle in question.Dienes (1963) developed an approach to the teaching of mathematics based to a large extent on this specific pattern of variation and invariance.Indeed,invariance in the midst of change is a central theme of modern mathematics (Mason ＆ Johnston-Wilder,2004).

When learning to deal with novel situations,people have to learn—as a rule—to take different features into consideration simultaneously.As an example,consider the situation of children learning Chinese words.In one of the classes the teacher created conditions for linking the three different aspects of Chinese words—character,pronunciation,and meaning.This happens when the different aspects vary together,resulting in what Marton and Tsui (2004) refer to as fusion.Another example of fusion is Itard's (1801/1962) attempt with the Wild Boy from Aveyron to link differences in sense impressions to differences in words,denoting them by simultaneous variation in both.

In the introduction to this article I expressed agreement with Lave's (1988) critique of selecting two situations and looking at the relationship between them in the researcher's narrow perspective only.The interesting question is how we manage to discern critical aspects of the widely varying concrete and complex situations of everyday life.In this article I have only tried to illustrate some fairly straightforward relationships between discernment,on the one hand,and variation or invariance on the other.Far more complex relationships between discernment and variation or invariance are elaborated upon by Marton and Tsui (2004).

Pedagogical Aspects of Transfer

For much of the 20th century,transfer was a well-researched topic in educational psychology.More recently,transfer is a much-criticized concept.Why does transfer continue to attract so much attention and interest? The reason is,I believe,that the question of how what we learn in one situation effects our capabilities for handling novel situations is,as Lave (1988) rightly pointed out,absolutely central to the educational enterprise.As I argued above,the question of transfer is closely linked to the question of what is learned.If we were to cast the transfer issue in a pedagogical form,we would not only ask “what is learned?” and “what is transferred?”, but also “what should be learned?” and “what should be transferred?” we would then ask how we can possibly increase the likelihood of learners handling novel,unknown situations in the future in powerful ways.Bransford and Schwartz's (1999) preparation for future learning approach points to such a reformulation of question of transfer.The general answer is that by learning (now) how to learn (in the future),learners will be better able to cope with novel situations.

Generative Learning

The notion of transfer as a function of sameness derives from the deeply seated view of learning as being based on repetition and habituation.However,the fundamentally fascinating question,both from the point of basic research on learning and from the point of schooling,is how learning one thing now can prepare us to learn something else in the future.Were we to widen the scope of the concept of transfer,such an effect could be called transfer:one learns something in some situations,and then one becomes better at learning something else in other situations.Let us call it generative learning in accordance with Mestre's (2002) conclusion from the first National Science Foundation Transfer Conference that generativity should be a main topic for future research on transfer.

One of the main goals of schooling is to enable students to handle novel situations in powerful ways.How can generative learning be instrumental to that? There is no action without perception.We have to perceive,discern,and distinguish in order to make sense of the world around us and to deal with it in powerful ways.We have to construct a personal narrative informed by the narratives of others.It could be the case that different people typically understand the same situation in the same way but handle it in different ways.That is to say,their perceptions may be the same,but they do different things in relation to the same perceived reality.However,a great deal of research shows that differences in expertise are reflected in differences in how situations are perceived or understood.For example,a chessboard is perceived differently by a master chess player than by a novice (de Groot,1965).Similarly,physics problems look different to physicists than to physics students (Chi,Feltovich ＆ Glaser,1981).Even cars look different to more and less successful engineers (Sandberg,1994).Differences in more and less powerful ways of handling simple arithmetic tasks originate from differences in how the tasks are perceived and understood (Neuman,1987).Differences in how good university students are at writing essays are closely linked to how they view the task of writing an essay (Hounsell,2005).Differences in comprehending text are intimately related to differences in how the same reading task appears to different readers (Marton ＆ Slj?,2005).

Looking at the chessboard and determining the meaning of what we see amounts to learning about its momentary status.Looking at a physics problem and ascertaining what kind of problem it is amounts to learning about that specific problem.Examining a patient as a doctor amounts to learning about that specific patient.Grasping what someone says or understanding a text in a certain way amounts to learning about what someone says or what a text is meant to tell us.In each case we remain in touch with the surrounding world by continuously keeping ourselves informed.This is perception,but it is learning as well.Perceptual learning is then a kind of learning to learn—learning how to learn from and about chessboard positions,physics problems,patients,what we hear,and what we read.Perceptual learning is generative (Holmqvist et al.,2005).

According to the line of reasoning followed in this article,perceptual learning amounts to learning to make distinctions.In order to be able to notice differences,the learner has to have encountered differences.In order to see how something differs,the learner must previously have seen something that it differs from.Seeing one thing affects how the learner sees another thing subsequently—not because of the sameness of the two,but because of both similarities and differences.

ACKNOWLEDGMENTS

First,I thank Joanne Lobato who organized the National Science Foundation “International Working Conference:Addressing the Transfer Dilemma” (REC-0450208) in San Diego,January 13-16,2005 from which this article originates.We were actually six people determined to challenge “the doctrine of sameness”:King Beach,Yrj? Engestr?m,John Mason,Ricardo Nemirovsky,Nephi Thompson,and myself.The joint article still remains to be written.When writing this version of mine,I immensely profited from our initial discussions and from the comments I had received.John Mason,Yrj? Engestr?m,and Thabit Al-Murani have read an earlier version of this article,and they contributed to its betterment with comments,suggestions,and support.After submitting the article,I received constructive critique and highly helpful suggestions from James G.Greeno,two anonymous referees,and the editors (Janet Kolodner ＆ Joanne Lobato).John Mason read and commented on this latest version of the article,too.Lisbetth S?derberg helped to bring the whole thing to-gether.I am deeply moved by the generosity of all involved.

The Swedish Research Council has financially supported the writing of this article,and I am very grateful for that.

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Correspondence should be addressed to Ference Marton,Department of Education and Educational Research,G?teborg University,P.O.Box 1010,S-431 26 M?lndal,Sweden.E-mail:ference.marton@ped.gu.se.

[1] The student actually did more than this in both cases.The simplification in my presentation is due to space restrictions.

[2] Beach (1999),however,argued for a view of transfer as consequential transitions (i.e.,as the transformation,construction,and reconstruction of knowledge,identities,and skills in new situations).By doing so,he emphasized discontinuities as much as continuities.Transfer in this sense is facilitated by expanding the boundaries of conditions for learning.Beach made a distinction between “examining transfer between tasks” on the one hand and “studying transfer between larger socially organized situa-tions” on the other .Obviously,I am doing the former,Beach is doing the latter.Tuomi-Gr?hn and Engestr?m (2003) presented a developmental view of transfer,similar to Beach's.The difference in“grain size” between their discussion of transfer and mine is even more pronounced,as are their concluding words:“...transfer is about changing communities rather than individuals” .

[3] The theory—or rather,the framework indicated in “Perceptual Aspects of Learning”—has been presented in its different stages of development by Marton and Booth (1997),Bowden and Marton (2004),Marton and Tsui (2004),and Marton and Pang (2006).It resembles quite closely another,independently developed framework by Mason and Watson (see,for instance,Mason,2001;Watson ＆ Mason,2005).