European Journal of Psychology of Education1993, Vol. VIII, n? 4, 375-387© 1993. I.S.PA

Routines in Classroom Discourse:An Ethnomethodological Approach

Helga JungwirthJohannes Kepler University, Linz; Austria

The approach to routines presented in this paper refers to thephenomenology of Schutz, to symbolic interactionism and in particularto ethonomethodology: The interest is focussed on teachers' and students'routines making them establish the common classroom discourse. Routinesimportant in the mathematics classroom - but presumably in othersubjects too - arepresented The discussion shows that they have positivefunctions for the interaction process as well as partly negativeconsequences for the learning of mathematics.

Introduction

Roughly spoken in the research on routines two different approaches can be reconstructed.One approach is based on the perspective of cognitive psychology. In this perspective

the term 'routine' refers to smooth-running, fluent acting carried out and learned individually.It is the expertise in problem solving, for example in physics, or chess, yet as well teachers'coping with classroom situations, that is analysed with this concept (cf. Bromme, 1985; Bromme& Brophy, 1986; Chi, Glaser, & Rees, 1982). Recent results show that experts do not differfrom novices by a knowledge-free acting in routine situations; they do use knowledge butit is organized in a way different from that on the part of novices.

The main interest within this approach to routines is directed towards the routine knowledgeand its structure. The routine knowledge of experts is 'condensed' (Bromme, 1985) in the waythat their conception of a situation includes an evaluation of it as wellas target-relevant reactions.As for the professional knowledge of teacher experts in particular, Bromme (1992) reconstructeda case-centred organisation of their knowledge, a knowledge that refers to relations betweenparticipants, contents and conditions of teaching and thus is relatively abstract. Specific featuresof this knowledge are analysed (for an overview see Bromme, 1992, or Shavelson & Stern,1981) based on the concepts 'implicit classroom theories' (cf. Heymann, 1982), 'practice-related

376 H. JUNGWIRTH

cognitions' (cf. Interdisziplinare Arbeitsgruppe Lehr-Lernschwierigkeiten, 1992) or 'everydaytheories' (cf. Hurrelmann, 19'80).

As for school students there is a huge amount of task- respectively subject-related studieson problem solving too; in this context, however, 'routine' is not a leading concept, on thecontrary: The focus is on non-routine tasks and the development of new knowledge.

The other approach to routines refers to the phenomenology of Schutz, to symbolicinteractionism and in particular to ethnomethodology: the interest is focussed on methodsof acting which permit the participants of an interaction to establish a routine situation asa routine situation. This is the approach that will be presented in this paper. IJIustrating exampleswill be taken from mathematics education as this approach has been developed mostly withinthis field of research.

The routine situation

After Schutz (1981; Schutz & Luckmann, 1988) the course of life is a sequence of situations.There are always situations the individual lives in and makes experiences. On the one handevery situation is limited and determined: by its temporariness, by the individual's body andits ordinary functioning, and by the individual's biography. On the other hand every situationis ambiguous and left for interpretation. It can be interpreted with respect to its relationsto other situations or experiences, to what happened before and to the development it willtake in the future. And of course the elements it is constituted of can be analysed and interpreted.Interpreting is not a process which is carried out totally before any acting in the situationstarts, and it is not at all a verbally explicated procedure. Interpreting the situation and actingin it are interlocked. Besides, the interpretation is pragmatically limited: it is actually doneonly as far as neccessary to master the situation. The process of interpretation or 'definition'(Thomas, 1923; Mollenhauer, 1972) of a situation can lead to two results:

«ne can make out different types of definition: in the first case thesituation can be defined by the routine knowledge so that the plan-guidedinterest is satisfied. All 'ambiguous' elements of the situation can be definedroutinely. If this can be attained the situation is unproblematic also in itsundetermined elements. We want to call this kind of situations routinesituations. In the second case there are undetermined elements of the situationwhich cannot be defined routinely. If such 'ambiguous' elements emergein a situation I have to think them over, that is I intentionally try to correlatethese elements with my stock of knowledge... ~mbiguous' elements tooare interpreted by the means of the available frameworks but this does nothappen in a way sufficient for my plan-guided interest. My knowledge aboutthose elements is not clear enough, not sufficiently free of contrarities, Iam not familiar enough with them to cope with the actual situation. HenceI have to continue the interpretation of the ambiguous elements of thesituation until they have reached the level of distinctness, familiarity andcontraritylessness provided by the plan-guided interest. We want to call suchsituations 'problematic situations: Consequently in problematic situationsI have to acquirenew elements of knowledge or I am compelled to transformold elements of knowledge not sufficiently elaboratedfor the actual situationinto elements of higher elaborateness» (Schlitz & Luckmann, 1988, p. 150;translation by the authoress).

In each case the individual interprets the situation by the schemes of interpretation heor she has acquired and activates in the situation. He or she tries to recover in the situationa certain 'type' of situation he or she is familiar with (Schlitz & Luckrnann, 1988, p. 277).

INTERACTIONAL ROUTINES IN THE CLASSROOM 377

In the routine situation the expectations joined with and arisen by the type are met, in theproblematic situation they are disappointed.

Routine situations are those interesting here. To sum up they are managed incidentallyand permit to focus the attention on still challenging aspects of everyday affairs; the routineactivities are just carried out using the corresponding routine knowledge which is always athand, but which is not thematised or reflected. Characteristic for routines is theirunquestionability, and thus their main function is the reduction of the complexity of the everydayworld.

As routines are a constitutive feature of the everyday world to cope with a situation routinelyis not something outstanding only a few people will succeed in; nor it is a way that shouldbe avoided. It is quite a common event, or even a bit more: In the everyday world there isa 'desire' for normality; new situations are treated as if they were already known, they aretransformed - as far as possible - into 'normal' routine situations (cf. Soeffner, 1983).

The interactive definition of a situation and the methods to do so

As already stated the members of society try to reduce the complexity of their everydaylife by treating situations as common, routine situations. In the treatise of Schlitz these actsare personal and subjective ones even if there is more than one individual in a situation. Socialrelations between individuals are not considered by him in this context and hence managingsituations as routine situations is not described as a social process.

In the research referred here this is done by adopting the symbolic interactionist's pointof view. It is based on the following three premises:

(The first premise is that human beings act toward things on the basisof the meanings that the things have for them. Such things include everythingthat the human being may note in his world - physical objects '" andsuch situations as an individual encounters in his daily life. The secondpremise is that the meaning of such things is derived from, or arises outof, the social interaction that one has with one's fellows. The third premiseis that these meanings are handled in, and modified through, an interpretativeprocess used by the person in dealing with the things he encounters» (Blumer,1969, p. 2).

Underlying this conception a routine situation becomes a routine situation in the interactionbetween the participants.

I want to mention two aspects of this sight. Firstly, the participants in the interactionare considered to be on an equal footing in principle - they all contribute to the definitionof the situation. Within a pedagogical context this might be thought as an inadequate positionbecause of the institution-based responsibility, or control, on the part of the teacher. Actuallysuch an unequilibrium is not denied; it is quite possible in this view too, that in a classroomsituation the teacher's interpretation comes to stay, but this can only happen if the studentsdo not oppose which means that they interprete the situation as one better to submit to (forwhatever reasons) and which does not say that they really accept the teacher's definition.Secondly, there is no objective knowledge to be taught in the classroom. The valid knowledgeemerges within the interaction, i.e. some meanings are taken as shared by the participants.All participants - the teacher as well as the students - start with their subjective meanings,whereby the teacher's view generally is closer to the official one held by the correspondingscientific discipline, But the students have their perspectives too - they are not like a 'tabularasa' - and they do not automatically accept the teacher's perspective. In specific in theinteractionist approach the idea of an immutable objective mathematics is suspended. Thevalid mathematical meanings dealt with in the classroom are the result of social negotiationprocesses.

378 H. JUNGWIRTH

The interactionist perspective emphasizes in comparison with Schutz the role of the socialinteraction within the construction of the meaning of whatever objects. The question, however,how this is really managed is not dealt with. The interest of the referred research in suchmethods leads to ethnomethodology as a third basis.

The subject of ethnomethodology are the methods the members of society use to constitutethe reality of their everyday world. The central assumption is that the social reality is constitutedin the interactions of the members of society by their simultanous settling their affairs andmaking them accountable:

«The activities whereby members produce and manage settings oforganizedeveryday affairs are identical with members' proceduresfor makingthose settings 'account-able' ... When I speak of accountable my interestsare directed to such matters as the following. I mean observable-and­reportable, ie. available to members as situated practices of looking-and­telling ... By his accounting practices the member makes familiar,commonplace activities of everyday life recognizable as familiar,commonplace activities» (Garfinkel, 1967, p. 1 and p. 9, setting off in theoriginal).

Thus the methods of constitution of meaning are identical with those of presenting meaning.

The underlying concept of routine

Basing on Schutz, the symbolic interactionism, and ethnomethodology the followingconception of the routine classroom has been developed.

Teacher and students manage the situations in classroom routinely. This is accomplishedinteractively - all participants contribute to it. To do so they make use of certain methods,not in the sense of a deliberated choice but just routinely. This means that the participantstake the adequance and the success of their methods for granted by interpreting the actualsituation as a common one and expecting it to be this in future too. They are imputing a'normal form' of the course of the interaction (cf. Cicourel, 1981; Voigt, 1984). Thus theyhave expectations concerning the behaviour of their fellow-praticipants: They presume thateach participant will act in a way that the routine situation will last. It is this socially sharedexpectation that makes the main difference to the psychological concept of routine.

Voigt (1984) who has been a pioneer with reagard to routine practices in the classroomat least within the mathematics education describes a routine as:

«a principle of acting- that becomes effective in certain situations within interpreting them in certain directions- that in the natural attitude the acting person takes for granted- that has certain functions for coping with the situation and- that has been acquired mainly socially» (Voigt, 1984, p. 69; translation by the authoress).

With his first condition Voigt eliminates simple stimulus-response schemes, or original,unique actions. With the second one actions 'intentionally set as tactics or strategies areeliminated. By the third condition the relevance for the actual situation is provided, and thefourth condition eliminates practices exclusively due to biographical specificities.

As for the formation of such routines it should be emphasized that routines are the resultof the individual's social experience of the adequance of (interpreting) activities. This obviouslyrefers to the indiviual's own coping with situations but to that one of the fellow-participantsin the situations as well. For example, an experienced student 'knows' how to act as a peerteacher too, or a novice teacher is able to act in a way he or she perceived his or her teacherto do. The amount of successful repetitions seems to be less important for developing routines

INTERACTIONAL ROUTINES IN THE CLASSROOM 379

than the intensity of the experience: Neth and Voigt (1991) for example have reconstructedthat first graders get used to methods typical for the mathematics classroom, as to turn theattention to numbers only in tasks related to the everyday world of children, within only onelesson.

Routines of teachers and students in the mathematics classroom

In this chapter I present relevant findings of the research in mathematics education basedon the concept of routine given above. Routines of teachers and students are shown withinthe context of teacher-students interaction in the mathematics classroom', The expectationsand presumptions underlying the concrete routine practices and their relevant functions inthe interaction are described.

As for the form of the presentation - analysing typical passages from transcripts ofteacher-students interaction - I want to indicate that transcripts of video- and audiotapedlessons are the basic material for the interpretational work which is the way this research isdone. The transcripts are interpreted with respect to the interesting features by the 'methodoj documentary interpretation' (Wilson, 1981, p. 60). Thereby each phenomenon is considerda specific expression of an underlying pattern which on the other hand is identified by thevarious phenomena. By interpreting many transcripts of a certain interesting event (theintroduction of a new mathematical concept for example) a hypothesis about the typical featuresof such a pattern is established. This means that one reconstructs certain features by analysingone transcript; then one takes another transcript and another one a.s.or and develops thehypothesis by generalizing, differenciating, specifying a.s.o. the first idea until additionaltranscripts only confirm what has already been reconstructed. This method is called the 'constantcomparative method oj qualitative analysis' (Glaser & Strauss, 1967; for further descriptionsof the method, cf. Voigt, 1991).

In each of the projects within mathematics education a large amount of lessons (at least30 to 40) in different schools and in different grades has been videotaped so that the findingshave a sound of empirical basis. Besides, other studies making use of other methods confirmrelevant aspects of these findings (cf. Grell & Grell, 1983; Hoetker & Ahlbrand, 1969; Hopf,1980).

In the following, two 'scenes' i.e, passages from transcripts of teacher-students interactionin Austrian schools, are presented and analysed. The translation of the dialogues spoken inthe Austrian dialect of German tries to preserve the meanings and the structure of the spokenlanguage as well as to use English idioms (original transcripts in Jungwirth, 1990). Besides,specific rules of transcription are used; they are listed in the Appendix.

Scene 1

It took place in a class of grade eleven (students aged about 17) within the teaching ofstatistics. The concept 'representative sample' is introduced, the introductory problem runsas follows: 'An inquiry of 2463 secondary school graduates showed that 182 graduates wantto study mathematics, 225 physics, and 316 chemistry. How many students can we expectin theses subjects if there are 72000 secondary school graduates all together?'

1 Teacher:234 Christof:S6 Teacher:7

well. (3 sec p) how could we solve this aboveall what do we assume if we want to solvethis. (Emma i)that the seventytwothousand have got thesame opinion (about this?) (3 sec p)that the seventytwothousand have got the sameopinion-

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8 Christof:9 Bertram:

10 Teacher:1112

13 Bertram:

14 Emma:

15 Teacher:1617181920

21 Detlef:

22 Teacher:23

24 Rainer:252627 Teacher:

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well that they split up in the same manner.that all take up a study- (4 sec p, Emma L)

well nor yet you know from thetwothousandfourhundredsixtythree graduateswhether they all want to study.

well (Emma i) but, thats what I just assume.

well but the ra (stops talking)

wait perhaps another consideration- (Detlef t)see what do I if one wants to solve this atall yes' (Emma I) if this should make sense, whatis presumed here in a way. (2 sec p, Bertram t,Rainer l) something very important withregard to polls , polling enquiries. turn

hey (waves his hand)

your attention to that. , Rainer. (Bertram ~,

Detlef nthat the distribution of interests among thetwothousandfourhundredsixtythree is equal tothat one among the seventytwothousand.right. (nods, Detlef i)

The scene shows how teachers typically manage introductory sequences.The teacher (lines 1-3) stans with the routine 'ambigous question' or 'provisional try'.

He aimes at the presuppositions for the solution of the given problem. For experiencedmathematicians it is obvious that he has the representativity of the sample in mind but hedoes not say this explicitly nor does he give any clues. This routine permits a teacher justto start teaching without having developed before elaborated concepts of the way the teachingprocess should take. Yet there is a basic presumption made as to the behaviour of the students:starting with an ambiguous question only makes sense if the teacher takes it for granted thatthe students will give a meaningful answer. An important function of this routine is to enablethe teacher to meet the pedagogical demand that students should develop the neccessary insightor understanding by their own activities as much as possible, and that the role of the teachershould be a mentor of this process providing a stimulating climate. Besides, this routine isa way to rise the attention of the students and thus is a medium to concentrate their activitiesin the 'official' stream of events in the classroom which is useful for keeping up discipline.

As already said the question of the teacher is ambiguous; one can make other or additionalassumptions. Bertram does so. He assumes that every secondary school graduate will takeup a study (line 9). It is quite possible to make this assumption even though it is neitherneccessary nor sufficient. Christof (line 8) makes another suggestion that seems to indicatethe representativity although his first formulation (lines 4-5) could have another meaning too.

What the students do is to use the routine of 'trial and error': Quickly they test differentmeanings in order to find out the teacher's expectation. Apparently they think - probablybecause of their experiences - that it is self-discriminating to keep silent in such situationsor to ask the teacher to specify his intention because this is considered a lack of competence.There is another presumption with regard to the behavoiur of the teacher: the confidencethat the teacher will clarify later on what he or she is aiming at. Therefore the students seetheir answers as preliminary offers they are not really accountable for. This can be reconstrutedexplicitly in other scenes when students by laughing or joking indicate that their suggestionsare not to be taken seriously. An important function of the routine of 'trial and error' forthe interaction is that it makes the interaction going on easily.

In line 15 another teacher routine can be reconstructed. The teacher reacts on Bertram(as Emma starts her contribution during Bertram's utterance and cuts it off by herself the

INTERACTIONAL ROUTINES IN THE CLASSROOM 381

teacher rather refers to him than to her). Apparently he does not want to discuss Bertram'ssuggestion any more. Having the representativity of the sample in mind it is not worth furtherconsideration. He rejects it, not by explicitly saying that it distracts him from his aim butby postponing the argumenation.

This is an exampleof a teacher's routine called 'liberated evaluation of a student's answer'.On the one hand, this evaluation has a positive connotation: The teacher indicates that theanswer is okay in a way, at least he or she does not call it a wrong answer. On the otherhand there is a negative connotation: The answer does not meet the teacher's expectationand he or she refuses to accept it.

With the routine of the deliberated evaluation the teacher can eliminate roundabouts orside-tracks leaving it up to him to come back to them later on. With regard to the studentsthis routine he!lps them to keep up the impression of being relative competent - the answeris not really wrong after ale.

At the end of this utterance (lines 20-21, 23) the teacher uses another routine - the routineof the 'suggestive hint'. He gives a clue to the notion aimed at. In this example this clueis referring to the everyday knowledge of the students; he apparently assumes that they knowthe expression 'representative poll' and hence can find out the notion 'representative sample'.

The routine of the suggestive hint reduces the scope of possible answers. It permits theteacher to atta.in his objective within the period of time he or she has scheduled for withoutsimply giving the answer by him- or herself. Such a behaviour would come into conflict withthe popular demand not to tell students what they can find out by themselves.

Regarding the interaction between teacher and students, it turns out that the reconstructedroutines are related to each other. The ambiguous question at the beginning provokes the trial­and-error method on the part of the students: How should one really find an answer unlessby guessing when one has to or wants to answer but slhe is left in the dark about the objectiveof the question? On the other hand, trial-and-error bears the risk of getting far away fromthe original intention. Hence the teacher has to bring the students back to it - by postponingtheir deviant answers or by giving suggestive hints.

Scene 2

Further routines can be reconstructed in the following scene. It took place in a class ofgrade ten (students aged about 16). The parabola y = >! and its graph have been introduced,and then the parabola y = a(x-cl + d and its graph (compared with the graph of the firstit's shifted in the coordinate system and has a wider or narrower bow). The class repeatshow the graph is modified by a, c, d. The effects of factor a have been discussed already.

1 Teacher: well, which other modifications are still2 missing. Arthur.3 Arthur: well if ad, is put to it for instance'4 Teacher: well to say if a number is added what happens5 then'6 Arthur: then the vertex I mean the the the the7 origin8 Teacher: the parabola yes'9 Arthur: the parabola is simply shifted on the hori

10 on the vertical axis'11 Teacher: is shifted upwards or downwards yes'12 Arthur: and if the d is greater than zero then it is13 shifted upwards' if it is less than zero14 Teacher: yes'15 Arthur: it is shifted downwards.16 Teacher: right. and , there is a final modification-

382 H. JUNGWIRTH

The striking feature of the acting of the student is his relative taciturnity. Though theteacher asks about both modifications missing, Arthur only refers to the one done by d, andhe develops his answer turn by turn - alwaysonly indicating what he might mean. For examplein his first utterance (line 3) he only considers that d is added but does not name themathematical operation (addition) nor does he say anything about the effect. He uses theroutine of 'verbal reduction', that is he routinely does not say more than absolutely necessaryin the actual moment.

Using this routine, students can minimize the risk of showing a lack of knowledge orunderstanding. Its function for the students is to help them to present themselves as competentstudents. Hence this routine can be reconstructed especially in situations where students areexpected to know, as in lessons where solutions are repeated or drilled. With respect to thevis-a-vis in the interaction (the teacher) the use of this routine depends upon the presumptionthat the teacher in his or her mind will complete the fragments to a comprehensive answermeeting his or her expectations.

In this scene the teacher does not disappoint the presumption of the student. In his rephrases(lines 4, 8, 11) the teacher specifies what the student might have meant using a variation ofa routine called 'teacher's echo'. This is a way to mark the meaning that should be takenas shared.

By his questions and his signals confirming the fragmentary answers and requestingcontinuation (for the latter, see for example the 'yes' in line 8) the teacher elicits the missingaspects. The solving process is developed step by step. To do so is a specific form of anotherteacher's routine, the routine of 'decomposing of a solving process into small pieces ofsubsequent actions' (Voigt, 1989'b). In this example, first the factor a is discussed, then d (inscene 2), and finally c.

By this routine a problem, respectively talking about a problem, is decomposed in a sequenceof steps the teacher considers elementary enough for the students to note or to understand.The teacher apparently presumes that decomposing problems will help students to do so. Inhis or her view, this is a way to meet in particular the demand to facilitate learning for poorstudents. Besides, students are kept in tension and must be aware of being called upon overa longer time than in the case of solving the task in one step.

Like in the first example, the teacher's routine and the student's routine are related toeach other: When students give verbally reduced answers the teacher is compelled to elicitthe missing parts of the answer .- at least when she or he takes it for granted that teachinghas to run in this way. On the other hand, when a teacher decomposes problem solving intosmall pieces there is no neccessity for the students to give comprehensive answers; on thecontrary, they should relate only to the part just asked about - at least when this is consideredthe normal form of participating. And the student's routine of verbal reduction becomes evenmore plausible by the teacher's echo: Obviously fragments are sufficient. With both sides usingthese routines there is the impression of a smooth-running interaction.

Gender-related modifications of students' routines

The interaction in the mathematics classroom is managed routinely in the ways described.This does not mean that always all students contribute actively to the interaction process ­it may be, for example, that in a certain class of 20 students only about ten really interactwith the teacher, Le., they are called upon, they put up their hands a.s.o. Up to this I didnot indicate that the normal forms of interaction might be constituted by a specific groupof students (as for example, the especially gifted), nor by a specific group of teachers (theolder ones, the females, ...). With regard to the teachers, really no restrictions have to bemade; the use of the routines 'described above (and some more) has not been reconstructedto be increasing within (or limited to) specific groups of teachers. With regard to the students,however, it is a bit different. Studies about the mathematics classroom as well as the computer-

INTERACTIONAL ROUTINES IN THE CLASSROOM 383

aided classroom come to the conclusion that the routines presented are more routines of boysthan of girls (Jungwirth, 1990, 1991a, 1992a). Although there are long sequences in whichteachers and girls as well as boys act as described gender-related modifications of interactionsequences have been reconstructed indicating that it's the boys who are more familiar withthe practices constituting the normal interaction. Modifications established in the interactionbetween teacher and girls can be interpreted as deviations from the common course ofinteraction: The smooth running of the interaction is destructed or interrupted because theydo not use the routines they are expected to do. There are also modifications in the teacher­boys interaction but these only are variant forms, not established by doing without the routinesbut rather by developing and perfecting them.

All together, five types of gender-related modifications of interaction sequences have beenreconstructed. Directly related to the findings presented here are the following: Firstly, girlsdo not seem to be as familiar as boys with the trial-and-error method; the more ambiguousa question is the less girls participate in the interaction. Their favourite reaction on such questionsappears to be waiting and saying nothing. Secondly, the findings indicate that answering bythe routine of verbal reduction is more a routine of boys than of girls. In several episodesit has been reconstructed that girls use another method of acting: They give comprehensiveanswers, that is, answers in which they describe already all the main aspects of the treatedproblem. Thus there is no obligation for the teacher to elicit missing aspects by further questions.In spite of this the teacher does so (and thereby confirms problem-decomposing to be a routine).In the retrospective - with regard to the teacher's (re)actions - the comprehensive answerturns out to have been a 'too complete description' (Jungwirth, I991a).

A possible explanation for the girls' using their specific methods of acting is that theirpeer group routines get the upperhand. What girls learn to do with words in their girls' groups(Maltz & Borker, 1982) is rather a handicap for routinizing the participation methods requiredwhile boys' peer group routines are rather a good basis (Jungwirth, 1991b).

A further look on routines - Implicit obligations and interaction patterns

I would like to come back now to an aspect I have already mentioned in the discussionof the two sc:enes. I stated that in the routine case the teacher's and students' routines arerelated to each other. There are 'implicit obligations' (Voigt, 1984, 1989a, 1989b) within theroutines, obligations with respect to the acting of the fellow-participant in the interaction.For example, because of the teacher's ambiguous question the students are under obligationto offer suggestions by the trial-and-error method; or because of the student's fragmentaryanswers the teacher is under obligation to elicit the missing aspects. The matching of theirroutines leads to the impression that there is a smooth-running of the interaction withoutany problems of teacher and students to understand each other. Perhaps it is due to thisimpression that the routine practice presented here is so popular in the classrooms or, in otherwords, that this practice is the routine practice.

By the implicitobligations within the routinesa pattern of interaction develops. By focussingthe attention on the interaction between the participants instead of analysing the participants'methods of acting, regularities in the structure of the interaction can be reconstructed. Thismeans that in the routine case the interaction in the mathematics classroom is stronglystandardized.

Several patterns of interaction have been identified! (cf. the 'funnel pattern': Bauersfeld,1978, 1987; the 'pattern of the staged everyday reference': Voigt, 1984, 1989a). Belowthe patternis described that - partly - can be reconstructed in the two scenes.

The 'elicitation pattern' (Voigt, 1984, 1989&) is typical for lessonsin which new mathematicalconcepts, or algorithms a.s.o are introduced. It consists of three phases:

{(- Open task set by the teacher, first offers by the students, and prelimenary evaluationby the teacher

384 H. JUNGWIRTH

- Guided and standard development oj a defintite solution- Reflection of the method and oj the context» (Voigt, 1989b, p. 652)

In the first scene, the first phase of the elicitation pattern can be reconstructed. The secondscene presented here shows a structure similar to the second phase of the elicitation patternas a guided development of the answer of the teacher's question takes place.

By abstracting from the specificities of the patterns of interaction, a more general structureof the interaction can be reconstructed - the tripartite scheme: teacher's question - students'answer - teacher's evaluation of the answer (cf. Streeck, 1979). The overwhelming majorityof mathematics lessons at least in the German speaking countries shows this scheme.

Functions and consequences of the routines

In the final pharagraph, I take up the discussion of the functions of the routines in themathematics classroom and I ask about possible consequences for the learning of mathematics.

First of all, managing the classroom discourse routinely is nothing to be avoided. Asalready mentioned routines in general have positive functions - they relieve of permanentlymaking decisions, and permit settling one's affairs without questioning these processes. Withregard to interaction, from the interactionist point of view, the interactive function has tobe emphasized: routines make ;ID interaction reliable for all participants. This holds for allroutine situations. As for the classroom situation in specific, it is important that the routineshelp to cope with the fragility of the mutual understanding between teacher and students.For example, we do not know whether Arthur in scene 2 could solve the task by himselfin a way satisfying the teacher. But eventual differences in the task-solving between him andhis teacher that would complicate- the interaction do not emerge - the student-teacher teamworkprevents such a complication.

As can be seen from this example, teacher and students smooth away problems of mutualunderstanding; and such problems are - from the interactionist perspective - common asteacher and students construct their different subjective meanings and they respectively activatethe frameworks (cf. Goffman, 1974; Krummheuer, 1982) they are used to when interpretingthe whole task solving situation.

This coping with the fragility of the mutual understanding can be considered a positivefunction - imagine how stressing a classroom discourse would be in which the mutualunderstanding is always at the risk of breaking down. The evaluation becomes yet more positiveif it is taken into account that the routine interaction is a way to meet common pedagogicaldemands, for example to provide a 'discovering' learning, or to let the students take muchshare in the classroom discourse, under the conditions of the regular school system.

On the other hand, studies indicate (cf. Bauersfeld, 1982; Krause & Reiners-Logothetidou,1981) that the common mathematics teaching has consequences for the learning of mathematicswhich surely are not welcome. Students can participate successfully in the routine classroomdiscourse without having gained the knowledge or the understanding they have been expectedto, and without developing the insights aimed at by the teacher. Only in tests misunderstanding,or failures would emerge. See for example Arthur in Scene 2: He appears to be competent,yet it is quite possible that he could not write down the whole solution for his own neitherbefore this dialogue started nor afterwards. The routine interaction is suspected of preventingthe attainment of important goals of teaching mathematics, in particular goals as the solvingof problems of higher cognitive complexity.

In view of this problematic: consequence of the routine interaction the question foralternative classroom practices might arise. Group working of the students seems to be a verypromising approach (Yackel, Cobb & Wood, 1992); which clearly does not mean that aroutinization of group working with negative by-effects is impossible. Learning processes,however, cannot be done without any teacher-student interaction. Hence the way they interact

INTERACTIONAL ROUTINES IN THE CLASSROOM 385

should change too - presumably towards expliciting much more what is going on in a situation:For example a teacher could urge the students to give comprehensive answers and argue whythis is important in the actual situation. I don't want to conceal that inducing changes likethis is an ambitious project: It has to be taken into account that the routine practice describedhere is a 'relative optimum' (Voigt, 1984) that tries to master dilemmata in teaching andsimultaneously minimizes potential conflicts. And besides, changing routines is never easy.

Notes

These routines have been reconstructed already by Voigt (1984), and in the computer-aided classroom too (cf. Jungwirth,1992a, 1992b); besides, studies indicate that they can be found in other subjects too (cf. Grell/Grell, 1983; Redder, 1982)

2 Of course more direct rejections of unwelcome contributions of students have been reconstructed too (see for examplethe routine of 'rejecting an answer by appealing to the plausibility of doing so', Voigt, 1984, or 'the authoritativeinsistence on the desired answer', Jungwirth, 1991a).

In the reality of the classroom they cannot be reconstructed always in the same distinctness.

References

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Appendix

Rules for Transcription

(a sec p)very short pause (max. 1 sec)pause lasting a secondslowering the voicemaintaining the pitch

exactexact(one?)(laughter)t, LA:B:

INTERACTIONAL ROUTINES IN THE CLASSROOM

raising the voiceemphasizingdrawlinginarticulate; supposed wordingcharacterizing environmental events and processesraising the hand, putting down the hand

let ubs begin t 1 B partly speaks simultaneously with Aut we wan j

387

Key words: Teachers' routines, Students' routines, Analysis of classroom interaction.

Received' May 1993

Helga Jungwirth. Institut fur Mathematik, Johannes Kepler Univesitat, A-4040 Linz - Auhof, Austria.

Current themes of research:

Adults' perspectives on mathematics, Adults' learning of mathematics, Foundations of the research on women andmathematics.

Most relevant publications in the field of Educational Psychology:

Jungwirth, H. (1991). Interaction and gender - findings of microethnograpnical approach to classroom discourse.Educational Studies in Mathematics, 22, 263-284.

Jungwirth, H, (1992). Die Realitat des Computerunterrichts - Ergebnisse einer empirischen Untersuchung. In R. T.Mittermeir, E. Kofler, & A. Sternberg (Eds.), Informatik in der Schule - Informatik fur die Schute, (pp. 6()..72).Weimar: Bolau.