Teaching and Teacher Education 18 (2002) 715–737

Developing teaching knowledge through peer discourse

Azita Manouchehri*

Mathematics Department, Central Michigan University, Mount Pleasant, MI 48859, USA

Received 24 January 2001; received in revised form 8 June 2001; accepted 30 July 2001

Abstract

The central focus of the research reported here was to evaluate the usefulness of peer interaction on the development

of professional knowledge of prospective secondary mathematics teachers. Tracing the fate of two students involved in

a teamed field-based practicum experience over the course of 11 weeks, the findings of the research indicate that the use

of peer collaboration and collaborative reflection has the potential to facilitate teacher development. Peers helped

problematize learning issues, teaching actions, and mathematics for one another. Their level of reflection increased in

the process. r 2002 Elsevier Science Ltd. All rights reserved.

Keywords: Pre-service teacher education; Secondary education; Mathematics teachers; Teacher collaboration; Teacher reflection

In recent years, the utility of reflective practiceas a means to facilitate teachers’ growth inprofessional knowledge has been explored by anumber of educational scholars (Schon, 1987;LaBosky, 1994; Louden, 1991; Noffke & Brennan,1991). Several researchers suggest that teachers’engagement in intentional efforts to think abouttheir experiences provides them opportunities tohighlight important actions and consequences andthus creates cognitive change in both their beliefsand practices (Barnett, 1991; Thompson &Thompson, 1996). This view guides the practicefor many innovative teacher education programs.Indeed, developing teachers as reflective practi-tioners defines the predominant mission of currentreform in teacher education (Darling-Hammond,1994).

In spite of widespread agreement on the value ofreflection for the development of professionalknowledge, a significant limitation of reflectiveteaching, as it is conceived today, is its groundingin the idea that the individual learns to reflect on aparticular experience individually. The primaryemphasis in the research and practice of reflectiveteacher education has been on how individuals‘‘make sense of the phenomena of experiences thatpuzzle or perplex them’’ (Grimmett, McKinnon,Erickson, & Ricken, 1990, p. 20). This emphasisfails to address the importance of socialization andsocial interaction in the development of profes-sional knowledge. In a general sense, reflectivepractice methodology builds around two primaryassumptions: (1) the teacher comes to realize aneed to reflect; (2) the teacher knows how toengage in critical reflection. Findings from recentresearch on teachers, however, indicate that thesetwo elements may not be present in teachers’ work(Manouchehri, 2001; Manouchehri & Goodman,

*Tel.: +1-989-774-3639; fax: +1-989-774-2414.

E-mail address: azita.m@cmich.edu (A. Manouchehri).

0742-051X/02/$ - see front matter r 2002 Elsevier Science Ltd. All rights reserved.

PII: S 0 7 4 2 - 0 5 1 X ( 0 2 ) 0 0 0 3 0 - 6

2000). There is a need to explore alternativeapproaches for helping teachers develop thedisposition to use reflection as a vehicle to improveteaching. Investigating the role of peer discourseand collaborative reflection on the development ofprofessional knowledge was the goal of theresearch reported here.

The purpose of this research was twofold. First,I intended to investigate the content of profes-sional discussions between two prospective sec-ondary mathematics teachers, as they wereinvolved in a field-based experience. Second, mygoal was to study the impact of these interactionson ways in which they analyzed teaching andlearning issues. The intent was to see whether bydesigning situations in which the students wereexpected and encouraged to discuss practice, theywould engage in more critical reflection onprofessional matters. In order to facilitate theparticipants’ interactions, two components wereadded to their practicum requirements. They wereasked to observe classrooms as a team and todiscuss their observations with one another duringformal discussion sessions. In addition they wereasked to observe one another’s teaching. Follow-ing each observation period, they provided feed-back on each other’s practice, and shared ideas forimproving their teaching.

1. Theoretical grounding

The purpose of this research was to determinethe ways in which peer interaction might con-tribute to developing meaning, action, and reflec-tive analysis related to teaching mathematics. Thisworks derives from a constructivist view ofthought and learning. On the one hand, theresearch is influenced by Piaget’s theory ofequilibration, cognitive conflict, and the impor-tance placed on peer interaction (Piaget, 1964). Onthe other hand, it has been guided by Vygotsky’sview of the importance of learning within thecontext of social interaction and the crucial natureof human discourse (Vygotsky, 1978; Cole, 1996;Almasi, 1995). The goal was to focus on the issueof how interaction and self-construction relate toone another.

Social constructivism provides a useful frame-work for understanding the individual and howthe individual acts in a certain way. As Vygotskyexplained, a person’s meaning and actions aresocial/cultural constructions and it follows that wecan only understand the individual within thecontext of social relations in which the individualexists (Wertsch, 1986). According to social con-structivist theory, successful members of a societymust know and understand the established moralorders and specific rules, as well as the rights andresponsibilities that the social system establishesand reinforces (Harre & Gillett, 1994). For theadoption of a public meaning of professionalknowledge to be viable and to be advantageous tothe individual, it must be a product of socialinteraction and understanding.

This perspective is particularly important ineducational settings. Because fellow students sharecommon experiences and a social unit or structure,processes and constructs of education have acommon sense character. In the Bruner (1990)view, students share a common folk psychology-anethno psychology, which is ‘‘a culture’s account ofwhat makes human beings tick’’ (p. 15). Brunerexplains that educational institutions enforce folkpsychology and that culture shapes people to itsrequirements. Therefore, what individuals valueabout an experience, their common sense of it, isdirectly related to and in fact dependent upon setcultural norms. These norms are established out-side of the individual with the individual’scooperation, if not support. The shaping is doneinteractively in situ as a person enters a historicallydeveloped and established culture and furthershapes it through personal influence. Individualsdo not merely learn the rules of their culture or thenorms of the community. They also learn certainattitudes, practices, and performances that work inpractical ways that hold personal rewards, andthey learn which practices and attitudes are notviable. They learn which attitudes and forms ofparticipation are intellectually safe and which onesare not (Guzzetti & Williams, 1996). Entering anyeducational setting is to enter a culture whichholds and maintains its own normative structures,all of which form and enforce common sense. Tobe a successful member of a society, a person needs

A. Manouchehri / Teaching and Teacher Education 18 (2002) 715–737716

to understand and gain access to social norms andsocial constructs that work within that society.Because individual sense making, or the formationof meaning, is intrinsically, inevitably, and pro-foundly social, each individual comes to knowwhat it means to hold a certain role in thecontext of social interactions. Although eachindividual brings her own constructs and meaningsto the situation, the situation in turn interactivelyinfluences the making of meaning and sets thestandard for cultural competence. Therefore,epistemic access, or beginning to understand inthe discipline, is socially derived (Danziger, 1990).

In light of this framework, I assume that futureteachers learn about the cultural norms of theprofession through dialogue and interaction withtheir colleagues and peers. Moreover, these inter-actions help them establish what is worthwhileknowledge and what is valued for practice. I argue,based on the perspective of social constructivisttheory, that by promoting communications amongthe pre-service teachers, and by orchestratingsituations in which they are motivated to exchangeideas, articulate their thinking, and attempt tounderstand the peer’s perspective, teacher educa-tors can help prospective teachers develop thecapacity to take on new perspectives and build newunderstanding about the profession. The researchwas designed to identify aspects of the students’thinking that were directly influenced by suchinteractions. The following questions focused theinvestigation:

1. How does peer collaborative reflection impacteach individual participant?

2. How do peers contribute to one another’sdevelopment of professional knowledge?

2. Methodology

I adopted a case study design for this investiga-tion (Glaser, 1978). My purpose was to gatherinformation about the participants and theirinteractions with one another. The data comefrom the study of two students, Rosha and Tina,who were engaged in a practicum experience.

While doing their field-based work they were alsoenrolled in a mathematics methods course Itaught.

This particular practicum experience is sched-uled at the end of the prospective teachers’program of study. A majority of the studentsenrolled in this practicum have either completedtheir methods course, or take it concurrent to thisexperience. This practicum requires the teachercandidates to work with high school teachers for aperiod of 11 weeks. They are expected to spend 2 heach morning, three mornings a week in theirrespective classrooms. This allows them to observeat least one instructional period a day since someof the schools in which they are placed followblock scheduling.1 During this field-based experi-ence they are required to teach five lessons. Thetimeline for implementing these lessons is generallyplanned by the cooperating teacher. It is alsoassumed that the pre-service teachers performnon-instructional duties and/or work with stu-dents needing individualized tutoring as assignedby their cooperating teachers. The universitysupervisor evaluates the progress of the studentsduring the practicum experience, assesses theirlessons, and observes them once or twice duringthe semester in their classrooms. This supervisionis often times constrained as the same individualworks with 20–25 students at a time. This heavyload of supervision makes it difficult for thesupervising faculty/staff to monitor the growth ofthe students in a systematic manner or toencourage critical reflection of their field experi-ence. The students also attend a weekly, hour-longseminar on campus that is led by the universitysupervisor. Once they complete this practicumthey enter their student teaching phase the follow-ing semester.

Rosha and Tina were two of the five studentstaking my course while completing this practicum.After negotiating with their cooperating teachersand the university faculty who supervised them, Imodified their practicum expectations to meet the

1Block scheduling, also called ‘‘semestering’’, is a restructur-

ing of the school day into fewer and longer classes, typically

four 90-min periods per day instead of the usual seven 50-min

periods.

A. Manouchehri / Teaching and Teacher Education 18 (2002) 715–737 717

research design. Rather than spending threemornings a week in the school, they were assignedto be there two mornings a week for 4 h each day.This new arrangement allowed them to observe anAlgebra I and a Geometry class each morning.

I divided the 11 weeks of practicum experienceinto three parts. During the first 3 weeks, Roshaand Tina maintained the regular routine ofobserving the cooperating teacher to whom theywere assigned. They assumed only some non-instructional responsibilities such as gradinghomework and tests. I requested that Rosha andTina be relieved of non-instructional duties thatrequired them to leave their classrooms. They werealso assigned to tutor individual students, conductclinical interviews with specific students, or toperform diagnostic tests.

During weeks 4–7, I asked Rosha and Tina toobserve their cooperating teachers as a team. Theyspent one morning a week in each others’ class-rooms and observed the cooperating teacher’sinstruction together. Following each team obser-vation episode, I required that they hold adiscussion session about the teaching episodesthey observed, to analyze the content of the lessonand the children’s reactions to it.

During weeks 8–11, Rosha and Tina were askedto observe each other’s teaching as they taughttheir lessons (once a week). Following eachobservation period, they met formally to provideone another feedback on what they had observed,and to share suggestions for improving the lesson.

2.1. Participants

I purposefully selected Rosha and Tina for thecurrent study. This was for several reasons. Theywere both placed in the same school during theirpracticum. This physical proximity allowed me todesign and implement this study, which includedorganizing their classroom visits and post-obser-vation meetings.

Rosha and Tina were completing their under-graduate degree in Secondary Mathematics Edu-cation. They were of the same age and of similarsocio-economic backgrounds. They both hadcompleted all subject matter requirements andwere completing the final year of their under-

graduate course work. Moreover, they had takenone course in learning theories together during theprevious year. Thus, they knew each other. Iimagined that this personal history could facilitatetheir communication throughout the data collec-tion phase. Once I approached Rosha and Tinaabout participating in the study they both ex-pressed a desire to be a part of the research. Theywere willing to complete the extra assignments andto comply with the new arrangements I imposedon their practicum experience.

Although Rosha’s and Tina’s backgroundsdistinguished them as appropriate candidates forthis study, there were other reasons that contrib-uted to their selection. Both students were placedin classrooms in which no innovative instructionwas taking place. Their cooperating teachers had atraditional approach to teaching. I was familiarwith both teachers. They had worked with two ofmy students in the previous semester. Neither ofthe teachers followed an instructional routinecompatible with the attitudes and goals I pro-moted in my methods course. I was also aware thatneither one of the cooperating teachers assumedmuch responsibility for educating the practicumstudents they were assigned; they did not providethem with feedback on the lessons they taught. Forinstance, although the practicum experience re-quired the teachers to hold a meeting with the pre-service teacher at the end of each week to discussteaching issues, neither one of the teachers haddone so in the previous semester. This had beenproblematic in the past because my students feltinconsistencies between my expectations and thoseof the cooperating teachers.

Although on a theoretical level it is agreed thatthe use of such examples in the course ofpreparation of future teachers is neither usefulnor desirable, in reality this is not a rare practice inteacher education. Two reasons contribute to suchselection. First, the number of classrooms in whichreform-based practice takes place is rare. Oftentimes the placement decisions are made basedupon availability of classrooms rather than acareful selection of cooperating teachers. Thishas been a dilemma in teacher education programsfor quite some time and is likely to remain as aweakness in teacher education. Second, it is

A. Manouchehri / Teaching and Teacher Education 18 (2002) 715–737718

assumed that by teaming pre-service teachers withless innovative teachers, teacher education willhave an opportunity to facilitate the continuedgrowth of practicing teachers. This is particularlytrue when Professional Development Schools areused as practicum sites for pre-service teachers(Goodlad, 1990). Both reasons applied to thecurrent practicum.

I envisioned that by creating a teaming ap-proach to their practicum experience I could alsoinvestigate the usefulness of this strategy onincreasing the future teachers’ capacity for reflec-tive practice even in the absence of adequate rolemodels.

2.2. Data collection

Table 1 summarizes the data collection scheduleand procedure. Activities are described below.

Initial data (weeks 1–3): In order to obtain baseline data on each participant’s style, approach,depth and quality of reflecting on teaching, I askedeach one to stay in her assigned placement and tosubmit reflective journals on her observations.Writing a reflective journal was not an unfamiliartask to them as they had been asked to do so intheir previous education coursework. The practi-cum supervisor also required these journals fromthem. I did not impose any particular structure onthe journals. This was done for two reasons. Onthe one hand, it was my intention to develop aprofile of each participant and their foci ofattention relative to instruction. Moreover, Iwanted to obtain data on the manner in whichthey analyzed and reflected on classroom interac-tions they observed. This base line data wouldallow me to trace any changes in their tendenciesand orientations over time as the result of the peerteaming process used in this research. Eachparticipant submitted six journals during thisperiod.

Teamed observations and follow up discussion

(weeks 4–7): During these 4 weeks, each Mondaymorning Rosha and Tina observed Tina’s coop-erating teacher and on each Wednesday, theyobserved Rosha’s cooperating teacher’s instruc-tion. Following each observation period, they metto discuss what they had observed. I instructed

Rosha and Tina to be open in expressing theirthoughts about the sessions they observed. Ireassured them that they could be critical in theiranalysis but I required that during their discus-sions they must go beyond criticizing the teacheror the students and should focus on analyzingaspects of classroom interaction that appearedproblematic to them. Both the sessions and thepost-observation discussion sessions were video-taped, and submitted to me at the end of eachweek. In addition, I participated in two of thesesessions on site. My field notes were used asadditional data sources. I also reviewed and codedthe videotapes of all other sessions during which Iwas not present.

Peer observations (weeks 8–11): During weeks8–11, Rosha and Tina observed each other’sinstruction once a week as they taught theirlessons. Following each observation session, theymet to provide one another with feedback on theirlessons and instruction.

I asked that the post-observation discussion bestructured to first provide a 10–15min individualreflection time for the person who was observed.The remaining 45min had a looser structure andwas intended to grant them an opportunity toexchange ideas on the teaching episode as well asto offer suggestions for improving instruction.This was done for one major reason. In order tomake any claims to the usefulness, or lack ofusefulness of peer observation/feedback on peerpractice, it was critical to collect data thatcaptured individual reflection by each participantabout her teaching episode. Any changes in thequality of reflection of each one then could beattributed to her exposure to the peer.

In addition to videotaping both the teachingepisode and the post-observation discussions, Iasked Rosha and Tina to write a formal journal inwhich they elaborated on ways in which thesediscussions impacted their subsequent planning. Irequired this written assignment in order to allowthem an opportunity to further consider theirdiscussions and to plan their subsequent instruc-tion in light of the suggestions they had receivedfrom one another. The written assignment, alongwith videotapes was submitted to me at the end ofeach week. I attended a total of four of the eight

A. Manouchehri / Teaching and Teacher Education 18 (2002) 715–737 719

peer observation episodes and their discussionmeetings. I reviewed and coded the videotapes ofthe sessions during which I was not present.

During the sessions when I attended theparticipants’ on-site meetings at phases I and IIof data collection, I took on the role of aparticipant observer (Glaser, 1978). I remainedsilent and only listened to Tina and Rosha’sdiscussions during the first half of their session. Idid this so as not to influence the natural course oftheir interactions. During the second half of eachsession I became more of a participant in their

dialogues, frequently asking questions such as:‘‘What if this were not the case? How would youact differently?’’ ‘‘How do you know they under-stood the lesson? What evidence do you have?’’‘‘How would you convince someone else that yourassumptions are valid?’’ ‘‘What research supportsyour position on this issue?’’ I posed thesequestions with the intent to create dissonance intheir thinking and motivate them to dig deeperwhen talking about practice. At times, I offeredmy point of view on children’s work and activitiesin class, or suggested additional sources they could

Table 1

Data collection schedule

September

(initial data)

October (teamed

observations)

November (peer

observations)

December (peer

observations)

WK1 1st teamed observation

and reflection

1st peer observation

and discussion

4th peer observation

and discussion

Mon—Rosha’s class

(discussion session)

Mon—Rosha’s lesson

(discussion session)

Mon—Rosha’s class

(discussion session)

Wed—Tina’s class

(discussion session)

Wed—Tina’s lesson

(discussion session)

Wed—Tina’s class

(discussion session)

WK2 Base line data

individual

reflection

2nd teamed observation

and reflection

2nd peer observation

and discussion

Back on Campus Final

Journal

Mon—Rosha’s class

(discussion session)

Mon—Rosha’s class

(discussion session)

Wed—Tina’s class

(discussion session)

Wed—Tina’s class

(discussion session)

Researcher present on

both days

Researcher present on

both days

WK3 Base line data

individual

reflection

3rd teamed observation

and reflection

School out

Mon—Rosha’s class

(discussion session)

Wed—Tina’s class

(discussion session)

WK4 Base line data

individual

reflection

4th teamed observation

and reflection

3rd peer observation

and discussion

Mon—Rosha’s class

(discussion session)

Mon—Rosha’s class

(discussion session)

Wed—Tina’s class

(discussion session)

Wed—Tina’s class

(discussion session)

Researcher present on

both days

Researcher present on

both days

A. Manouchehri / Teaching and Teacher Education 18 (2002) 715–737720

use when teaching certain mathematical topics. Inaddition, I answered their questions about themathematical accuracy of a lesson or the develop-mental trajectory of curriculum and learners.These interventions did not conflict with the goalsof the research. Moreover, these interventionsmatched my teaching behaviors while teachingthe methods course. Thus, Tina and Rosha werenot the only students who were exposed to such a‘‘confronting-supporting’’ style of interaction.

2.3. Data analysis

Data analysis began with a review of thereflective journals Rosha and Tina submitted tome during the first 3 weeks of their practicumexperience. The content of their journals wasexamined in order to determine their predominantfoci of attention as they talked about theirobservations and ways in which they evaluatedthe teaching and learning that took place in theirrespective classrooms. These initial categories werematched against those that appeared later in thecourse of the data collection phase.

Fuller and Bown (1975) described the transitionto pedagogical reasoning as going through fourstages: teaching concerns, self-concerns, task con-cerns, and pupil concerns. The authors suggestedthat teachers will not develop concerns aboutstudent understanding until they resolve concernsabout their own survival and teaching situation. Inlight of the stages identified by Fuller and Bown, Ibegan the first round of coding by identifying fivedimensions of the experience on which they couldpotentially focus in their journals and during theirdiscussions. These included: concerns about self,concerns about curriculum, and concerns aboutstudent learning. Due to the nature of theirpracticum placement I had anticipated that con-cerns about the instruction they observed (tea-cher’s actions and management issues) might arise.Therefore, these two items were also added to thelist. I had hypothesized that the teaming processwould also result in explicit mathematical discus-sions among the participants. Thus, ‘‘concernsabout mathematics content’’ was also added. Ifeach of the participants addressed issues that didnot fit within any of these categories, I added new

items to the list and continued this procedure untilan exhaustive list of issues was generated. In placeswhere an issue could be classified under more thanone category, I counted it once in each of thecategories. As the data collection progressed, Imaintained a summary of those issues mostfrequently cited by each of the participants intheir journals or during their peer discussions. Inthis way I was able to trace any changes in thecontent of their reflections from beginning to endof the study. Table 2 presents these categoriesalong with examples of descriptors I used toclassify the participants’ remarks.

In addition to categorizing the participants’journals according to their foci of attention, alayers of reflective discourse model (Manouchehri,2001) was used to complete a second level ofcoding of the participants’ journals (see Table 3).The model distinguishes five levels of reflection as:Describing, Explaining, Theorizing, Confronting,and Restructuring. At the lowest level of reflection,Describing, the individual offers a descriptiveaccount of an experience. The intent at this phaseis to provide descriptive information about anevent. This is the ‘‘story telling’’ phase as thereflector is not engaged in the act of reflecting withthe intention of analyzing the various pieces ofthe event. At this level, the reflector describes theevents of the classroom as separate entities. At thesecond level of reflection, Explaining, the indivi-dual attempts to offer an initial assessment of how,in her perspective, various events are connected.The individual identifies and discusses the causalfactors in the course of an interaction. Here, forinstance, an identification of specific teacheractions that led to particular student reactiontakes place. Though the individual acknowledgesthe existence of a problem, this acknowledgementis not supplemented by a description of how onecan analyze the event or further study the problem.At the third level of reflection, Theorizing, theindividual’s explanation is substantiated by rea-soning from data. The reflector refers to what sheknows from research, from experience, or fromprevious coursework to justify her explanation.The Confronting stage is where the individualquestions the validity of her analysis and seeksalternative ways of assessing an event. The person

A. Manouchehri / Teaching and Teacher Education 18 (2002) 715–737 721

asks if there are other points of view, other factorsthat need to be considered when reviewing theproblem, or planning a solution method. At thehighest lever of reflection, Restructuring, theindividual revisits the event and/or the problem

in its entirety and attempts to offer a strategy forresolving the tension identified earlier. Here, theindividual’s attention is sharply focused on re-designing the experience to avoid the problem inthe future.

Table 2

Foci of discussion

Foci of attention Descriptors

Self I don’t know if I can handle this

I think I can do a better job here

How should I deal with it when I have my own class?

Mathematics I am not sure about what she taught

I had not seen geometry since high school

What does this problem mean?

Why is this assignment here?

Learners’ actions and understandings How can I help her understand?

They all missed questions—on the test

Why don’t they know it?

They did not do homework

They just looked at the teacher and did not even ask questions when I knew they did

not really understand it

Activity/task It was a fun thing to do

It was long and boring

I am not going to use this activity

Management/control They were not at all on task

She kept sending them to the principal’s office

Curriculum What comes after this chapter?

Do they really need to know this now?

Teacher’s actions Lesson sequence

Mode of representation

Interactions with children

Responses to the children

Concept development

Learners’ backgrounds They don’t even know their facts

Are they expected to know this?

What have they seen?

Aren’t they supposed to know their fractions by now?

Assignments Too many homework assignments

Test was long

The assignments are not appropriate

School culture Faculty/staff relationship

Class size

A. Manouchehri / Teaching and Teacher Education 18 (2002) 715–737722

These categories allowed me to establish aprofile of each of the participants as it related tothe level of their reflection on classroom events atthe beginning of the study. The same model wasused to code the content of their discourse duringthe peer discussion sessions and other individualjournals they submitted throughout the entire datacollection phase.

The content of Rosha’s and Tina’s discussionsduring the remaining weeks (4–11) was analyzed todetermine dominant themes of discourse betweenthem. Analysis began with cataloging video-segments, and examining field notes to provideevidence related to the kinds of discussions thatthey had and the issues that were raised in thecourse of their meetings. Once cataloging wascompleted, I viewed the segments again to developmore complete tracing of each individual teacherand the nature of their interactions in eachsegment. Annotations about important contextualfactors such as actions and gestures were added inthe transcription process. After completing this

level of analysis I then tried to identify thosefactors that seemingly influenced Rosha’s andTina’s thinking and forced a higher level ofreflection on their part.

3. Findings

During the 11 weeks of data collection Roshaand Tina met on school site 16 times. During thesemeetings they discussed various professional mat-ters ranging from school culture to specific class-room events. These interactions directly influencedthe initial habits and conceptions they brought tothe experience and helped them modify their waysof talking about practice. The peer discussions alsoassisted the participants to develop a disposition toassess teaching and student learning in a criticalmanner. These discussions facilitated a shift intheir level of reflection, moving them fromdescribing-explaining, to a theorizing and restruc-turing phase. The participants’ attention shifted

Table 3

Layers of reflection

Level of reflection Description

Describing Story telling

Recall of classroom events

Explaining Connecting interrelated events

Exploring cause and effect issues related to teaching/learning actions

Theorizing An explanation of how one knows what she knows

References to research on learning and teaching

References to past experiences

References to past course work and reading

Confronting Search for finding alternative theories to explain events and actions

The individual challenges her own views and what she knows in the process of search

Is there another way of looking at this?

Is there another way of explaining this?

Did I do it right?

Am I right in my assumptions?

Restructuring Revisiting the event with the intent to re-organize teaching actions and/or curricular

choices

What can I do differently?

How can I do it differently?

What should I change?

What else should I do?

A. Manouchehri / Teaching and Teacher Education 18 (2002) 715–737 723

from assessing classroom events as isolated enti-ties, to viewing the learning environment as adynamic organism.

Tina and Rosha also forced one another toexamine their professional perspectives and stand-points in greater depth. They asked one another toelaborate on their thinking about teaching, tojustify decisions about how to work with studentsand plan lessons, and to substantiate their assess-ments with actual data or research. This motivatedboth teachers to seek relevant literature thataddressed aspects of learning and teaching whichconfused them. In essence it moved the directionof their discussion about professional issues from alocal and personalized level of analysis towards atheory-based discourse structure. Moreover, in thecourse of their practicum experience the partici-pants investigated both mathematics content andthe strategies useful for teaching the subject. Inwhat follows I elaborate on these findings.

3.1. Initial data

Each of the participants brought a distinctstrength and orientation to their practicum. Thesedistinct characteristics became significant in estab-lishing benchmarks not only in their initialapproaches to analyzing teaching/learning pro-cesses but also in tracing their developing perspec-tives and knowledge base in the course of thestudy.

During the first 3 weeks of the data collection Iasked Tina and Rosha to submit journals on theirschool experiences. Table 4 summarizes thenumber of times various topics were addressedby each of them. In their journals Rosha and Tinadescribed the daily events of the sessions they hadobserved. They talked about the rituals of eachclassroom. They described the sequence of instruc-tion, how each session began, the activitiesteachers assigned in class and the amount of timethat the teacher devoted to each part of her lesson.Tina and Rosha also talked about their encounterswith other mathematics faculty, the culture of theschool, and ways in which teaching responsibilitieswere shared by the staff. They also listed the taskstheir cooperating teachers assigned and theamount of time it took to complete these tasks.

In their journals, both Rosha and Tina com-pared and contrasted their current experience withthe previous practicum. Statements such as ‘‘Ms.K was much more student centered than Ms. J’’,or, ‘‘kids did more group activities’’ were cited atleast once in each of their journal entries by bothRosha and Tina. They identified what they liked ordisliked about their placement, the managementstyle of each teacher, the way teachers sequencedtheir lessons, and the styles in which they dealtwith students’ lack of participation in classactivities. Both Tina and Rosha commented onhow the teachers handled homework assignments,dealt with students who did not turn in dailyhomework, and monitored group activities.

Tina and Rosha also talked about the range ofsocial and mathematical behaviors and skillslearners brought into the classes they observed.They both expressed concerns about their ownability to deal with difficulties such as ‘‘students’lack of participation in class’’, ‘‘students not doinghomework’’, ‘‘controlling the disruptive students’’,and ‘‘pacing and coverage’’ issues. They madereferences to the mathematical topics each teachertaught along with the skills level of the students asthese specific concepts were discussed in class.They offered an account of what the learnersseemed to know, as well as what they were notcapable of doing, and speculated on the knowledgethe students needed to master the new concepts.

Despite the fact that Tina and Rosha addressedsimilar issues in their journals, the frequency atwhich topics were addressed by them was differ-ent. Tina frequently raised concerns about self(n ¼ 13), management (n ¼ 14), and learners’background knowledge (n ¼ 12). Rosha statedconcerns about teacher’s actions (n ¼ 20), waysin which mathematics was communicated andexplained to students (n ¼ 10), the nature of tasksstudents completed (n ¼ 21), and learners’ under-standing and actions (n ¼ 15).

Rosha and Tina exhibited different levels ofreflective thinking as well. Table 5 summarizes thelevel of reflection that each participant exhibitedon the six journals they submitted during the first 3weeks of practicum. Tina’s level of reflection wasmostly at the describing phase and in only two ofher journals did she reach the explaining phase.

A. Manouchehri / Teaching and Teacher Education 18 (2002) 715–737724

Table 4

Foci of attention

Foci of attention Descriptors Tina Rosha

Self I don’t know if I can handle this 13 5

I think I can do a better job here

With all the grading I have to do I am not sure I can do

much planning

How should I deal with it when I have my own class?

I had not seen geometry since high school

Mathematics I am not sure about what she taught 1 10

She did not really tell them why

This problem does not really address the content well

I was not sure what she was getting with that explanation

Learners’ actions and understandings Why don’t they know it? 7 15

They all missed questions—on the test

They did not do homework

They just looked at the teacher and did not even ask

questions when I knew they did not really understand it

How can I help her understand?

Activity/task It was a fun thing to do 8 11

It was long and boring

I am not going to use this activity

Management/control 14 6

Curriculum What comes after this chapter? 6 12

Do they really need to know this now?

Teacher’s actions Lesson sequence 9 20

Mode of representation

Interactions with children

Responses to the children

Concept development

She could have used the graphing calculators to do the

transformations

Learners’ backgrounds They don’t even know their facts 12 12

Are they expected to know this?

What have they seen?

Aren’t they supposed to know their fractions by now?

Assignments Too many homework assignments 5 10

Test was long

The assignments are not appropriate

School culture Faculty/staff relationship 3 4

Class size

Note that there may have been multiple references to various categories in each of the journals. Each of those references was counted

once to compute the frequency of references for each participant.

A. Manouchehri / Teaching and Teacher Education 18 (2002) 715–737 725

Rosha not only described and explained the eventsshe observed, but also theorized about them.

3.2. Rosha

Rosha began to identify the philosophicaldifferences she detected between her own way ofthinking about teaching and her cooperatingteacher’s actions early in her practicum. Shecommented on aspects of her teacher’s choicesthat she disliked. She questioned the appropriate-ness of the methods the teacher used to disciplinestudents, manage her classroom, and monitorstudent progress. Rosha criticized that the teacher‘‘lectured kids all the time’’. She complained thatthe ‘‘kids only did worksheets’’, and many of themseemed lost. She expressed concerns about howmathematics was presented to children and thetypes of tasks they were assigned. She felt theteacher did not provide opportunities for childrento work on ‘‘worthwhile’’ mathematical problemsand failed to help children make connectionsamong the various topics they studied. In herjournals she elaborated on things she would dodifferently. In essence, the journals provided her achance to share her beliefs and those constructsthat defined her as a teacher. She shared her visionof ideal teaching and proposed ways in which shehoped to meet these visions.

She lectures all the time. The kids seem lost anduninterested. Some of them just play. Sheignores them most of the time, like she doesnot want to deal with them. She just turnsaround and tells them to take notes or that theywon’t pass the test if they don’t listen. In myclass I will try and reach every kid. There is noreason for Danny to sit there and just playvideogames. Ms. J (Rosha’s cooperating tea-

cher) always asks Jason to answer questions orto come to the board to do homework assign-ments. Jason is always prepared but she is nottrying to get other kids involved, she never callson the quiet ones, kids like Danny are justignored. I know now how important it is to tryand call on all the kids, and try to involve all ofthem whether they volunteer or not. I will neverlet that happen in my class.

Rosha seemed confident about the conclusionsshe drew about her cooperating teacher’s inten-tions, knowledge base, and the influence sheexerted on class discussions. She made remarksabout what the teacher should do to address thechildren’s emotional and cognitive needs. How-ever, she never tried to solicit a different perspec-tive or ask if there were different ways of analyzingthe problems she identified.

3.3. Tina

In her journals, Tina seldom went beyonddescribing the daily classroom events she observed.Throughout the entire 3 weeks of individualobservation period she only provided a synopsisof the class activities, what she had done, and aclose account of what the teacher did in class. Thefollowing is typical of Tina’s journals during thefirst 3 weeks of data collection.

Today Ms. A (Tina’s cooperating teacher)started the class by putting a few warm upquestions on the board. She gave them 15minto do the problem. Then they moved to thehomework assignments. A few kids were havinga real hard time with three of the homeworkproblems. She did the problems on the boardand then asked them to turn in their homeworkand I graded them for her. Ms. A asked them to

Table 5

Level of reflection exhibited by each participant during the first 3 weeks of practicum

Participant Level of reflection

Journal 1 Journal 2 Journal 3 Journal 4 Journal 5 Journal 6

Rosha D/E D/E/T D/E D/E/T D/E/T D/E/T

Tina D D/E D/E D D D

A. Manouchehri / Teaching and Teacher Education 18 (2002) 715–737726

open their books to page 39. They read thedefinition for the slope and she showed them onthe picture that slope was rise over run and toldthem the order was very important.

Tina identified aspects of her cooperatingteacher’s practice that she liked and approved.However, she rarely explained ‘‘why’’ she likedthose strategies. In reviewing classroom events,Tina’s primary focus was on the teacher’s manage-ment style and ways in which she handleddisruptive students. She asked questions aboutresources she could use when teaching certaintopics and articulated concerns about her ability todeal with students who exhibited behavioral and/or learning difficulties. Although Tina raisedconcerns about what students seemed to be doingor not doing in class she did not explain in herjournals what she thought caused these problemsor how they might be addressed. She did notchallenge or question the teacher’s actions and herstyle of pedagogy. Neither did she associatestudent behaviors with teacher actions. It ap-peared as though Tina accepted her cooperatingteacher as the authority, someone that knew herstudents better than anyone else and madedecisions based on that personal knowledge. Thefollowing is typical of Tina’s journals in suchsituations.

Larry was asleep again. Ms. A went to his deskand just touched him on his shoulder. I likedhow she did this. 5min later though he wasasleep again. This happened at least 6 timestoday. Nothing she does seems to help this kid.When we talked after class Ms. A told me Larryis not going to pass this class. I mean how canhe pass when he is behind every one else? Ms. Athinks he can’t catch up now, it is so late in thesemester. To make the matters worse, this is thesecond time he is taking Algebra I. I know thisshould not surprise me. I am sure I will have alot of kids like him in my classes.

Tina’s journals during the third week of herobservations were brief. She was concerned aboutthe learners’ lack of basic skills and the difficultiesthis situation created for teachers.

3.4. Teamed observations

Peer interaction provided Tina and Roshalearning opportunities by encouraging them toexchange their viewpoints and by forcing them toelaborate on their personal perspectives andknowledge. Barnes and Todd (1977) describedthe value of collaborative dialogue as:

{Collaborative} moves are mutually supportive:by taking the trouble to elicit an opinion fromsomeone else, or by utilizing what has been saidby extending it further, the group membersascribe meaningfulness to one another’s at-tempts to make sense of the world. This helpsthem to continue, however, hesitantly, with theattempts to shape their own understanding bytalking (p. 36).

As Barnes and Todd articulated, the value ofcollaboration goes beyond that of resolving con-flicts that may arise when partners work to achieveconsensus. Learning opportunities are created inthe course of a commitment to communicate.When individuals attempt to make sense of eachother’s thinking they must extend their ownconceptual framework to try to construct aconsensual domain with their partner. Such wasthe case for the participants in this study.

Although Tina and Rosha were placed inclassrooms in which traditional teaching practiceswere taking place, only Rosha raised issues withthis type of practice. Also, only Rosha tried toassess students’ learning in the presence of variousteaching actions. Though her analysis was framedby constructs rooted in her own likes and dislikes,her interactions with Tina forced her to examineher ideas. This process was educational for Tina aswell. Although during the first 3 weeks of herpracticum experience little about classroom inter-actions seemed problematic to her, having beenconfronted with Rosha’s questions and the strongconvictions she held, Tina was pressed to talkmore about what she saw and heard in class. Inessence, the teamed observations provided themthe necessary platform to reconsider teaching/learning issues and engage each other in a higherlevel of reflective thinking. During the first week ofteamed observations Tina and Rosha’s discussions

A. Manouchehri / Teaching and Teacher Education 18 (2002) 715–737 727

centered around the organizational ritual of eachclass. During the second week they began toanalyze the two teaching approaches they saw, andthe students’ social and mathematical behaviorsand their performance relative to the curriculartopics they were taught by both cooperatingteachers. Tina and Rosha compared and con-trasted the two teachers, the two groups ofstudents, and the instructional sequence eachteacher used. In the process they explored class-room interactions in ways that neither one hadpreviously addressed in their journals either inscope or depth. In essence, the teamed observa-tions facilitated the development of their profes-sional knowledge by creating situations in whichteaching, learning, and mathematics content wasproblematized for them.

3.5. Problematizing instruction

Tina and Rosha came to identify and investigatecurricular and instructional issues in the course oftheir social interaction and as the result of theirwork with one another. They confronted eachother’s interpretations of what occurred in each ofthe classes they observed together and thusencouraged each other to elaborate on theirthinking, or to justify their view points.

Rosha began each discussion period by ques-tioning the way in which the cooperating teacher‘‘shared’’ mathematics with the students. Sheobjected that the teacher did not pose interestingquestions for student investigations. She attributedthe students’ lack of interest in the teachers’lessons precisely to such instructional routine.She asked Tina if she noticed the same problemand whether she agreed with her assessment.Although Tina initially maintained a non-evalua-tive approach to her experience, Rosha’s persis-tence on soliciting feedback from her forced her toreconsider her position. In contrast, Tina’s reluc-tance to abandon her own interpretation of whatthe teacher did or the reasons she chose to docertain things in class forced Rosha to reconsiderwhat she felt she knew and to search for theoriesthat supported her views.

The following excerpt illustrates this point. Thevignette comes from the second discussion session

during the second week of the teamed observationphase. The participants had spent that morning inTina’s class. Ms. A, Tina’s cooperating teacher,had taught a lesson on addition and subtraction ofintegers the day before. Ms. A. began herinstructional period by demonstrating severalexamples on the board, and stating the rules.The students then were assigned a worksheetconsisting of 30 exercises. They were asked tocomplete the handout in small groups. Following ahalf-hour of seat-work, Ms. A asked students tocome to the board and to share their solutions withthe whole group. She then proceeded withintroducing multiplication of signed numbers. Thissequence of instruction was the starting point ofTina and Rosha’s conversation in their follow upmeeting.

Rosha: Have you noticed that they don’t useapplication problems? I mean the kids just doworksheets and exercises. She did not even askthem if they could come up with some ideasabout where and when they might be dealingwith signed numbers.

Tina: But Ms. A uses a lot of word problems,the kids never do them though. Ms. A says it isbecause they can not read or that they don’twant to try them cause they think they are hard.

Rosha: Is it in your Geometry class or Algebra?Cause I think Geometry kids can handle it.Don’t you think? I mean don’t you think bothour Geometry kids are more, morey

Tina: I know what you mean. They are moreserious.

Rosha: Yeah, serious.

Tina: They are more advanced too. They don’tneed someone to tell them what to do all thetime.

Rosha: But even in her Geometry class she isnot doing problem solving and applications.They are not even using Sketchpad.2 I asked MsJ if she had seen Sketchpad and she said that

2GSP (Geometer’s sketchpad) is an interactive geometry

software I introduced to the participants in my methods course.

A. Manouchehri / Teaching and Teacher Education 18 (2002) 715–737728

she has taken a couple of workshops on it. Inmy Geometry class they only go over definitionsand then the kids do simple identification tasksor do work with compass and ruler. Either shejust does not care or she just does not knowabout all these new things she can do.

Tina: I guess she is thinking why do it if the kidsare not even interested in learning math.

Rosha: But why do you think they are notinterested in learning math? I mean whyshouldn’t they enjoy it?

Tina: ‘Cause, ‘cause math is not like othersubjects. There is a structure and they have tolearn the basic stuff before moving on to ahigher level. I mean it isn’t like reading. Youknow? In reading once you learn to read youcan just pick up any book and read what youlike. You can not do that in math.

Rosha: I think they don’t like math becausethey just sit and listen and do worksheets. Theynever do projects, they are not active, theynever do anything fun.

Tina: Ms. A says she does not know how to getthem to do problem solving when they can noteven add or subtract fractions.

Rosha: (silence) I don’t think you have to waitand not do any problem solving. I think theteacher should let them use calculators if theyneed them but they should learn to solve realproblems.

Tina: I don’t see how they will even learn thebasic skills if they keep using the calculators. Ithink the calculators have caused the problemin the first place. Some of my kids can not evenadd in their heads, they have to get thecalculator out and punch in the keys.

Rosha: I guess it means that you really have toknow when to start using the calculator. Imean, think about how to use it so it does notdamage them in the long run. The textbook hassome problem solving activities with graphingcalculator that I think the teachers should use. Iknow Ms. J does not use them, I noticed Ms. Askipped them too.

Tina: I did notice that too, but I thought maybeit was because she did not have time to do them,she usually assigns those as homework.

Rosha: Don’t you think it would be better to dothose activities in class so she could monitorwhat they are doing rather than giving them ashomework?

Tina: Why? I mean, why would you say that?

Rosha: ‘Cause most times in my class the wayshe checks homework is that she just puts theanswers on the overheads and asks them tocheck their answers. There is never a discussionunless one of the kids asks to see the solution.

Tina: I see. I think what you are saying makessense. I mean it would be better to assign thoseas small group activity.

At the end of the discussion period Tina andRosha agreed to pursue two issues in the followingweek. While Tina volunteered to find alternativestrategies for teaching operations on signednumbers and application contexts that could beused when teaching the topic, Rosha volunteeredto find articles that described how to use calcula-tors effectively in class. They shared their findingswith the rest of their peers in the methods courselater in the semester. The same result occurred onfive other occasions during the data collectionperiod. In fact, Rosh and Tina were the onlystudents in class that initiated such self-motivatedinquiry despite the fact that I had repeatedlyencouraged all class members to do so since themethods course commenced.

3.6. Problematizing student learning

The team observations also assisted Tina andRosha to identify specific problems associated withlearning mathematics. This was particularly influ-ential on what and how they talked about learner’smathematical understandings and misunderstand-ings, and what seemed to be hard for themto do. They speculated on particular instructionalactions that could help learners overcome thosedifficulties.

A. Manouchehri / Teaching and Teacher Education 18 (2002) 715–737 729

This point is illustrated in the following dialoguebetween Tina and Rosha. This discussion occurredfollowing their third teamed observation of Ms.A’s geometry class. During this session the teacherhad done a ‘‘guess my function activity’’ with thechildren. The children were given a worksheetconsisting of 10 problems. In each problem a tableof values was presented to them and they wereasked to find a function that generated the tabularvalues. Although almost all students were capableof completing the numerical pattern, the majorityof them failed to abstract the symbolic representa-tions of the relationship in each case. Both Tinaand Rosha recognized the difficulty as theyworked with individual students. In their post-observation discussion they addressed this issue.

Tina: These kids were asking the exact samequestions—I was thinking—you know? Whenthey got to the 20th row I thought to myself, allright, they got it. So they got the 20th row and itall fell apart. I looked at their papers and Ithink only 3 of them got it right.

Rosha: When I looked at their papers I noticedalmost all of them identified the rule, that youshould add 5 to the previous term. They evendid it for the first 20. Then there was the jumpfrom the 20th term to 200th term. Most of themused ratios to find the value of it. I had to thinkabout what they were doing. Then when I askedthem to tell me what the nth term was, all theysaid was that it changed. They did not call it avariabley They could not extend the pattern.

Tina: And you know this is Geometry! I meanthey do so much work with this guess myfunction stuff in Algebra I that you would thinkit would not be a problem. I mean they can tellyou the numerical pattern though.

Rosha: Yeah but they cannot use symbols todescribe the pattern. They don’t know whatdependent and independent variables are.

Tina: They get confused with letters?

Tina and Rosha decided to administer the sameproblem to Rosha’s Algebra I students as a warmup activity that week. After reviewing the students’responses they noticed the same difficulties were

exhibited in their work. Their discussion revealedtheir struggle to make sense of their findings.

Rosha: It is amazing. It seems like they aremaking the same mistakes, they are confusedabout the same concepts. I don’t understandwhat the problem is here.

Tina: Maybe the idea of a variable is tooabstract for them. Maybe they are just not clearabout what that variable is supposed to be—When I was working with my group I kepttelling them to remember that X means that itcan be anything, sometimes it is 20, sometimes1000, sometimes 1,000,000y It is just avariable.

Rosha: I did the same thing and they said theyunderstood what I was saying, then when I gavethem a different problem they made the sameerror.

Tina: Maybe there is something else involvedhere. I am not sure doing more examples helpsthem. To be honest I cannot even rememberhow I learned this stuff myself.

On four occasions Tina and Rosha carried theirdiscussions to the methods course meetings duringwhich they asked specific questions about commonmisunderstandings of the children, and cognitiveobstacles they encountered when learning Algebraand Geometry. This practice was particularlyuncommon among pre-service teachers at theirlevel of development since frequently they assume‘‘practice of basic skills’’ as the sole method fordealing with students’ learning difficulties. Rarelyare they sensitive to or curious about children’scognition or cognitive elements that influencemathematics learning. Indeed, Tina’s and Rosha’sattempt at implementing their action researchproject encouraged seven other methods classstudents to conduct similar studies in theirrespective settings.

3.7. Problematizing mathematics

Although the teaming process motivated theirinvestigation of important teaching and lear-ning issues as illustrated in previous sections, a

A. Manouchehri / Teaching and Teacher Education 18 (2002) 715–737730

significant outcome of Tina and Rosha’s interac-tions was their own investigation of the mathema-tical concepts they taught. Their classroomobservations allowed Rosha and Tina to talkabout and study the mathematical topics coveredin the curriculum.

Although this was not apparent at the time ofparticipant selection for the study, it becameobvious later and during the course of the studythat Tina and Rosha brought to their practicumvarious levels of interest in, and understanding ofmathematics, as well. Rosha was curious to learndifferent ways in which mathematical concepts ofAlgebra I and Geometry courses could be taught.She talked about how these same concepts wereexpanded later in more advanced mathematicscourses. In places where she was unsure of ‘‘whycertain things worked’’ she asked me for guidanceand consulted with various resources. Her atten-tion to mathematics was also manifested in howshe evaluated the teachers’ choice of problems forstudent investigation or the type of explanationsshe provided the learners. This, however, was notthe case for Tina, as her references to the subjectmatter had an incidental nature and rarely focusedon tracing the development of mathematical ideasor ways of teaching various concepts.

During their discussions Rosha raised concernsabout how students’ mathematical difficulties werehandled by the teachers. She wondered why theteachers spent so much time on certain proceduresthat she herself considered as peripheral to thestudy of mathematics. She asked Tina if she knewalternative ways of explaining the concepts tostudents or if she had a rationale for why certaindiscussions were not covered in class. Whenconfronted by these questions, Tina expressed thatshe had not thought about these issues andsuggested that they study them together. Thefollowing is illustrative of this outcome. Theparticipants’ discussion followed their observationof Tina’s cooperating teacher during the last weekof their teamed observation sessions. In thepreceding week the teacher had taught childrenhow to construct perpendicular bisectors, perpen-diculars, and angle bisectors. On that day, theteacher showed the procedure for constructingparallel lines. The children had used, with diffi-

culty, compass and straight edge to complete theseconstructions. During their discussion session Tinaquestioned the value of learning to do suchconstructions.

Tina: I am not saying they should not do thembut I don’t think we should spend all this timeon doing the constructions on paper. I meanthey will never have to do this.

Rosha: I think she should use GSP. I reallythink they should spend more time on thecomputer rather than doing this on the paper.These are really important things for them tolearn. I mean the applications of these con-structions are really important.

Tina: I am still (umm) I am still not sure wherethey use these constructions. I mean it is truethat it is a part of the Geometry curriculum butso what? (pause) I cannot even remember theseconstructions anymore. I have to really lookover the geometry text. I think we will have toteach a section of it next semester.

Rosha: They need them you know? They needthese constructions so they will get to constructcentroid and orthocenter of triangles. Theyhave to study the Euler line and learn how toconstruct the 9-point circle.

Tina does not respond

Rosha: It is not that I don’t think they shouldspend all this time on doing the drawing. I amnot even sure how many of them really got whatthey were doing. But these constructions areimportant for them. Almost all of EuclideanGeometry depends on these constructions.

Tina: I mean what if one of them asks, hey whyam I doing this? Why is it important? What doyou say then? I don’t even know what a 9-pointcircle is. (Covering her eyes with her handswhile shaking her head)

Rosha: But I think they are so applicable—Here, look. (She picks up a paper and penciland draws the figure) Say you are here at thispoint, and say you want to find the shortestpath that gets you out of this locationy Orsuppose you have three cities and want to build

A. Manouchehri / Teaching and Teacher Education 18 (2002) 715–737 731

a warehouse that is the same distance awayfrom each of themy

This conversation lasted nearly 40min duringwhich Rosha presented Tina with three applica-tion problems and showed her how the construc-tions became useful in solving them. In thefollowing 20min they discussed how they couldteach the same concepts without spending 2 weeksof instruction on basic constructions.

3.8. Participant’s reaction to each other’s teaching

The participants were asked to teach fourlessons each during the last phase of theirpracticum. They were also assigned to observeeach other’s teaching and to provide feedback onthe lessons they observed. Two weeks prior to thisphase, they asked me and their practicum super-visor if they could design their lessons in colla-boration with one another. They also proposedthat they both teach the same lessons. Toaccommodate their individual practicum expecta-tions they were willing to submit additional lessonsif necessary. I found their suggestion acceptable.Each participant then taught four common lessonsduring the last 4 weeks of their experience. Two ofthese lessons were about solving systems of linearequations in Algebra I curriculum. The other twowere on similar geometric figures.

During their post-observation discussion meet-ings, Tina and Rosha’s reactions to one another’steaching followed a general pattern consisting offour levels. At the first level of peer interaction,each one provided the peer with emotionalsupport. They made positive comments aboutwhat they observed. They then reported specificstudents’ behaviors and named students who paidlittle or no attention in class, as well as those thatdid not participate in discussions. During thisphase the person that was observed asked forspecific information on aspects of her lesson fromthe peer. For instance, she asked if she had givenstudents enough wait time, or if she allowedsufficient time for small group investigations.

At the second level of interaction and in light ofwhat they had seen or heard in each other’s class,they reflected on their own instruction. They began

this phase by saying, ‘‘I do the same thing’’, ‘‘mykids act the same way’’, or ‘‘I am having the sameproblem’’. They then told specific stories fromtheir own classroom encounters that matched thechallenge each had experienced in class.

At the third level of response, in their discus-sions they tried to refine the lesson. They talkedabout things they could do differently, additionsthey would make to the lesson, or parts they wouldexclude from the sequence. Moreover, they hy-pothesized about how these revisions couldeliminate some of the problems they experiencedduring the teaching episode.

Although during the first 2 weeks of the peerobservations/feed back process Rosha and Tinawere reluctant to explicitly confront each other’sinstructional choices, starting in the third weekthey began to identify instances from the instruc-tional period on which they disagreed. Even thenthey both seemed careful not to jeopardize therelationship. Consider the following dialoguebetween Rosha and Tina. The discussion followedTina’s third teaching episode during which she hadbegun her instructional period by reviewing theprevious night’s homework assignment. She hadwritten the answers on an overhead transparencyand asked the children to check their responsesagainst the ones she provided. Several studentsobjected to Tina’s answer to one of the problemsand suggested a different response.3 Tina decidedto solve the problem on the board so all childrencould see her procedure. The students continued toargue that the mathematical procedure Tina wasusing was not necessary. Tina announced that hermethod was the correct way of solving the problemand proceeded to start her new lesson. Several ofher students became disengaged following thisgroup conflict. Though these events did not seem

3The problem asked students to consider the following

scenario: ‘‘The video store in Almo’s neighborhood charges

$2.95 for each video rented. A subscription to cable TV costs

$29.95 and has movies on all day and night. If Almo rents eight

movies a month, should he switch to cable TV?’’ A majority of

the students argued that no mathematical calculation was

necessary as they felt it would be more beneficial to buy the

subscription to the cable TV and have access to an unlimited

number of movies than to rent them.

A. Manouchehri / Teaching and Teacher Education 18 (2002) 715–737732

to be problematic to Tina, they disturbed Rosha.Rosha addressed her concerns after her lesson.

Rosha: I don’t know (pause) but I think youshould have let them talk about their answersySee? When you think about their solution, itmakes perfect sense. I mean if I did not knowthat the problem came from the algebra book Iwould have approached it the same way (shemeans the same way as students).

Tina: But you don’t understand! He alwaysdoes this (she is making references to one of thestudents who was most vocal in objecting to hersolution). He comes up with these off the wallcomments that have nothing to do with what weare doing. He does it when Ms. A teaches aswell.

Rosha: They were saying it is just not how it isdone in the real world. Besides I think youshould have given them time to express whatthey were thinking. Like, I would have let themexplain their solution first.

Tina: I thought I did let them talk about theirprocess.

Rosha: Yeah, I just don’t think it really pushedthem to use math. I just think they had a point.

(Tina is silent)

(Rosha, noticing Tina’s silence, elaborates onwhat she views as the impact of Tina’s reactionto students on the remaining part of herinstructional period.)

Rosha: I saw that right after you stopped Jim,they basically stopped paying attention to you.

I mean when you told them to put away thehomework. I mean after that and when youstarted the new topic they basically did notwant to do anything. That was when youstarted having problems.

Tina: But I needed to start my lesson.

Rosha: I know. But it was a good problem andthey seemed really interested in arguing theirpoints. I don’t know, I would probably askthem to think of a situation where they actually

have to set up a system of linear equations tosolve a problem.

(Rosha changes the discussion as she raises asimilar experience from her own teaching.)

Rosha: I really don’t know what to do whenthey get to that point. You know? When theyjust don’t want to do what they are asked to do?Sometimes they just get so out of hand, there isno telling what could happeny

Tina: I know what you mean y I think you areright though, maybe I should have said thattheir solution was also reasonable.

The same pattern was revealed in the content ofthe feedback Tina provided Rosha. Though Tinanever explicitly challenged Rosha’s teaching styleor her interactions with the students, she followeda similar feedback cycle when she shared herthoughts on what she had seen or heard in Rosha’sclass. Both participants felt the need to authenti-cate each other’s choices and decisions. Only whena particular belief of a peer was violated would shebe willing to address the point directly. Even thenthey either dismissed the issue so to avoid personaltension, or they agreed that they were entitled tohave different opinions. This occurred four timesduring the course of the data collection.

3.9. Issues

In spite of the positive influence of peers on theprofessional development of both participants,issues also emerged in the course of their interac-tions. These related to their need for outsideauthority and perspective and the need for creatingimmediate closure on problem areas.

During the practicum experience the partici-pants’ need for outside perspective and authoritywas manifested in two distinct ways. Both Tinaand Rosha exhibited the need to be validated byme when they analyzed teaching and learningissues. Although this was most visible in Tina’scase because she was less assured about herdecisions, Rosha too insisted that I validate hertheories and beliefs. This was particularly evidentwhen they faced a conflict they could not resolveby relying on their own resources. During both the

A. Manouchehri / Teaching and Teacher Education 18 (2002) 715–737 733

methods course sessions and site-based meetingswhen I was present, they were adamant that I tellthem how to interpret certain events or to offerthem options that would lead to immediate results.This need was most pressing when they talkedabout learners and mathematics curriculum. Theyrarely felt insecure in their analysis of teachingactions. The need for outside authority andperspective carried itself into the methods courseduring which time they requested that I settle theirdisagreements and insisted that I provide themwith the correct solution to the problems theyidentified.

Second, both participants showed the tendencyto seek immediate solutions to the pedagogicalproblems they identified in class. The need for aquick fix and for reaching immediate closure onissues prevented them from analyzing problems ingreat depth independent of my intervention. Insome cases, this need motivated them to resort toartificial or idealistic conclusions. In fact, in theabsence of my intervention, there were occasionswhen they both trivialized solution methods tocomplex curricular and learning dilemmas. Theysuggested, for instance, that certain topics shouldbe removed from the curriculum since studentshad difficulty learning them.

Neither one of these behaviors, however, wassurprising. Moreover, neither one of these beha-viors was unique to Tina and Rosha. Theexpectation that they should find immediateanswers to questions or use their instructor asthe authority to resolve disagreements and clarifyambiguities is consistent with teacher educationstudents’ previous experiences as mathematicslearners. An overwhelming majority of prospectivemathematics teachers’ learning experiences consistof passive receiving of ideas, transmitted throughdirect instruction. Throughout their past experi-ences as learners they are asked to find exactanswers, and the teacher/instructor determines theaccuracy of solutions to problems, and providesthem with the correct answer. Tina and Roshaonly mirrored a common belief among mathe-matics teachers, that there must be an immediateand quick fix to pedagogical problems. Throughtheir discussions Rosha and Tina made public thetype of practices and beliefs that their peers may

have been reluctant to pronounce. This could bedue to several reasons. On the one hand, myinvolvement in their school-based activities couldhave made them comfortable enough to persist onsoliciting explicit information regarding the dilem-mas they experienced. On the other hand, sincethey both shared the same issues they felt evenmore pressed to find answers to their questions.

When Tina and Rosha raised issues in class, Iused them as occasions to discuss critical issuesrelated to short- and long-term curriculum plan-ning, mathematics, teaching, and learning. Thesediscussions engaged all other methods students inpedagogical investigations that were in line withthe goals of the course.

4. Discussion and implications

This study investigated whether peer interactionpromoted teacher development. The case studyshed light on the nature, content, and thepredominant themes of discourse between twoprospective secondary mathematics teachers, aswell as the impact of their interactions on each ofthe participants. Findings of this study support thepotential of peer interaction to promote thedevelopment of professional knowledge, andemphasize the value of peer contributions, feed-back and observations for the development ofboth self and peer reflective inquiry into practice.

In this study, the peers helped problematizecurricular and instructional issues for one another.The peer discussions were the medium throughwhich the participants confronted each other’sthinking and forced one another to defend theirinterpretations of the classroom events, and toextend their local knowledge to a theoretical level.Their interactions motivated them to exploremathematics, and current literature on studentlearning and curriculum innovation. These weresignificant outcomes of their work. Although thesesame behaviors and actions were encouraged andreinforced by me during the methods course, it wasthe participants’ need to regulate and coordinatetheir understandings so as to sustain their interac-tions that helped them accomplish these outcomes.In fact, these behaviors were not exhibited by their

A. Manouchehri / Teaching and Teacher Education 18 (2002) 715–737734

peers who were completing the same practicumassignment in other settings. From the perspectiveof those responsible for educating teachers, thesefindings are of particular significance and haveboth epistemological and methodological implica-tions for teacher education.

The current study implies that peer discourse,peer observations, and peer feedback have animpact on teacher development. In the course ofthe semester the participants came together anddiscussed what was acceptable practice and theissues they needed to think about when planninginstruction. Their interactions also helped them torecognize gaps in their own professional know-ledge. This is evidence that once placed in asituation where the teachers need to explain theirchoice of pedagogy and practice, greater under-standing of the learning and teaching issues mayarise. In addition, engagement in collaborativeplanning and analysis of teaching helps thedevelopment of a more sophisticated understand-ing of the content as well as teaching issues.

These epistemic outcomes have direct relevancefor teacher education. Researchers have portrayedteachers’ knowledge as a mixture of idiosyncraticexperience and personal synthesis. For example,Lortie (1975) argued that teachers lack a technicalculture, a set of commonly held, empiricallyderived practices and principles of pedagogy. Asa result, teachers must individually develop prac-tices consistent with their personality and experi-ence. Jackson (1968) also argued that teachers arecontent with simple explanations. They justifytheir teaching on the basis of feelings and impulserather than reflection and thought. They takestrong stands against practices different from theirown and rely on personal experience to defendwhat they do. The meanings they give to abstractterms are limited to the boundaries of their ownexperience. Lortie attributed this picture of teach-ing knowledge to the absence of a technical culturein teaching. Sarason (1971) ties the fact thatteachers lack a shared body of practical knowledgeto teacher isolation. Because most teachers workapart from their colleagues, they have littleopportunity to articulate and compare what theyknow. Moreover, the need to respond constantlyto classroom demands is thought to foster a

reliance on intuition and impulse rather thanreason. This has become the culture of practicein teaching. Changing this culture is not possiblewithout orchestrating learning environments inwhich teaching is problematized and collegialpedagogical problem solving is fostered andpracticed. Most frequently teachers’ experiencessubstantiate the primitive culture of teaching inwhich the individual is expected to draw from selfand her intrinsic resources when constructingpedagogical decisions and conclusions. Rosha’sand Tina’s case illustrates that capacity for sharedlearning through collegial reflection can be devel-oped. I argue that the potential of peer discoursefor modifying the culture of isolation as practicedin the teaching profession should be explored earlyin the course of teachers’ preparation. The teamedpracticum has the potential to serve as a usefulvehicle for enculturating future teachers to thetype of practice that builds upon collegiality, peerfeedback, and socialized knowledge.

5. Recommendations for further study

In this study, although not planned, theparticipants brought varying reflective orienta-tions. They also differed in their level of mathe-matical competence. I am unsure what the impactof the peers would have been if the participantshad brought similar orientations, attitudes, andweaknesses to the experience. It is legitimate thento hypothesize that in the absence of thesedifferences the results of the study might havebeen different. The tentative status of the results inthe absence of these differences demands thatintense care be taken when grouping participantsfor such collaborative work. Cooney’s categoriesof reflective orientation (1999) provide a vehiclefor initiating a systematic inquiry into creativeteaming strategies.

Cooney (1999) classified pre-service teachersinto four categories: isolationist, naive idealist,naive connectionist, and reflective connectionist.These categories were constructed to distinguishthe various orientations that pre-service teachersbring to teacher education and their reflectivetendencies. According to Cooney, a naive idealist

A. Manouchehri / Teaching and Teacher Education 18 (2002) 715–737 735

is likely to accept ideas or beliefs of others, such asprofessors, about teaching, without any criticalconsideration and so without control over anydecision to be made. A naive connectionist, on theother hand, tends to reflect on others’ ideas orbeliefs compared to one’s own. The differencebetween a naive and a reflective connectionist isthat a naive connectionist cannot resolve conflictor differences in belief (p. 172). In retrospect onecould classify Tina as a naive idealist, and Rosha anaive connectionist. It is curious to examine thevarious permutations of such reflective orienta-tions in an attempt to find the optimal format forcollegial teams when placing teachers in experi-ences similar to those described in this study.

Data also indicated that Tina and Rosha werereluctant to confront each other’s pedagogy. Inaddition, they both demonstrated the tendency tobe satisfied with the generalizations they madewhen discussing teaching and learning issues. Inplaces, where neither one of the teachers possessedthe intellectual tools to further analyze a problem,the problem was abandoned. Unless a newperspective was offered to them, both participantstended to be satisfied with their primitive solutionmethods. This was particularly problematic whenthey failed to make sense of cognitive obstaclesstudents faced as they encountered various math-ematical topics. In fact, in the absence of myintervention and the appropriate resources Iprovided the participants, it was likely that theywould have neglected critical and essential topics.Supervision of prospective mathematics teachersinvolved in such experiences then becomes ofparamount importance. This supervision shouldbe grounded in research-based knowledge aboutcurrent theories of mathematics learning, curricu-lum and instruction. Currently in many institu-tions the supervision of field-based practicums,and at times even the student teaching phase ofpre-service teachers, is conducted by universitystaff and faculty members who are neitherfamiliar with mathematics content nor the epis-temic underpinning of reformed mathematicsteaching and learning. Alternative ways of super-vision should be conceptualized so to accommo-date the specific needs of secondary mathematicsteachers.

References

Almasi, J. F. (1995). The nature of fourth graders’ socio-

cognitive conflicts in peer led and teach led discussions of

literature. Reading Research Quarterly, 30, 314–351.

Barnes, D., & Todd, F. (1977). Communication and learning in

small groups. London: Routledge & Kegan Paul.

Barnett, C. (1991). Building a case based curriculum to enhance

the pedagogical content knowledge of mathematics tea-

chers. Journal of Teacher Education, 42(2), 1–9.

Bruner, J. (1990). Acts of meaning. Cambridge: Harvard

University Press.

Cole, M. (1996). Cultural psychology: A once and future

discipline. Cambridge, MA: Harvard.

Cooney, T. (1999). Concpetualizing teachers’ ways of knowing.

Educational Studies in Mathematics, 38, 163–187.

Danziger, K. (1990). Constructing the subject: Historical origins

of psychological research. Cambridge: Cambridge University

Press.

Darling-Hammond, L. (1994). Professional development

schools: Schools for developing a profession. New York:

Teachers College Press.

Fuller, F. F., & Bown, O. (1975). Becoming a teacher. In: K.

Ryan (Ed.), Teacher education (74th yearbook of the

National Society for the Study of Education, Part 2,

pp. 25–52). Chicago: University of Chicago Press.

Glaser, B. G. (1978). Theoretical sensitivity. Mill Valley, CA:

Sociology Press.

Goodlad, J. I. (1990). Teachers for our nation’s schools. San

Francisco, CA: Jossey-Bass.

Grimmett, P. P., McKinnon, A. M., Erickson, G. L., & Ricken,

T. J. (1990). Reflective practice in teacher education. In

R. T. Clift, W. R. Houston, & M. C. Pugach (Eds.),

Encouraging reflective practice in education (pp. 20–38). New

York: Teachers College Press.

Guzzetti, B. J., & Williams, E. O. (1996). Gender, text, and

discussion: Examining intellectual safety in science class-

room. Journal of Chemical Education, 81, 561–575.

Harre, R., & Gillett, G. J. (1994). The discursive mind.

Thousand Oaks, CA: Sage.

Jackson, P. (1968). Life in classrooms. New York: Holt,

Rinehart & Winston.

LaBosky, V. K. (1994). Development of reflective practice: A

study of preservice teachers. New York: Teachers College

Press.

Lortie, D. (1975). Schoolteacher. Chicago: University of

Chicago Press.

Louden, W. (1991). Understanding teaching: Continuity and

change in teacher’s knowledge. New York: Teachers College

Press.

Manouchehri, A. (2001). Professional discourse and teacher

change. Action in Teacher Education, 1, 89–115.

Manouchehri, A., & Goodman, T. (2000). Implementing

mathematics reform: The challenge within. Educational

Studies in Mathematics, 42(1), 1–34.

Noffke, S. E., & Brennan, M. (1991). Student teachers use

action research: Issues and examples. In B. R. Tabachnick,

A. Manouchehri / Teaching and Teacher Education 18 (2002) 715–737736

& K. M. Zeichner (Eds.), Issues and practices in inquiry-

oriented teacher education (pp. 186–201). New York: Falmer

Press.

Piaget, J. (1964). Development and learning. Journal of

Research in Science Teaching, 2, 176–186.

Sarason, S. (1971). The culture of the school and the problem of

change. Boston, MA: Allyn & Bacon.

Schon, D. A. (1987). Educating the reflective practitioner. San

Francisco: Jossey-Bass.

Thompson, A. G., & Thompson, P. (1996). Talking about rates

conceptually, Part II: Mathematical knowledge for teachers.

Journal for Research in Mathematics Education, 27(1), 2–25.

Vygotsky, L. S. (1978). Mind in society: The development of

higher psychological processes. Cambridge, MA: Harvard

University Press.

Wertsch, J. (1986). Culture, communication, and cognition:

Vygotskian perspectives. New York: Cambridge University

Press.

A. Manouchehri / Teaching and Teacher Education 18 (2002) 715–737 737