Teachers as Peer Coaches in High School Mathematics

232

Teachers as Peer Coaches in HighSchool MathematicsKenneth TobinDepartment of Curriculum &. InstructionFlorida State UniversityTallahassee, Florida 32306

Mariona EspinetDepartment of Science & Mathematics TeachingUniversity of BarcelonaBellaterra, Spain

Enduring problems in mathematics learning were highlighted in a recentreport of the National Council of Teachers of Mathematics (Grouws &Cooney, 1988). The report urges comprehensive reform. But are teachers ableto change what happens in classrooms and improve student learningappreciably? Can teachers implement mathematics curricula in ways thatenable students to learn with understanding? Can teachers assume roles asfacilitators of learning? And to whom can teachers turn for assistance whenthey need help? The purpose of this study was to investigate the extent towhich teachers working within the same department could assist one anotherto improve teaching. The study investigated how teachers coached oneanother, accepted advice and feedback from colleagues, and the extent towhich changes occurred in classroom practices. The initial approach to teacherenhancement was based on peer coaching (Showers, 1985), but as the studyprogressed, greater attention was given to the role of reflection in the changeprocess (Grimmett & Erickson, 1988).

Peer coaching appealed as a means of enhancing teaching within a school.Joyce and Showers (1983) differentiated between mastering a skill in aworkshop setting and transferring the skill to the classroom. Theydemonstrated that continuous practice, feedback, and the companionship ofcoaches is essential to enable even highly motivated teachers to bring additionsto their teaching repertoire under control. Joyce and Showers stated that inorder to adopt a new strategy a teacher should first develop a high skill levelin the strategy. Next, the teacher needs to attain executive control to enablethe skill to be transferred and appropriately adapted to the classroom settingand students. A number of studies (e.g., Baker & Showers, 1985; Davis, 1987;Sloan, 1986; Tobin & Espinet, 1989) indicated that, with the assistance of acoach, teachers can acquire new and complex teaching strategies andsuccessfully transfer them into their on-going teaching practices. However,

School Science and MathematicsVolume 90 (3) March 1990

Teachers as Peer Coaches 233

there is evidence to suggest that teachers do not always cooperate when anoutsider is involved in identifying teaching and/or learning problems. Forexample, Davis (1987) described how a middle school science teacher refusedto cooperate in a coaching study because school administrators had, on hisbehalf, requested coaching assistance from university educators. At no stagedid the teacher actually acknowledge that he had a problem to solve. Heregarded coaching as an exercise in which he had to participate and appearcooperative, but not one that would lead to improvements in learning ofstudents in his classes. Since the teacher did not have a commitment tochange, it was not surprising that few improvements in teaching were reportedby Davis.An obvious way to overcome this type of problem is to involve the teacher

in identifying problems in his/her classroom; however, such involvementmight lead to other problems if the teacher opts to change an aspect ofteaching which is of little consequence when compared to other changes whichneed to be made. For example, Tobin and Espinet (1989) described howJonathon, a science teacher, had major problems managing student behaviorand keeping students on-task. Jonathon decided to improve the clarity of hislectures. The researchers acknowledged that Jonathon had a clarity problem;however, in their opinion, increases in clarity were unlikely to improvelearning as much as controlling student misbehavior and providing studentswith more opportunities for active engagement.

Peer coaching provided a context in which colleagues within a mathematicsdepartment could observe one another teach, discuss what they saw, and assistone another to identify potential problems and strategies to improve thequality of student learning in the school. Peer coaching was preferred to theuse of an external coach because a peer is likely to have knowledge ofcontextual factors that need to be considered if changes are to be initiated andsustained.

Method

Sample

Five of the six teachers (Pam, Sally, Michael, Helen, Judith) from themathematics department of an urban county high school in a southern state ofthe USA agreed to participate in the study. As an inducement to participate,teachers were offered inservice credit by the local education authority and 5quarter-hours of graduate study at a nearby university. The teachers had beentogether as a team for 5 years, and several of them had taught together for 10years. Their experience of teaching mathematics ranged from 5 to 14 years.Each teacher was certified to teach mathematics.

Design

During the study, seven observers gathered qualitative data from the classestaught by five teachers over a period of six months. The data for this study


234 Teachers as Peer Coaches

were drawn from the entire data collection period. After an initial period offive weeks, the coaching phase of the study commenced. Each teacher wascoached by another and was the coach of a peer. At a given time, no teachercoached the person who was coaching her/him.

The coaching study had two components. In the first component, a teacherobserved a lesson of a colleague. During the observed lesson, the coachconstructed field notes and, at the conclusion of the lesson, gave them to theteacher. In the second phase, one week later, the coaching session occurred.At this time, teachers collaborated about the observed lesson for one hour.

During the first round of peer coaching, we provided a bulletin to allcoaches to assist them to coach their colleagues. The bulletin containedinformation about the coaching schedule, how to provide a supportiveframework during coaching sessions, and specific information relating to theweaknesses and strengths of the teacher being coached. The data included inthe bulletin were obtained during the initial five weeks of the study.

Teachers generally found it hard to work with the ideas contained in thefirst bulletin. As a consequence, the bulletin was discontinued and an activepresence by the research team was maintained at the coaching sessions. Wheninput from the coach was completed, a member of the research team wasavailable to provide relevant information about research and prior coachingadvice. This practice added to the value of the reflective discussions whichoccurred during coaching sessions.

After three observations and three coaching sessions, the first roundcoaching schedule was changed because of a perception among coaches thatthey had given as much assistance as they could. During the second round,which consisted of two observations and two coaching sessions, the coachingsessions occurred in the same week as the observations.A third round of observations and coaching was scheduled to enable

teachers to have additional experience. Due to the proximity of the end of theschool year, only one observation and one coaching session was possible in thethird round.

Data Sources

Field notes collected by participant observers during direct observation ofcoaching sessions and interviews with teachers were the principal data sourcesin this study. Other data sources included observations of teaching, interviewswith students, teachers observing one another, and members of the researchteam teaching selected classes involved in the study.

Data Analysis

The data were analyzed and interpreted throughout the study. Assertionswere constructed from the multiple data sources and provided a focus forsubsequent data collection. The team of researchers met regularly throughoutthe study to facilitate interpretation of the data. The frequency of team



meetings ranged from one to four occasions per week. The team discussedsubstantive issues related to the assertions, supporting data and vignettes aswell as procedural aspects of the study. Through subsequent discussion,assertions were retained, modified, or rejected.

Background Information

The level of confidence and self-esteem among Pam, Sally, and Michael wasvery high. This was evident in their dealings with the research team,colleagues, and students. Each of these teachers was highly regarded withinthe school and school district. In contrast, the problems faced by Helen andJudith were numerous and major. Partly due to plummeting expectations forstudents to achieve reasonable standards, they taught in dysfunctional learningenvironments in almost every class period. Misbehavior was disruptive and rifein all lessons that we observed, and the teachers had developed an attitude ofhelplessness to cope with the situation. Helen described her condition as"burned out," and Judith just hoped for better class assignments next year.These teachers needed help long before the coaching study commenced, yetthe administration of the school and their mathematics colleagues had ignoredtheir problems. In Helen’s case, complaints from parents had resulted in herteaching assignments being changed after classes had commenced at thebeginning of the year. As a result, she had been given even lower abilitystudents to teach. In an important sense, Judith and Helen were isolatedbecause of their inability to cope with classroom management. Theircolleagues and school administrators perceived the problems to be for theteachers to solve, and when they could not, they were classified as poorteachers and were left to fend for themselves.

Enhancement of Teaching and Learning

Each teacher’s performance as a coach was a reflection of her/his teachingperformance; Pam, Michael, and Sally were successful coaches and teacherswhereas Judith and Helen were relatively unsuccessful in both roles. Thefindings of the study are presented below in terms of three assertions.

Assertion 1: The peer coaching program produced improvements inteaching of all participants.

All teachers reported that they learned from observing their colleaguesteach. An interesting finding in this regard was that the teachers appeared tobenefit from observing both the stronger and the weaker teachers.Observations of a colleague followed by discussion led to reflections onteaching and produced a context which was conducive to changes in teaching.Whereas the stronger teachers often reflected on their practice when they werealone or when they were observing a colleague teach, the weaker teachersseemed to need their colleagues to provide answers and foci for discussion.During discussion sessions, teachers often made a commitment to change andsought the practical knowledge necessary to implement change. Each teacher



seemed assured that the source of the advice was from a current practicingteacher who had knowledge of the local school climate.Each of the teachers perceived the coaching program to be beneficial. As

far as Pam was concerned, the main advantage related to opportunities forher to observe others teach and to reflect on practice. She explained that "inobserving other teachers and questioning their philosophy I was forced to takea look at my own philosophy, not necessarily to change it but at least to thinkabout it.’* Pam described peer coaching as a nonthreatening method ofworking with someone else to improve the classroom environment. She stated:

I think that peer coaching is an excellent way to learn how others feelabout teaching. Peer coaching also encourages the sharing of ideas. As aresult of the peer coaching program I am making a conscious effort tobreak up the activities in the classroom, to call on students by name, andto keep students involved in classwork closer to the end of the period.The program has made me more aware of my own feelings aboutteaching and learning. Just knowing that someone will be observing myclass encourages me to do my best, and in order to do my best I have tounderstand why I am teaching a given topic in a particular way.

For Helen and Judith, the coaching session was a reflective process wherethey could discuss their problems with others. Initially at least, Helen andJudith attributed their lack of success to the students they had to teach ratherthan themselves. In particular, low-ability students were seen as the cause ofmany or most of the discipline problems that occurred in their classes. As thecoaching program progressed, however, each of the weak teachers showed apreparedness to accept responsibility for what transpired in their own classes.The following statement from Judith exemplifies the advantages she

perceived of the peer coaching program:

/ like the idea of peer coaching because it allows you release time todiscuss motivational and disciplinary ideas with other teachers which wewould not otherwise have time to do. Also, seeing different ways topresent the same material is helpful. The peer coaching made me realizethat I have let my expectations for my basic classes slip downward. Sincethe expectations have been raised, particularly in second period, I nowrealize how much more pleasant and teachable the class is and could havebeen if I had approached them that way in September of last year. Also,the coaching experience has shown me that I am not the only one whohas discipline or classroom management problems and through ourdiscussions it has helped me to feel better about those days when it seemseverything goes wrong.

Helen’s perceptions were similar to those of Judith and are represented inthe following comment:

The thing that I enjoyed most was having time to meet with Sally and



having a chance to talk with my peers. It was beneficial to observe andshare with each other. Suggestions mean a lot when they come from otherpeople in the field. As a result of the coaching I am using more groupingin my classes and I have reaffirmed and organized discipline proceduresto implement for this year and next. The study has given me more insighton ways to improve discipline management and to try different techniqueswith the basic classes as well as the more advanced groups. I wasreminded to not expect any less of students in the basic groups incomparison to the more advanced.

Michael explained that the greatest benefits from the coaching programwere associated with opportunities to observe others teach. Occasionally heidentified some things to avoid in his own teaching. For example, he explainedthat Helen tended to talk over the voices of other students. When he nexttaught, he ensured that he did not make the same error and dealt with anystudent talk before proceeding with the lesson. Michael emphasized that hewas now very conscious of the pitfalls of trying to teach over a background ofstudent noise.

Michael also was pleased with the assistance he received from Pam. Sheadvised him to incorporate more variety into his lessons, especially with hisaverage classes. He noted that his teaching improved as a result of thecoaching program. His focus was on improving student motivation to learn,and he had introduced variety into his lessons through the use of more groupwork and new techniques.The use of groups represented quite a shift in Michael’s philosophy of

teaching. Before the coaching component of the study, Michael explained thathe had used groups as a beginning teacher but that management problemsarose and he had not utilized small group activities since that time. However,acting on Pam’s advice, he attempted to incorporate small group activitiesinto his lessons. The feature of his changes was the use of computers andsmall groups as a means of covering the content of a chapter on area andperimeter of prisms. Instead of using his conventional approach, centered onthe teacher presenting information and students working problems from thetextbook, Michael instructed students to write computer programs for specificproblems in the textbook. He judged the five weeks spent on the activity asextremely successful.Pam, Michael, and Sally gave valuable assistance to the weaker teachers on

classroom management and motivation. Gradually management problemsstarted to improve and the teachers could focus on student learning. Althoughmost changes were incremental in nature, a revolution occurred in oneinstance. Judith could not teach her second period class (and neither could theresearch team) because of blatant unacceptable behavior from about two-thirds of the students. During a coaching session involving Judith andMichael, it was agreed to obtain assistance from the principal to overcome theproblem. The agreed strategy was to reset the expectations for behavior and



performance at a high level and to have consequences for not meeting thestandards. With the help of the principal, the standards were set in place anddramatic improvements occurred overnight. In this case, the teacher wasimpotent to change without the assistance and support of the administration;however, with the necessary support, the teacher’s confidence soared, and theimprovements persisted until the end of the school year. Although there wereobvious limits to the extent of the improvements which would occur with thistype of coaching, the improvements were certainly not cosmetic and over aprolonged period of time substantial improvements would undoubtedly occur.

Assertion 2: Some teachers perceived their teaching to be strong and didnot seriously consider recommendations to improve.A problem which was immediately obvious was that the more effective

teachers did not perceive problems with their teaching. When the researchteam discussed the results from the baseline period of the study, Sally andPam (in particular) accepted the feedback graciously but did not appear tohave a commitment to change any aspect of their teaching. They seemed tohave accepted the validity of the observations of the research team but did notagree with the implication that change was necessary or even desirable. Thus,Sally did not agree that the use of small group activities would enhancestudent learning opportunities or that less lecturing would be beneficial tostudents. Similarly, in the early stages of the study, Pam did not see that timeoff-task was a problem that should be addressed in her class. These findingsalso were applicable, to a lesser degree, to the three other teachers.When coached by Sally, Pam stated that she was teaching satisfactorily and

would change only if and when she wanted to. Pam acknowledged that shereceived good constructive criticism from Sally but, after only one coachingsession, expressed the view that Sally could not help her any more. Sheclaimed that an external mathematics specialist was needed if there were to befurther benefits from coaching. Although Pam declared publicly that she didnot wish to change her teaching, she endeavored to increase the amount ofgroup work and to enhance student motivation to learn. Furthermore, sheendorsed coaching as a means of improving teaching.

Sally was most steadfast in her views about teaching. Sally valued theacquisition of facts and algorithms for obtaining a correct answer. Shebelieved that understanding emerged after an algorithm was mastered andstudents could correctly solve problems. She had learned mathematics this wayherself and believed it was the most appropriate way for her students to learnmathematics. Consequently, she did not concern herself too much withensuring that students understood particular concepts when they wereintroduced, and she always stressed the procedures to be followed whenparticular types of problems had to be solved. Her emphasis on rote learningby drill and practice was evident in the advice that she gave to her colleaguesduring coaching sessions. Inevitably, she described how she implementedinstruction and suggested that her colleagues teach in this manner also. During



sessions in which Sally was coached, she did not solicit feedback on herteaching performance from any of the coaches and disagreed with suggestionsthat small group activities might enhance student learning.

In contrast to Sally, the research team valued meaningful learning in aconstructivist-styled classroom (von Glasersfeld, 1988). This constructivisitperspective was evident in advice given to teachers in the bulletin and indiscussions on teaching, and it filtered our observations and interpretationsthroughout the study. Consequently, we valued small group work andopportunities for students to construct their own knowledge as a result ofactive mental processing. We advised teachers to provide opportunities forstudents to test their understandings by solving problems with their peers andto clarify their knowledge through discussion. The clash between thesomewhat opposing frameworks was evident early in the study but became lessof a problem as the study progressed. The opportunities to discuss teaching inthe coaching sessions led to a situation where four of the teachers activelyconsidered the use of groups in their teaching. Only Sally remained convincedthat her approach to teaching was optimal.

Yet an interview with Sally indicated that even she was considering somechanges in teaching. She stated that:

I think it is probably one of the best methods of teaching improvementand growth. It means the coach is also involved in the real life situationof the school. As a result of the coaching program I have shortened mytime for "working examples. By the second or third example the class isnow working with me. When I work problems on the board I now askstudents for input rather than working the problem for them. It has mademe stop and analyze some of (he ways I conduct my classes. I am still atthe analyzing stage not really sure I can accomplish as much another way.

Assertion 3: Strong teachers were perceived to be strong coaches and weakteachers were perceived to be weak coaches; however, knowledge limitationsdiminished the effectiveness of all teachers as coaches.

Personal qualities appear to be important factors in determining whichteachers were good coaches. Pam was an effective coach for all teachers. Incontrast, Michael and Sally were effective with one another, less effective withPam, and even less effective with the weaker teachers.

Because of her extensive pedagogical knowledge, counseling qualities, andpersonal characteristics, Pam was the best coach, especially for the twoweaker teachers. She did not tell others directly what they should do but askedopen-ended questions designed to draw her colleagues into a discussion onteaching. Rather than explaining how she did things in her own class, Pamplaced the focus on what students did in class and ensured that discussionfacilitated reflection about student engagement. Pam endeavored tounderstand her colleagues and was empathetic when dealing with teachers whowere having difficulties. She discussed weaknesses in a supportive manner and



usually confided "I had problems like that, too." Pam was aware of apotential credibility problem attributable to the perceived ease of teachingstudents from the gifted program. She explained:

7 think I have some good ideas but I am not sure how they are accepted.I feel uncomfortable advising someone on classroom management withbasic students since I only work with advanced students.

Extensive knowledge of sports coaching, knowledge of teaching, andknowledge of mathematics enabled Michael to be an effective coach. Michaelwas not authoritarian in coaching sessions, but he was straightforward inoffering suggestions on weaknesses and how to improve them. He also wassensitive to the reasons offered by weaker teachers for their problems. Michaelwas more effective with the weaker teachers because their managementproblems were within the range of his experience. The biggest problem thatMichael faced was that he did not assist teachers to understand their problemsin rational terms. He explained what worked for him but did not explain whyit worked. Michael appeared to have an abundance of professional knowledgewhich allowed him to be an effective teacher, but his effectiveness as a coachprobably was limited by his inability to verbalize what he knew.Each of the teachers had limited pedagogical knowledge which reduced their

effectiveness as coaches. All teachers had difficulty diagnosing weaknesses inteaching, communicating these to their colleagues, and assisting them toimprove their teaching. Indeed, even the best of the coaches felt that they hadprovided as much assistance as they could after one coaching session. Forexample, Pam acknowledged that limitations in her own knowledge ofteaching made her coaching role difficult. She stated that:

/ did not feel that I had an adequate background to help Michael in thearea of motivation. I could share with him your ideas but I did not haveexperience in dealing with a similar situation. He has so many differentability groups in the room that it makes it difficult to teach the entireclass and yet breaking into groups can cause management problems.

Knowledge limitations prevented Sally from offering substantive advice tothe teachers she coached. For example, when coaching Pam and Michael,Sally set the agenda for discussion and controlled the meeting in a mannerwhich provided teachers with opportunities to reflect on practice, albeit in anenvironment which was dominated by her own advice. Inevitably, thediscussion centered on difficulties that Sally had experienced in her own classand how she had managed to overcome them. Sally talked about herselfduring the coaching sessions, focused on her own successes, and to anappreciable extent, did not discuss the observations from the lessons she hadobserved.

Sally did not use small groups in her teaching. The district curriculumcoordinator noted that Sally was insecure about using groups and, in the past,



had tried anything rather than group her classes. Her clear preference was touse whole-class and individualized activities. When asked about this, Sallyresponded that she taught the way that she had been taught. This involveddrill and practice which had been an effective learning method for her. Whenshe used small groups in her own classes, she found that students wereoff-task to a greater extent than in other activities. Sally’s aversion to usingsmall groups may have limited her effectiveness in assisting Michael andJudith to vary the activity structures in their classes. Michael was trying toutilize groups instead of relying on lecture and seatwork activities. Thus, thecoach was not overly enthusiastic about one of the strategies that shesupposedly was assisting Michael to implement. In addition. Sally did notsuggest the use of groups to Judith as a means of overcoming managementproblems.Although the teachers had vast reservoirs of knowledge, most of it had been

developed through experience as a teacher and was not necessarily accessiblein verbal form. In addition, unless they had experienced problems of the typeevident in their colleague’s class, they did not identify a problem. Apparently,Helen did not have the knowledge necessary to analyze teaching and formulateappropriate feedback. She had difficulty identifying weaknesses in teachingand completed her feedback and coaching assistance in just a few minutes. Asa result, coaching sessions became opportunities for Helen to obtain assistancefrom her peers. Helen observed that she "needed assistance in coaching Sallyas I thought that she did a super job. I felt inadequate to constructivelycriticize. I needed more input into what to look for in coaching." Much thesame situation occurred w^hen Helen coached Pam. Pam remarked that "myteaching situation is so good compared to Helen’s that she had a difficult timefinding fault with what w^s going on in my room." Michael also highlightedHelen’s inadequacies as a coach.

When we sat down she said one or two things and then we reversed roles.She sought advice so I volunteered a few of my ideas on classroommanagement and then we talked about the algebra course. The sessionswere beneficial even though Helen did not coach me.

Judith was not a successful coach for Pam. She also appeared to bedistracted by the ability and cooperation of the gifted students in Pam’s class,and she was hampered by a lack of knowledge necessary to identifyweaknesses in Pam’s teaching. Pam observed that Judith was so impressedwith her teaching and the students in her class that she did not offer anysuggestions for improvement.

Helen lacked enthusiasm for Judith as a coach as well. A possible reasonfor Helen’s lack of enthusiasm was that she did not want to reveal her ownteaching weaknesses to her colleague. In addition, she may have hadreservations about Judith’s capacity to assist her to overcome the problemsthat confronted her. Since the two teachers had similar problems, Helen mayhave felt that Judith’s limitations as a teacher would prevent her from being


242Teachers as Peer Coaches

an effective coach.

Implications

The findings of the study indicate that opportunities for observation,discussion with colleagues, and coaching from skilled practitioners aredesirable. Within-school resources can be used to improve mathematicsteaching by organizing an observation and discussion schedule which enablesteachers to help one another to improve instruction. The teachers’ reactions tothree different coaching arrangements suggest that one observation and onediscussion session were insufficient bases for change; however, threeobservations together with at least two opportunities for discussion withcolleagues appeared optimal. In addition, there appeared to be advantages incoaching and being coached by more than one teacher (i.e., coaching severalteachers on separate occasions and being coached by different teachers onseveral separate occasions). In this study, the weaker teachers appeared to

derive some comfort from observations which indicated that other teachersalso had problems. In addition, the stronger teachers observed problems to beavoided in their own classes. As a consequence, a schedule should be arrangedso that teachers have opportunities to observe and discuss teaching with moresuccessful and less successful colleagues. Because of marked differences in thelearning environments in classes taught by Pam, Helen, and Judith, relevantdiscussion points did not emerge from the observations. Helen and Judithwere almost overwhelmed by the differences between their classes and thosetaught by Pam. Because of the differences in the type of students beingtaught, the teachers attributed Pam’s relative success to the fact that she hadcooperative and talented students. For this reason, teachers should observeothers teaching classes similar to their own. Given the necessary resources, acoaching program might be implemented on the basis of several 3-week rostersfor each teacher in a given school year.A problem which appears to be inherent in peer coaching programs is that

the beliefs and knowledge of the coach might not be congruent with changesdeemed necessary by experts in the field. In this study, coaching from acolleague was beneficial for the weaker teachers in particular. Yet who shouldbe the coach? The obvious selection is the chair of the department; however,in this case, Sally was not the ideal person to coach her colleagues because ofher style of relating with others and her beliefs about what ought to be taughtin the curriculum and how students learn. Sally’s performance as a coachraises the issue of an influential coach promoting changes in directions whichare not desirable. In addition, the findings of the study suggest that the coachshould be an exemplary teacher. The weaker teachers were regarded as weakcoaches as well. Consequently, there is a need for specialist coaches withstrengths in knowledge of coaching, pedagogical knowledge, and discipline-specific pedagogical knowledge. In addition, the coach must have acommitment to keep abreast of the latest developments in all relevant fields.



Because of the level of expertise required of the coach or mentor teacher,special -programs should be designed and implemented to prepare teachers tobe effective mentors.The findings of this study also have implications for further research.

Investigations of the role of observation and reflection-on-action in enhancingteacher performance are needed in order to begin the task of explicating therelationships between beliefs, knowledge, and classroom behavior. Research ofthis type is a priority in subjects such as mathematics and science wherehigh-level cognitive learning has proved to be an elusive goal for many years.

Conclusion

The results of this study suggest that a within-school approach to staffdevelopment can be successful. Most schools could implement such anapproach at relatively low cost by using more-able teachers in advisory rolesand by scheduling time for teachers to observe their colleagues. We observedthat discussions on teaching appear to be more successful than prescriptionsand seem to set up an environment which is conducive to improving teaching;however, there do appear to be limitations to the extent to which within-school resources can enhance learning. Is it possible that reflection on practicecould lead to a ceiling effect which is characterized by universal mediocrity?In this study, all teachers needed more knowledge of mentoring, morepedagogical knowledge, and more pedagogical content knowledge. Additionalresearch is needed to understand the roles of teacher knowledge and beliefs inthe process of improving teacher performance. In the absence of suchresearch, teacher educators should reflect on their own practice giving closeattention to the methods currently used to educate teachers.

References

Baker, R.. & Showers, B. (1985). The effects of a coaching strategy onteachers’ transfer of training to classroom practice: A six month follow-upstudy. Paper presented at the annual meeting of the American EducationalResearch Association, New Orleans, LA.

Davis, N. (1987). An application of coaching in middle school science. Paperpresented at the annual meeting of the National Association for Research inScience Teaching, Washington, DC.

Grimmett, P. P., & Erickson, G. L. (Eds.). (1988). Reflection in teachereducation. New York: Teachers College Press.

Grouws, D. A., & Cooney, T. J. (Eds.). (1988). Perspectives on research on

effective mathematics teaching (Volume 1). Reston, VA: Lawrence EribaumAssociates, National Council of Teachers of Mathematics.

Joyce, B. R., & Showers, B. (1983). Power in staff development throughresearch on training. Washington, DC: Association for Supervision andCurriculum Development.



Showers, B. (1985). Teachers coaching teachers. Educational Leadership, 43,43-48.

SIoan, P. (1986). An interpretive study of peer coaching in middle schoolscience. Unpublished masters thesis, University of Georgia, Athens.

Tobin, K., & Espinet, M. (1989). Impediments to change: An application ofpeer coaching in high school science. Journal of Research in ScienceTeaching, 26(2), 105-120.

von Glasersfeld, E. (1988). The reluctance to change a way of thinking. TheIrish Journal of Psychology, P(l), 83-90.


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Teachers as Peer Coaches in High School Mathematics