The effects of teacher collaboration in Grade 9 Applied Mathematics

Educ Res Policy Prac (2011) 10:189–209DOI 10.1007/s10671-011-9104-y

The effects of teacher collaboration in Grade 9 AppliedMathematics

Gunawardena Egodawatte · Douglas McDougall ·Dorian Stoilescu

Received: 30 November 2010 / Accepted: 16 April 2011 / Published online: 4 May 2011© Springer Science+Business Media B.V. 2011

Abstract The current emphasis of many mathematics education reform documents is onthe need to change the environment of mathematics classrooms from the transmission ofknowledge by the teacher to the transaction of knowledge between the teacher and the stu-dents which promotes mathematical investigation and exploration. In this article, we discussthe details of a Collaborative Teacher Inquiry Project which was aimed at increasing thequality of learning of Grade 9 Applied Mathematics, while at the same time, improvingprofessional development opportunities for the teachers. A total of 11 schools participatedin this project which spanned over three semesters. Participants included teachers, depart-ment heads, curriculum leaders, and administrators. Each school created an implementa-tion team of administrators and teachers to implement collaborative strategies and improveteaching and learning in Grade 9 Applied Mathematics. The main benefit to the participantswas that they were able to increase their knowledge and skills through collaboration in sixinterconnected areas: (a) achieving the goals, (b) student success, (c) professional develop-ment, (d) co-planning and co-teaching opportunities, (e) increased communication, and (f)improved technological skills. Bringing in different partners to achieve a common goal wasthe most challenging aspect of the project.

Keywords Teacher education · Teacher collaboration · Teacher professional development ·Mathematics teaching · School improvement · Professional learning communities

G. Egodawatte (B) · D. McDougall · D. StoilescuDepartment of Curriculum, Teaching, and Learning, Ontario Institute for Studies in Education,University of Toronto, 252 Bloor Street West, Toronto, ON M5S 1V6, Canadae-mail: [email protected]

D. McDougalle-mail: [email protected]

D. Stoilescue-mail: [email protected]

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1 Introduction

Research has shown that teachers have difficulties in adapting to curricula reforms evenwhen well-designed implementation processes are in place. Adaption to change requires deepawareness of the nature of these changes and their importance. Sometimes, reform effortsunderestimate the complexities of the changing process (Fullan 2009). The current emphasisin mathematics education reform documents (National Council of Teachers of Mathematics1991, 2000, 2007) is on the need to change the environment of mathematics classrooms fromone in which the teacher “transmits” knowledge to the students, to one in which teachers andstudents interact as a community of learners in mathematical investigation and exploration.This emphasis is based on a constructivist view of learning and denies the transmission ofknowledge as not promoting a deep understanding (Moon 2007). However, there are manychallenges in training a teaching community to embrace non-transmission teaching methods,and to determine the extent to which teachers had progressed towards reform ideals.

Mathematics reforms are expected to have good faith on improving instructional quali-ties of the subject. According to Schoenfeld (2002), there are four necessary conditions inproviding high quality mathematics instruction for all students. They are (a) a high qual-ity curriculum, (b) a stable, knowledgeable, and professional teaching community, (c) highquality assessment that is aligned with curricular goals, and (d) stability and mechanismsfor the evolution of curricula, assessment, and professional development. To achieve thoseobjectives, we believe that teachers should be given adequate opportunities to work togethertowards common goals. When teachers are treated like professionals and they are given theopportunity to develop their skills and understanding over time, the results can improvestudents’ mathematical performance significantly (Schoenfeld 2002). Creating collabora-tive partnerships between and among schools, school boards, and universities is one way ofenhancing professional learning communities to raise the quality of instruction.

Although there are many research studies conducted in the US and the UK on collabo-rative professional learning communities of teachers, there is comparatively fewer studiesin this area in Canada. Further, there are no large studies conducted in Canada on teachercollaboration involving several school boards and a university to improve the learning ofGrade 9 Applied Mathematics. This shortage of research is our point of departure from otherstudies and the current study has especially been designed to study grade 9 students, who sitfor the standardized mathematics test known as the Education Quality and AccountabilityOffice (EQAO) test. We believed that we would be able to get reliable feedback from teach-ers on preparing students, not only for this test but also for other learning activities. In thisarticle, we contribute to the current understanding in this area by discussing a CollaborativeTeacher Inquiry Project that sought to improve the teaching and learning of Grade 9 AppliedMathematics by examining how teacher collaboration enhanced and shaped opportunitiesfor teacher learning. Especially, we chose Grade 9 since it is the beginning year of the highschool and also the year for the EQAO test. A university and four school boards in the GreaterToronto area in Canada agreed to focus on the teaching and learning of the Grade 9 AppliedMathematics program and to improve it through teacher collaboration. There were two tofour secondary schools per school board who participated in the project. The teachers hadan opportunity to meet and collaborate with other teachers who were also teaching Grade 9Applied Mathematics, both in their own school board and in the other three school boards.

Teacher collaboration has the potential to move the field of teaching mathematics forwardby energizing teams of teachers within schools to activate and guide teacher improvement,thereby sustaining the learning (Dallmer 2004). Hence, there is a need to increase our knowl-edge of collaborative inquiry, and to show how teacher practice can be enhanced through close

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The effects of teacher collaboration 191

collaboration with other colleagues. The outcome of this enhancement could be a meaningfulimprovement in instructional practice. The teachers and administrators in the project collab-oratively explored their teaching and learning process and they planned and implementedimprovement strategies together for Grade 9 Applied Mathematics courses. The overarchingresearch question for the project was: How could teaching and learning in Grade 9 AppliedMathematics classrooms be improved? In this paper, we propose and explore two sub researchquestions: (1) What types of in-depth interactions, mutual support, and professional learningoccurred during the project? (2) What are the benefits and challenges of collaboration to theteachers and the education system?

2 Collaboration in education

In education, the word collaboration is used to describe a mode of working together towardeducation reforms. It also describes a relationship that collaborative partners want to achieve.This relationship has been described as “working with, not working on” (Lieberman 1986,p. 29). In fact, parity and equality in this relationship are shared values. According to Johnston(1990), collaboration is a way to “increase quality, bridge the gap between theory and practice,and improve communication between universities and schools”(p. 173). A collaborative rela-tionship further implies that decision making is democratic (Hord 1986). Hence, decisionmaking at all stages of the work becomes an appropriate collaborative task (Oakes et al.1986).

The widespread terms that are used to explain collaborative approaches indicate varioustheoretical stances of researchers. Terminology that has been used frequently to characterizethese theoretical approaches include artisan communities (Talbert and McLaughlin 2002),collaborative learning communities (Cooper and Boyd 1997; Haberman 2004; Kasper 2000),communities of practice (Wenger 2007), and professional learning communities (DuFour2004; DuFour and Eaker 1998). Collaborative efforts within teacher education should beginwith a “recognition that multiple realities, voices, and discourses conjoin and clash in theprocess of coming to know” (Britzman 1991, p. 33). Working collaboratively means par-leying all the diverse positions and roles that people bring to the relationship. Collaborationdoes not mean giving up individual differences. Rather, it means that we must trust in thosedifferences to accomplish our mutually agreed purposes (Dallmer 2004). Collaboration hasthe possibility to provide “opportunities for reflection about practice, shared critique, andsupported change” (Clark et al. 1996, p. 196).

The significance of teachers’ collegial relationships as a factor in school improvement hasbeen widely reported in research (Horn and Little 2010; Hubbard et al. 2006; Little 1982;Louis et al. 1996; McLaughlin and Talbert 2001). Collaborative practice in teacher educationprovides personal and professional development for the participants. It also offers the oppor-tunity for professors and teachers to develop new ways of knowing and learning (Dallmer2004). In this way, research is converging on a common set of effective professional devel-opment characteristics and strategies that stem largely from concepts about communities ofpractice (Schlager 2000). In a meta-analysis of professional development initiatives, Wilsonand Berne (1999) concluded that effective collaborative efforts (a) involve communities oflearners redefining teaching practice, (b) seek to activate (rather than deliver) teacher learn-ing, and (c) support teachers’ interactions with one another. The collegial practices, whichconstitute the professional development initiatives in most studies, are considered separatefrom the daily work of the teachers involved. Some recent research studies have focused on

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the informally formed collaborative groups of teachers and the types of discourse that fosterteacher learning (Horn 2005; Little 2003a).

A number of studies have confirmed that, in secondary schools, the most efficacious com-munities tend to reside at the level of subject matter departments (McLaughlin and Talbert2001; Siskin and Little 1995). Within a department, teachers are socialized into a traditionwith its own norms of teaching, learning, grouping, and assessment which in turn shapetheir work and their students’ classroom experiences (Gutierrez 1996). Departments typi-cally have an infrastructure in place to allow for collegial work on professional projects likecourse modifications, implementing new curricula or learning about technology. Subgroupsof teachers often arise to meet short-term demands such as modifying or even creating newcourses of study (Gutierrez 1996).

Another potential of collaboration is the opportunity for reciprocal peer coaching whichenables teachers to observe one another and exchange support, companionship, feedback,and assistance in a co-equal and a non-threatening fashion (Ackland 1991). Unlike someother methods of collaboration, peer coaching is specifically designed to foster teachers’development and to test new instructional practices in the classroom (Joyce and Showers1982). Coaching allows teachers to reflect upon current practices, refine and expand theirinstructional capabilities (Robbins 1995). According to Showers (1985), coaching provides“a safe environment in which to learn and perfect new teaching behaviors, experiment withvariations of strategies, teach students new skills and expectations inherent in new strategies,and thoughtfully examine the results” (p. 47). In addition, peer coaching promotes skills thathave been associated with reflective and responsive teaching (Osterman and Kottkamp 1993;Zeichner and Liston 1987).

There are many benefits of teacher collaboration whether it is happening inside a schoolor between a school and other educational agencies. Collaboration provides teachers withprofessional development opportunities such as co-teaching, co-planning, and many otherpositive experiences. However, there are many impediments and constraints that make dif-ficult for the teachers to engage in interactions, to generate new insights into their teachingdilemmas, and to foster instructional innovations. These constraints include but are not limitedto the difficulty of making tacit knowledge explicit (Eraut 2000), the challenge of confrontingwell-established norms of privacy and non-interference (Little 1990), the disagreement anddifferences that have to be contended (Achinstein 2002; Grossman et al. 2001), the insuffi-ciency of structural and social supports (Louis and Kruse 1995), the invalidity of assumptionsabout learners and learning (Coburn 2006; Horn 2007), and the urgency of the teachers’ otherimmediate and multiple tasks (Kennedy 2005; Little 2003b). We acknowledge that these chal-lenges occur partly because individual knowledge, skills, experience, and dispositions arepart of the resources available to collaborative teacher groups and there are variations to theseresources within and across groups in potentially consequential ways. However, we arguethat the differences of success rates in various collaborative group discourses cannot only beattributed to the individual teachers’ personal and professional dispositions but it should beseen as resulting from each group’s collective orientation and its contextual resources andconstraints.

Based on the above ideas, we view our study not as making a general claim about allteacher collaborative groups but rather as contributing to the existing literature of the condi-tions conducive to instructional improvement in an urban school context. Our principal aimin this study was to advance understanding of the ways in which collaborative teacher interac-tions will provide the opportunities for teachers’ professional development, while improvingthe quality of student learning. In the forthcoming sections, we discuss the CollaborativeTeacher Inquiry Project and its implications in more detail.

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3 The Collaborative Teacher Inquiry Project

This project which spanned three semesters during 2009–2010 was a partnership between auniversity and four school boards in the Greater Toronto Area in Canada. The main objec-tive of the project was to work with a collaborative model that values consensus building, anapproach that is less hierarchical and top-down than a model that implies that one party shoulddefine the scope and breadth of the relationship between the university and the schools. Theuniversity was particularly concerned with the collaborative endeavor, as a way to set asidepower differences between the teachers and the administrators in the schools and to ensurethat all of the participants’ voices were heard.

From the four school boards, a total of 11 schools participated in the project. Partici-pants included teachers, department heads or curriculum leaders, and administrators. In eachschool, the mathematics implementation team comprised with an administrator, the depart-ment head of mathematics or the curriculum leader, and all participating teachers involvedin the project. The principal researcher and the coordinator of the project, a university pro-fessor, visited each school to talk to the mathematics implementation teams at the beginningof the project. These informal conversations focused on the agenda for the future. Some ofthe questions raised in the meetings were (a) What do the schools want to get out of thisprocess? (b) How do the schools improve their EQAO scores? (c) What are the benefits ofpeer coaching? and (d) How do the schools want to proceed for the remainder of the academicyear?

At the end of the first semester, participants attended in-service sessions and they were vis-ited by the principal investigator in their schools. Teachers recorded personal reflections abouttheir work so far in the project. Some of the in-service sessions were conducted by mathemat-ics consultants from the four participating school boards. A series of workshops were orga-nized for the teachers to get an opportunity to share ideas with teachers from other schools. Inthe in-service workshops, the participants were introduced to wiki technologies from whichthey could learn to share teaching resources. This website also provided participants with up-dates on the project and it was linked to professional development opportunities and teacherresources. The site was operated for the entire duration of the project and monitored by themathematics coordinators of the participating school boards and the university researchers.

In addition, some workshops for SMART Board technology and Geometer’s Sketchpadwere conducted for interested participants. These workshops allowed participants to exper-iment with the SMART Boards and learn valuable strategies on how to integrate technologyinto their lessons. The participating schools shared resources and strategies that had beendeveloped during the semester. At the end of the first semester, participants completed a surveyto reflect on their participation in the project. The survey asked participants to provide writtenanswers to questions about strengths, weaknesses, challenges, and benefits of the project.

During the second semester of the project, participants were invited to attend anotherseries of workshops facilitated by the mathematics consultants of the four participating schoolboards. These workshops were framed on specific strands in the curriculum where studentshad difficulties with the EQAO results. The third and the final in-service session targetedon issues of assessment and evaluation. The project administrators met separately to reviewtheir role as instructional leaders in implementing assessment and evaluation policies and todiscuss their progress and intentions for the remainder of the project and beyond.

During the third semester, a team of four researchers visited the schools and conductedindividual interviews with the department heads and participating teachers at each school.These 30–45 min interviews were focused on the background of the interviewee, vision ofsuccess, goals for students in mathematics and in general, school context, challenges, and

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participation in the project. All participants were asked the same series of questions (Appen-dix 1). The interviews were audiotaped, transcribed, and the data were analyzed using thequalitative data analysis software, NVIVO 8, to uncover prevalent themes. The six themes—achieving the goals, student success, professional development, co-planning and co-teachingopportunities, increased communication, and improved technological skills—were selectedas prominent themes based on their frequency of appearance in teacher interviews.

In the final phase of the project, the participants were asked to volunteer as a school teamto give presentations to fellow participants in the project and to highlight areas of the Grade 9Applied Mathematics program that contributed to increased student learning. The teams pre-sented the mathematical tasks and shared resources that they had created during the project.Some sections of student activities presented by a group appear in Appendix 2. In the finalday of the gathering, four distinguished researchers presented some current research trendsin mathematics education in Ontario for the benefit of the participants.

4 Results

Teacher collaboration occurred in four different levels in this project: collaboration withinthe mathematics department, within the school, within the school board, and between andamong school boards. Teachers worked together in groups formed by the courses that theytaught or as a whole department to focus on improving the mathematics program and meetingtheir school goals. Many teachers in this project described the outcomes and the impact ofthe project in many ways. They articulated the benefits, the challenges, and some solutionsto these challenges. We will discuss the gains of collaboration in the points of view of theteachers under the six themes: achieving the goals, student success, professional develop-ment, co-planning and co-teaching opportunities, increased communication, and improvedtechnological skills. As can be seen from the forthcoming discussion, these themes are inter-connected, not mutually exclusive.

4.1 Achieving the goals

One of the benefits that teachers received through collaboration was to achieve their collec-tive goals. They tried to redesign their programs to respond better to the interests of theirstudents and their particular classes. By this improvement, they tried to find new and betterways to communicate with each other and to achieve their common goals. One departmenthead explained how this goal was achieved.

I think the teachers in the math department would like to see students with an interestin doing problems and asking questions. The parents are also looking for a brilliantfuture for their children and I think they are aligned with our expectations and with ourgoals. (School J)

A teacher from another school stated that their mathematics department worked in agreementtowards the same set of goals. She said,

We get together at lunch. We talk and basically we exchange ideas and informationwhatever that is needed and we are all accepting the goals of each other. I think mygoals are well accepted in the department and the school. (School G)

As a result of the collaboration, teachers were able to formulate their department goalsand all the members of the department benefitted from this. They reiterated that the team was

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successful because of the energy that each member contributed to the team. They planned,delivered, and reflected together. Commenting on these issues, one teacher said,

We sit down and plan the units and pull out the activities that, we think as a team, willbetter work for the students and then afterwards reflect upon our work. So after eachunit, we sit together and reflect on what worked well, what did not work well, whatneeds to be changed, and what should be done differently in the next year. All thesetypes of reflections, I think, are great. (School J)

One of the teachers in another school mentioned that his goal was to make students inde-pendent learners. If it was difficult to make them love mathematics, he wanted them to becomfortable with mathematics.

My personal goal is to see my students become independent learners, to become self-learners. Also, I like them have some appreciation for math. Maybe I cannot expectthem to love math, but at least I would like them to feel more comfortable with math-ematics. (School C)

One teacher was interested in helping students to best achieve their personal goals. She said,

Just to achieve their personal best, whatever that might be, to be motivated, we wantthem to try at their personal best. They might see the personal outcome when they tryto perform at their best. (School C)

Teachers’ goals were sometimes influenced by parents’ goals. Teachers said that some ofthe parents were more interested in the academic success of their children. Therefore, therewas a disparity between goals as the teachers believed that their primary concern was to helpstudents to become better people as opposed to better mathematicians. One teacher describedthis conflict.

My general feeling is that the [parents] goal is for kids to pass the credit. I think mygoals are different. The parents focus on marks and pass rates. But to me, the mostimportant thing is to appreciate the subject and critical thinking, but generally it is verymarks-focused. (School I)

In achieving the goals, teacher collaboration within the mathematics department wascharacteristic as an ongoing, reflective process that supported participants to increase theirself-knowledge. This increase provided the basis for negotiation of new meanings. Anotheraspect of this negotiation was increased communication within the department and a tendencyto have a reflective dialogue on the goals. Sometimes, there were disagreements betweenteachers’ and parents’ goals. This mismatch was an indication of the disconnection betweenintentions of the parents and classroom realities. In a way, this was a hindrance to achievecommon goals.

4.2 Student success

One of the common goals of the teachers was to improve the quality of student learning.They believed that teacher collaboration is an integral part of creating a positive work envi-ronment where teachers work together to make way for students to achieve success. Oneteacher shared why all of their effort was worth the work.

Every school should strive to have students—each and every student working towardtheir full potential. Create an environment where you have people available who are

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willing to take the extra steps and have student success as their primary goal. We wantto have teachers working in this direction. (School E)

One school had benefited immensely by forming a collaborative partnership with otherdepartments within the school. They had an excellent cooperation between the mathematicsdepartment and the special education department, so that some identified students benefitedfrom the extra help. This cooperation was extended up to and beyond writing the provincialassessment test, EQAO. As this school had a high number of students with IndividualizedEducation Plans (IEPs), the teachers attributed part of the increase in their EQAO results tothe improved relationship they had during the project.

Another school established a core team to work together on everything, from lessonplanning to writing new activities for the EQAO test. The teachers reported that “our newGrade 9 Applied program is more cohesive and purposeful to address student engagementand achievement gaps” (School D). At another school, collaboration among the teachers inthe mathematics department provided them a chance to share their success stories with usand relay what the department had achieved. A teacher described how they transferred theirefforts to their individual classrooms.

The plan is created in terms of improving the passing rates and the EQAO scores,helping the students to practice and drill, and teaching them the concepts. Just try andsee what results we get from class to class. From there, we can see what strengths kidshave and emphasize those. I try to improve those by using different group activities,with more emphasis on teaching and practicing the concepts. (School C)

One team reported that collaboration within the department was productive in planninglessons and preparing common assessments. Another school had embedded more EQAOitems into their intended curriculum. Collaboration led to valuable learning for the teachersand progress for the students. The teachers were able to adjust the lessons and tests that oneteacher had taught earlier in the day and teach them in their classes. The team reported that, asa result, students were more engaged in their learning and their EQAO scores had improved.

A teacher said that collaboration with other departments in the school was necessary toensure student success. She described one such collaboration with the Special Educationdepartment.

We have a student success team and we have the Special Education team that we workcollaboratively. We target specific kids so we can make them successful by pullingthem out of the class and working one on one,… either in the resource room or inanother room or even before or after school. (School J)

In this school, the teachers conducted a mock EQAO test with the support from the resourcedepartment and other teachers to accommodate their schedules as well, especially for English.

Departmental collaboration was the key to student success. Under normal circumstances,this collaboration would not have occurred automatically. A concerted effort was necessaryto formulate a common goal—in this case—to raise the EQAO scores. The teachers wereable to interact frequently with each other and plan quality instruction by drawing on oneanother’s expertize through building up common practices. The power derived from a sharedvision, values, and beliefs had a great impact on this effort.

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4.3 Professional development

One of the benefits of teacher collaboration was the capacity to initiate and improve profes-sional development. One young teacher had enjoyed the opportunity to collaborate with col-leagues in the mathematics department and the impact it had on her professional development.She said,

Why reinvent the wheel when there is a lot of experience out there that you can learnfrom. Sometimes when I am confused about things like, ‘How do I write a communica-tion question that evaluates this, what does that look like? What makes this a thinkingquestion and not just sort of a random knowledge and understanding question?’ I mightapproach it that way. I have a lot to learn, so I see [myself] being involved in this projectand having some collaboration time is really helpful for me. (School D)

Many teachers involved in the project did not have prior experience of co-teaching orco-planning and they did not have much experience in collaborating with their colleagues.In a team reflection, teachers valued their new co-teaching experience as part of their profes-sional development.

This [collaboration] involved the Grade 9 Applied team planning the lesson and thenhaving one of them delivering the lesson while others were observing. Each co-teachingopportunity was followed by an opportunity to debrief and address issues found in thedelivery of the lesson. (School H)

In another school, the mathematics department was mainly comprised of veteran teach-ers and many of them had spent most of their career time at the school. The departmenthead described how he collaborated with less experienced teachers who may need additionalsupport to improve their professional practice. He explained some guidance methods in hisschool-based professional development plan.

I have been teaching long enough, that I know how to teach my own classes prettywell. Working with some of the newer teachers, that is a bit of a challenge; becauseI can see issues they have in motivating their students. [I am] Just trying to help outwithout telling them what to do, just guiding them. (School K)

For the benefit of some veteran teachers in his staff, the department head operated a dif-ferent plan. He encouraged them to try new strategies and initiatives to improve their skills,hoping that communicating with some of their more traditional colleagues, comfortable prac-tices could get uprooted. He said,

Some of my [veteran] teachers are using things that were not necessarily used a coupleof years ago. Because of this project, I see a couple of my teachers using SMARTBoards, and they say, ‘Can I try that?’….. so it is kind of interesting. (School K)

One teacher said that she enjoyed the opportunity to learn from colleagues in other schoolboards and collaborate with them in professional development sessions. The opportunity todiscuss ideas, trade resources, share success stories, and hear about what was happening inother schools and school boards was invaluable for her. Another teacher said that the impactof this project and the chance to dialogue with other teachers across the four school boardsimproved her teaching practice. She mentioned that her school’s EQAO results jumped sig-nificantly in the last year and it was mostly because of the collaboration with other schools,other boards, and other teachers. The teachers also shared assessments, workbooks, and otherresources with other schools in the board.

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These opinions indicated that shared disposition toward improvement is necessary for col-laboration to yield opportunities for professional learning. This opportunity stimulated notonly novice teachers, but also veteran teachers to experiment with new teaching methods.The collaborative conversations called on teachers to make their goals, strategies, issues, andconcerns public what has otherwise been private. The discussions gave teachers someoneto talk to and to improve their classroom practices individually and collectively. An impor-tant result of this interaction was that each teacher was able to access the ideas, materials,strategies, and talents of others.

4.4 Co-planning and co-teaching opportunities

Teachers believed that planning together had lightened their workload and increased theirefficiency. One teacher described how collaborating with a colleague who was teaching thesame course transformed the difficulty of incorporating technology and other resources easierto handle. She found more time for preparations, such as putting the desks together for groupwork or even laying out the materials before the students arrive in for the next class, whenshe worked with another teacher.

Another teacher described how he discovered the value of collaboration along with theshift at the school. He shared what can be learned by visiting other teachers doing the samelesson.

I think what supports success in mathematics is the teachers’ collaboration. That ishuge. For example, with this program, we did a teacher inquiry thing, where we wentto each other’s classroom and that was really interesting because then, to see someoneelse teach the same lesson that you have done, to create the dialogue... and you canactually get some improvement. (School I)

Another teacher at this school shared how he benefited from collaborating with othermathematics teachers.

I think collaboration and support amongst teachers, especially teaching the same courseis very successful in improving mathematics. That is a kind of encompassing a lot ofthings……collaboration with other teachers. You start planning together; you startco-planning….. perhaps, co-teaching. (School I)

Teachers also believed that there need to be some collaboration between secondary schoolsand their feeder elementary counterparts, since there were no programs in place to have suchlong-term collaboration with feeder schools. One head of department believed that this col-laboration is important because they need to discuss what their curriculum looks like toothers. His school had tried this once or twice before, but it had not been sustainable.

4.5 Increased communication

The teachers in the project talked about what they had accomplished as a group by communi-cating with the administration to gain support for the project. On their turn, the administrationprovided them with additional resources and professional development opportunities. Theteachers believed that an open line of communication is important. One teacher said,

The administration is wonderful. If we need any resources and if you have some fan-tastic ideas, bring it on to the table or if you need to communicate with parents or

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reducing class sizes, they were more than willing to accept our ideas, rearranging ourschedules to mark EQAOs and so on. Again, they were very generous when we werecommunicating and having the kids moving from one level to the other which is verydifficult. So they are more than willing to help us to deliver this to parents. You know,‘This kid is at a particular level and need to be moved’. So again, there was consensus.We communicate with each other. (School J)

A teacher said that within their school board, there is an initiative called TransformationalPractices and this program opened the lines of communication between secondary and feederschool teachers to ensure that students have a smooth transition between the two divisions.She explained,

I am involved in Transformational Practices, where we go to feeder schools and try tocollaborate with them and see what they can do to prepare students for high school.They give us feedback on what the students are like when they come to high school,what are they thinking, or where they are at, at this or that skill level and stuff like that.I think that is a good program. (School B)

One of the teachers highlighted the importance of increasing communication within thesubject. He said that he attempted to improve student organization and discipline to commu-nicate mathematics clearly. He was of the view that course passing rates and EQAO scoresare correlated.

We want to improve the passing rates and the EQAO rates. I see them hand in hand. [Stu-dents] need to have organization and discipline in order to communicate their thoughtsclearly. Another goal is to improve their thinking and communication categories ontheir tests and on their EQAO scores. (School B)

In the conversations, teachers discussed about managing different levels of communi-cation. Some teachers were eager to communicate within their department, while otherspreferred to have a dialogue with the administration. Another level of communication wasbetween schools to get to know the academic level of their incoming students. Teachers usedincreased communication strategies to narrow down their broad objectives and to have acommon shared vision. Effective leadership in their schools immensely contributed to theteachers’ efforts through mobilizing resources and ideas.

4.6 Improved technological skills

Many teachers involved in the project reported that they had opportunities to enhance theirtechnological skills to improve their teaching. One school used the resources that their schoolboard had officially provided to improve the Grade 9 Applied Mathematics program. Theteachers said that they “collaborated with a math coach from the school board to co-plan aninteractive lesson on solving equations using both the Targeted Implementation and Plan-ning Supports (TIPSs) resource and the interactive Gizmos on the www.explorelearning.comwebsite” (School D).

Another teacher said that they found their school board and their resource personnel to bevery supportive. The teachers described this support as individual. A teacher said,

[A resource person] comes from the board. We communicate with her… She did theSMART Board with us and gave us many resources and we just shared with her expert-ize on this area. So we definitely have the board’s support. (School J)

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www.explorelearning.com


The Collaborative Teacher Inquiry Project also allowed teacher participants to work withtheir counterparts from other school boards. A teacher stressed how this component helpedher to improve her technological skills.

We have a wiki from this project where we post our resources and tasks. The teach-ers are collaborating with other teachers, and trying to work towards the same goal,basically, how to get students to be more successful. (School B)

The teachers at school A mentioned that technology was their principal concern. Threeyears ago, a computer lab especially designed for mathematics classes was opened. One ofthe teachers mentioned how they made use of these facilities.

In our math department, all our teachers use technology. We use new methods. Any-thing is new, we are adapting and we are doing. We have a math department that iswilling to try new things that are adaptable. (School A)

Further, the teachers from this school confirmed that technology is an important way to makemathematics more engaging for students. One teacher explained that they made changes inhow they used technology.

We transitioned from ‘teaching from the textbook using repetition of exercises’ towards‘using an investigative approach with technology, in particular with graphing calcu-lators, and experimental discovery with manipulatives while working collaborativelywith peers’. We have had some success with teaching in computer lab settings andusing Smart Technology. (School A)

The team listed the use of technology and manipulatives was the most successful strategythat they implemented in their Grade 9 Applied Mathematics classrooms.

This discussion elaborated that using technology not only improved teacher communica-tion through online forums and other methods, but also paved way to co-planning and sharingvisions. There was no doubt that technology made the teaching easy and manageable. Fur-thermore, students were the recipients of new methods of instruction by getting exposed totechnology. This would not have been possible unless the teachers had improved their tech-nological skills through participating in this project. Therefore, these schools had developedthe collective capacity of their staff by achieving a coherent focus and developing teachers’skills to improve the quality of ongoing instruction.

5 Challenges

We do not claim that the project was successful in every aspect of learning improvement. Theparticipants and administrators faced many challenges. One school realized that their math-ematics department was not very popular within the school community and there was a needto make an effort to show its presence in the school community. The mathematics teachersin this school said that the departments in their school are often segregated and the teachersshould reach out to make connections with the administration and other departments. Thischallenge was posed by lack of communication within the school.

Some teachers said that “finding time to prepare lessons collaboratively” was a challenge(School B). Also, collaboration was not possible without respect for each member’s pro-fessional practice. The teachers were concerned that changes in staff affect collaboration.They said that “staffing (keeping the team intact) and training new members as they comeon board” (school D) were a challenge. Since collaborative inquiry with co-teaching/peer

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coaching was new to many of the mathematics teachers involved in the project, they requiredtime and space to flourish and grow. A department head metaphorically implied that theirschool is in fertile soil but if there are too many farmers and the administration keeps chang-ing the workers, then the sustainability of the project would be in danger. Even though theteam wants to work collaboratively, they are unable to create a cohesive unit if their group iscontinuously changing. The team said,

There has been a high turnover in the makeup of the team and it was very difficult tomaintain consistency and momentum. Only one of our Grade 9 Applied teachers is thesame for both semesters. The changes to the administration have not contributed to astable, supportive environment for the work of the team. (School G)

Another challenge was adding new members to the team. Some teachers echoed that con-sistency of the mathematics team is integral to the success of the collaborative group. Theysaid that if new members are to be added to the team, it should be done gradually with thesupport of the already existing members. For adequate planning, there is some support thatneeds to be given to the teachers. Although teachers enjoyed working collaboratively withtheir colleagues, they found that sustaining or maintaining a core team of teachers was achallenge in achieving progress. They acknowledged that they may not be in control of thischallenge, as course assignments change and teachers move to other departments or schools.Therefore, working as a core team is demanding and draining, because teachers may quicklymove on to other initiatives.

Another challenge for the teachers was to instill a similar collaborative spirit with otherteachers who were not involved in the project, since some of the other teachers did not showmuch enthusiasm of involvement. For instance, some teachers mentioned the difficulty ofpersuading others, even to share the activities that worked for them, because they were notinterested in sharing. Similar initiatives to collaborate with other courses were also not effec-tive. One reason was that the other teachers were not teaching the same lesson with them orsimply did not have time. Sometimes, they faced resistance from other departments whenseeking out opportunities to collaborate. A teacher shared his experience.

Some of the resistance comes from some teachers not knowing exactly how to cooper-ate. They feel that math does not feed into their curriculum. We have to find examplesto prove our point. With Science, it is easy to prove that it is linked with math. ButGeography, Civics, everything has to do something with math. The kids have to dealwith some basic math. It is similar with literacy. Everybody has to do with literacy aswell. (School E)

The mathematics implementation team in one school was concerned that after the studentswere exposed to alternative teaching strategies and assessments through the CollaborativeTeacher Inquiry Project, they will struggle in the future if the methods that they were usedto practice get changed. Therefore, more collaboration within the department with teacherswho teach different grade levels would be necessary because there may not be a continua-tion of many of the current alternate assessments into Grade 10. To sum up, continuity andconsistency were a practical obstacle for most of the teachers.

Some teachers went beyond the project itself and mentioned about their day-to-day chal-lenges. Their interactions with other teachers in other schools were on a casual basis atin-service sessions. For instance, they said that there were no formal opportunities to shareideas, resources, or teaching strategies. One teacher expressed that there was not enough timeto collaborate with colleagues at other schools within the same school board at in-service

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sessions. Nonetheless, teachers had invented some casual mechanisms for keeping in touchand follow some of the board’s trends.

Another complaint was the lack of resources. A teacher described that teachers within hisschool board learned about the lack of resources through inter-school e-mails.

There is this whole, grass is greener on the other side mentality where we kind ofthink that the …… board (another school board) has better access to technology, if youlook at technology specifically. The last five e-mails in my inbox were from teacherslooking for textbooks, so I think we are probably pretty similar. (School I)

The teachers’ enthusiasm to articulate the problems that arose in their day-to-day practiceindicated the level of their discomfort. There feeling was that a strong will was necessaryto overcome these challenges. These problems were interconnected in such a way that theypropagated beyond the school level. Lack of proper coordination and resources is a problemthat has to be addressed by higher authorities. Transforming the culture and habits of peoplewas the main challenge that was echoed. Were these teachers had a sense of resignation, inwhich they believed that their individual and collective actions cannot improve teaching andlearning? Based on our overall observations, we conclude that this was not noticeable to us.

6 Overall discussion

The Collaborative Teacher Inquiry Project aimed to make available new perspectives andpossibilities in teacher education by providing opportunities for the voices of the school edu-cators to be heard, and to influence decisions made by individual schools and school boards.Such a collaborative effort required participants to shed power differences and suspend thenorms and assumptions that had traditionally sustained both in isolation and in hierarchicalrelationships. It also required a willingness to listen deeply to others’ points of view and toentertain new possibilities. Most typically, teachers are the objects, rather than the agents,of their professional development. In our project, we allowed the teachers to be their ownagents of professional development. The teachers’ sentiments indicated that organized effortis necessary to make collaborative work successful. This effort should arrive from outside,as teachers simply may not have time or the organizing capacity to do this by themselves.

In our project, teachers inquired together into their practice; this inquiry provided a struc-ture that enhanced opportunities for them to grow both professionally and personally. More-over, the work was viewed by the participants as a good professional development opportunityto reflect on what teaching is all about, in a way not normally possible otherwise. Also, teacherinteractions in our project were in a rich manner because the dialogue was across schools,school boards, and the university. For these reasons, we believe that the project enabled theparticipants to develop new skills and attitudes.

In this article, we had attempted to convey the views of the teachers who were involvedin bringing changes to their daily practices through collaborating with others as opposed to“teacher isolation” (Dufour et al. 2005). We designed our project in a way that teacher col-laboration has to happen in many levels: with others in their department, with others in theirschool including the administration, within their school board, with other school boards, andwith the university. Our assumption agrees with Schmoker (2005), who said, “Teachers donot learn best from outside experts or by attending conferences or implementing programsinstalled by outsiders. Teachers learn best from other teachers, in settings where they literallyteach each other the art of teaching” (p. 141).

As Ma (1999) observed, US teachers usually have very limited time outside the class-room to study carefully what they have to teach. The situation, as we believe, is not any

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better in Canada. This problem contributes to the gaps in teachers’ pedagogical contentknowledge.

The six themes that we studied were interconnected in many ways. Student success was themain aim of the project. Teachers used co-planning and co-teaching techniques with increasedcommunication activities to achieve this goal. Teachers’ professional development was themajor outcome of this exercise, and one of the co-achievements within that outcome was theimprovement in their technological skills. The whole process ultimately contributed towardsstudent success. In short, this project helped novice teachers to improve their pedagogicalskills, veteran teachers to experiment on new methods, administrators to rethink about theirstrategies, university professional to extend their knowledge on teacher collaboration, andstudents to be successful.

Constructivist approach to change is based on collaboration rather than compliance (Wag-ner 1998). As proposed by the National Council of Teachers of Mathematics (1991), theschool culture created through this project transformed the teaching model from a “trans-mission” to a “transaction” mode. This is in line with the constructivist views of teaching.Our findings suggest that the distribution of collaborative functions across a school, givenadequate time and resources to handle the tasks, could provide the capacity, coherence and,most importantly, the ownership necessary to sustain and deepen reforms. Further, as artic-ulated by Schoenfeld (2002), we were able to provide high quality mathematics instructionto the students by creating a knowledgeable and professional teaching community and pro-ducing high quality assessments that were aligned with curricular goals. We believe thatworking in the project was a constructivist exercise for the teachers since they constructedtheir professional development program for achieving student success.

With the help of inquiry groups, teachers were able to identify special contextual issuesthat influenced collaboration. They felt that collaboration was important between the second-ary schools and their feeder schools. This collaboration helps to provide a smooth transitionof students between the two divisions. To overcome the difficulties of collaboration within thedepartment, teachers suggested that an effective way to deal with this challenge is to ensurethat the teachers planning for the same course should have the same preparation period. Theyreiterated that it is highly impractical to offer teachers to take time away from classes to plan.Even though this is still worth and it works well for specific lessons, taking time out of theclass eventually will have diminishing returns. Another suggestion was to allow teachers toco-plan during their professional development days or staff meetings.

From our project, we identified some common themes that were challenging to collabora-tion. They were the difficulty of initiating innovations without outside help, developing andapplying shared knowledge, sustaining the changes, updating the existing policies, programs,and procedures, coping with various degrees of motivation, transforming the beliefs, assump-tions, expectations, and habits of people, and managing power imbalances among differentgroups. We also found that the most important aspect of the sustainability of collaborationwas the commitment and persistence of the teachers within the team and their accountabilityto self and to others. In this way, the participants felt more secured and less isolated.

University researchers also faced several challenges during this project. Our main chal-lenge was maintaining the coherence among different participating bodies, such as schoolsand school boards. We usually expected equity and collaboration across these various insti-tutions. Although we all had similar goals in the project, we realized that expecting equityand collaboration across school boards was not always possible, since these institutions func-tion on different agendas. Finally, the solutions to these challenges would sometimes spreadbeyond the school level. As Fullan (2005) said, the responsibility of collaboration lies on threelevels: school/community level, district or regional level, and state or provincial policy level.

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Appendix 1

Teacher questions

Background questions

1. What is your name?2. What courses are you currently teaching or what is your role in the school?3. How long have you worked at this school?4. Where did you teach before and what courses have you taught?5. How many years have you been teaching?6. Where did you go to university?7. Why did you become a teacher?

1. Vision of success

For you, what counts as success for students in this school?What are your goals for students in education?How widely accepted are your goals with other teachers in the department? Theschool? Among parents?In what ways do you see your goals for students reflected in your school improvementplan?How does your school improvement plan incorporate your goals for students?How is the school improvement plan created in this school?

2. Challenging circumstances

What are the most challenging things for you in this school as you go about yourwork?Do you think this school is different from other schools in its challenges?How would you describe the community of parents with whom you work?How has the school context changed over the past few years, and what changes aregoing on now?

3. Mathematics

How would you describe your goals in mathematics?How widely accepted are these views in the department? In the school? Among theparents?How would you describe the provincial ministry’s vision of mathematics?Which of the Ten Dimensions has your department selected for your school improve-ment plan? Why did you select those dimensions?Which of the Ten Dimensions have you selected for your personal growth? Why werethose dimensions selected?

4. School culture

How do you create an environment, which supports success in mathematics?What challenges have you faced in trying to create a culture that supports studentachievement in mathematics?How do you work with staff and administration to develop the goals/vision of theschool?

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5. Overall

What programs or resources support success in mathematics outside of the classroom?What do you think we should say in our report about how schools can be more effectivein supporting mathematics improvement?

Appendix 2

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The effects of teacher collaboration in Grade 9 Applied Mathematics

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