Effective Professional Development for Teachers of Mathematics: Key Principles from Research and a Program Embodying These Principles Doug Clarke Australian Catholic University (Melbourne, Australia) Barbara Clarke Monash University (Victoria, Australia) Abstract A variety of curriculum and policy documents around the world have promoted a vision for mathematics teaching and learning that has growing support from the mathematics education community.
There is increasing recognition, however, that without carefully planned professional development programs, the chances of idespread implementation of these exciting reforms is small. Support is essential for practising teachers who express an interest in teaching in a more “constructivist” way, with all that such teaching implies in terms of content, pedagogy, and assessment. This paper offers Strand II of the Study ten important principles from the research literature that can be used to guide the planning and implementation of professional development programs.
This is followed by a discussion of the key features of a research and professional development program, the Early Numeracy Research Project (ENRP), in Victoria Australia. This project involved 70 schools, 350 teachers of five- to eight-year olds, and over 11,000 students. Information is provided on the three main components of this project: research-based growth points in young children’s mathematics learning; a one-to-one, task-based assessment interview; and a multi-level professional development program.
The content and structure of the professional development program of the ENRP are then discussed in relation to the ten principles. Ten Principles from Research on Effective Professional Development Schlechty (1983) bserved that professional development can serve an “establishing” function to function to improve the individual teacher’s practice. The latter purpose will underpin the content of this contribution to the Study. An extensive review of the literature resulted in a list often key principles for professional development programs.
Although the evidence for their inclusion will not be elaborated here (see Clarke, 1994; Clarke, 2003, for a more detailed discussion), the research literature is clear that these features of a professional development program increase the ikelihood of the long-term professional growth of teachers: 1 . Address issues of concern and interest, largely (but not exclusively) identified by the teachers themselves, and involve a degree of choice for participants. 2.
Involve groups of teachers rather than individuals from a number of schools, and enlist the support of the school and district administration, students, parents and the broader school community. 3. Recognise and address the many impediments to teachers’ growth at the individual, school and district level. 4. Using teachers as participants in classroom ctivities or students in real situations, model desired classroom approaches during inservice sessions to project a clearer vision of the proposed changes. . Solicit teachers’ conscious commitment to participate actively in the professional development sessions and to undertake required readings and classroom tasks, appropriately adapted for their own classroom. 6. Recognise that changes in teachers’ beliefs about teaching and learning are derived largely from classroom practice; as a result, such changes will follow the opportunity to validate, through bserving positive student learning, information supplied by professional development programs. 7.
Allow time and opportunities for planning, reflection, and feedback in order to report successes and failures to the group, to share “the wisdom of practice,” and to discuss problems and solutions regarding individual students and new teaching approaches. 8. Enable participating teachers to gain a substantial degree of ownership by their involvement in decision-making and by being regarded as true partners in the change process. 9. Recognise that change is a gradual, ifficult and often painful process, and afford opportunities for ongoing support from peers and critical friends. 0. Encourage teachers to set further goals for their professional growth. The Early Numeracy Research Project: A Successful Professional Development Model The Early Numeracy Research Project (ENRP) was established in 1999 by the Victorian Department of Education, with a focus on the first three years of school (typically involving five- to eight-year olds). The project was funded to early 2002 in 35 project (“trial”) schools and 35 control (“reference”) schools (see Clarke, 2001 , for more etails).
There were three main components of the ENRP, all focused on enhancing teachers’ knowledge and therefore their practice. A framework of research-based “growth points” provided a means for teachers to understand young children’s mathematical thinking in general, a one-to-one, task-based assessment interview provided a tool for assessing this thinking for particular individuals and groups and therefore information on achieved growth points, and a multi-level professional development program was geared towards developing further such thinking.
Each of these three components is now discussed. It was decided to create a framework of through these growth points in trial schools could then be compared to that of students in the reference schools. The project team studied available research on key “stages” or “levels” in young children’s mathematics learning (e. g. , Clements, Swaminathan, Hannibal, & Sarama, 1999; Lehrer & Chazan, 1998; Wright, 1998), as well as frameworks developed by other authors and groups to describe learning. There were typically five or six growth points in each mathematical domain.
For example, Counting All and Counting On are two important growth points in children’s eveloping understanding of Addition. A one-to-one assessment interview with every child in trial schools and a random sample of around 40 children in each reference school at the beginning and end of the school year, over a 30- to 40-minute period. The disadvantages of pen and paper tests have been well established by Clements & Ellerton (1995) and others, and these disadvantages are particularly evident with young children, where reading issues are of great significance. The face-to-face interview was an appropriate response to these concerns.
The professional development program occurred at three levels. The 250 or so teachers from trial schools met with the research team each year for around five full days, spread across the year. The focus of these days was on understanding the framework and interview, and on appropriate classroom strategies, content and activities for meeting identified needs of students. Many teachers commented that their own mathematical knowledge has been enhanced considerably as they had focused on children’s mathematical thinking. Readings were provided, as were follow-up tasks, for later sharing.
In addition, Early Numeracy Coordinators from the trial schools met for an dditional three days each year, and the principals for two days. The focus of these days was on finer grained data analysis and school leadership roles within the ENRP. The following table gives examples for each year of the project of the kind of content addressed in the teachers’ professional development program, using five broad headings: 1999 2000 2001 Knowledge of how children learn mathematics developing key ideas underpinning counting young children’s play and spatial concepts where do ideas of patterns and notions of equality lead?
Collecting and analysing information on individual and group understanding of athematics rich assessment tasks in measurement ongoing assessment looking at our class data in groups Pedagogical content knowledge (the “intersection” of mathematical content and short, flexible mathematics games using materials and manipulatives in mathematics multiple intelligences and the mathematics classroom Implementing design elements for change parent participation in mathematics learning insights from mathematics additional assistance specialists planning in professional learning teams Teachers’ personal knowledge of mathematics principles of measurement two-dimensional geometry uilding my own knowledge of number It will be evident that the program focused on knowledge for teaching. On five occasions each year, the teachers met in regional cluster groups of four to five schools for two hours after school. One member of the university research team was responsible for each cluster group.
The focus of these meetings was to complement the statewide professional development. The third level of professional development took place at the school and classroom level. The cluster coordinator (a member of the research team) visited each school approximately three times per year, spending ime in classrooms team teaching or observing, participating in planing meetings, jointly leading parent evenings, and acting as a “sounding board” for teachers, coordinators and principals. Also, the Early Numeracy Coordinator at each school conducted weekly or fortnightly meetings of the “professional learning team,” to maintain continuity, communication, team cohesion and purpose.
Teachers’ Stated Professional Growth Given the successful efforts of trial school teachers in developing children’s mathematical skills and understandings (see Clarke, 2001 for a discussion of the data ndicating significant differences in all mathematical domains at all grade levels between trial and reference schools), teachers were asked to identify changes in their teaching practice as a result of their involvement in the project. Common themes, in decreasing order of frequency were: More focused teaching (in relation to growth points). Greater use of open-ended questions. Provision of more time to explore concepts. Greater opportunities for children to share strategies used in solving problems. Provision of greater challenges to children, as a consequence of higher expectations. Greater emphasis on “pulling it together” at the end of a lesson.
More emphasis on links and connections between mathematical ideas and between classroom mathematics and “real life mathematics”. Less emphasis on formal recording and algorithms, allowing a variety of recording styles. Teachers were also asked to necessarily reflected in movement through the growth points. Although the research team had a great interest in cognitive growth as demonstrated by the response to interview tasks, important growth can take other forms. Common themes were the following: Children are better at explaining their reasoning and strategies. Children enjoy maths more, look forward to maths time, and expect to be challenged.
There is a development of greater overall persistence. Children are thinking more about what they have learned and are learning. All children are experiencing a level of success. Links Between the ENRP Professional Development Program and the Ten Principles In this section, each of the ten principles will be addressed briefly in relation to their embodiment in the Early Numeracy Research Project. 1 . Addressing issues of concern. At all stages of the project, teachers’ input was sought and acted upon in elation to professional development content. At all full-day professional development, at least one-third of each day involved a choice of sessions. 2.
Groups of teachers and links to school administration and community. Every teacher involved in mathematics in the first three years was involved, as were principals and numeracy coordinators. Each school ran two parent evenings each year (one a parent information night, one a “family mathematics night”). 3. Addressing impediments. Teacher knowledge in all its forms was initially an impediment to change, but, as iscussed, the professional development program targeted this knowledge. Time was potentially another impediment, but this was acknowledged in providing all teachers with two to three days twice per year to interview their children. 4. Modelling classroom practice.
Although most professional development involved 250 teachers at once, the use of break-out rooms meant that teachers could experience the kind of classrooms that the research team and they were working towards. The interview also modelled the kinds of interactions that were to become increasingly common in lassrooms, with its focus on eliciting student thinking. 5. Soliciting commitment. All schools volunteered for the project and were selected from over 400 who applied. There was an extremely high level of commitment to the project as teachers saw the potential and actual benefits. 6. Validating new approaches through classroom practice. It was recognised that participants needed the opportunity to try out new approaches, with appropriate support.
Numeracy Coordinators, supported by 576 visits to schools by the project team spent much time in classrooms, offered crucial support, modelling, and feedback. 7. Time for planning, reflection, and feedback. Regular meetings provided this opportunity. Increasingly, teachers conducted professional development for colleagues. 8. Ownership. Teacher feedback indicated that they believed themselves to be true partners in the change process, and were decision makers at the school and state level. 9. Change is gradual and difficult. The support and the time scale of the project acknowledged this understanding. 10. Setting future goals. During the last year of the project, considerable time was given to the issue of schools continuing the momentum, once the research team support as withdrawn.
We trust that the reader has seen evidence of the match between the ten principles and the ENRP professional development program, and has a sense growth points and student interview, in facilitating the professional growth of teachers and student learning. We believe that the ten principles offer an important contribution to the Study, and the ENRP professional development program provides a model of these principles in action. References Clarke, D. M. (1994). Ten key principles from research for the professional development of mathematics teachers. In D. B. Aichele & A. F. Croxford (Eds. ), Professional development for teachers of mathematics (pp. 37-48). Reston, VA: NCTM. Clarke, D. M. (2001). Understanding, assessing and developing young children’s mathematical thinking: Research as powerful tool for professional growth. In J. Bob’s, B. Perry, & M. Mitchelmore (Eds. , Numeracy and beyond (Proceedings of the 24th Annual Conference of the Mathematics Education Research Group of Australasia, Vol. 1, pp. 9-26). Sydney: MERGA. Clarke, D. M. (2003). Effective professional development: What does research say? (ACU/CEO Research Monograph Series). Melbourne, Australia: Mathematics Teaching and Learning Centre, Australian Catholic University. Clements, D. H. , Swaminathan, S. , Hannibal, M. A. Z. , & Sarama, J. (1999). Young children’s conceptions of space. Journal for Research in Mathematics Education, 30(2), 192-212. Clements, M. A. , & Ellerton, N. (1995). Assessing the effectiveness of pencil- and-paper tests for school mathematics. In MERGA (Eds. , Galtha (Proceedings of the 18th Annual Conference of the Mathematics Education Research Group of Australasia, pp. 184-188). Darwin: MERGA. Lehrer, R. , & Chazan, D. (1998). Designing learning environments for developing understanding of geometry and space. Mahwah, NJ: Lawrence Erlbaum. Schlechty, P. (Ed . ). (1983). Understanding and managing staff development in an urban school system. Washington, D. C. : National Institute of Education. Wright, R. (1998). An overview of a research-based framework for assessing and teaching early number learning. In C. Kanes, M. Goos, & E. Warren (Eds. ), Teaching mathematics in new times (Proceedings of 21st Annual Conference of the Mathematics Education Research Group of Australasia, pp. 701-708). Brisbane: MERGA.