Problem Solving Task Centres
and the
Professional Development of Mathematics Teachers

Margarita Pavlou & Doug Clarke Mathematics Teaching and Learning Centre

Australian Catholic University (Christ Campus), Oakleigh, Victoria, Australia

Abstract

In the past ten years, there has been a considerable growth in the development of mathematics task centres across Australia and, more recently, the United States, New Zealand, and the United Kingdom. In this study, thirteen teachers, all experienced in the use of problem solving task centres, were interviewed by telephone. The focus of the interviews was on the perceived benefits to teaching and the professional growth of teachers, and to staff collegiality within schools, from the establishment and maintenance of the task centres. All respondents were positive about individual and group benefits of such task centres. In particular, teachers spoke of the opportunity that task centres provided to explore the teaching of problem solving, to encourage the development of problem solving strategies, to broaden their view of mathematics and their notions of what it means to "do mathematics", and to work collaboratively on establishing a "risk-taking atmosphere" in their teaching and in the learning environment which they offered to their students. An important additional feature of the teachers' responses was their comments on the role of tasks and task centres in enhancing their own view of mathematics,their mathematical content knowledge, and that of their colleagues.

Introduction

What are Tasks?

A task in these centres is a mathematical problem, typed or written on a card, and usually accompanied by manipulative materials which may be of assistance in solving the problem. These manipulative materials include for example counters, cubes, plastic animals, dice. The tasks are usually stored in sturdy plastic boxes, or large plastic bags, and each task is coded by the teachers according to mathematical content area(s) and difficulty level. The tasks are intended for the use of students from K-10, with the greatest use occurring in the middle school years, grades 5-8. The tasks address a wide range of major mathematical content, including number, measurement, chance and data, geometry, algebra, and logic. The sample task cards shown in Figure 1 give a sense of the style of a typical task:

Coloured Cubes

Arithmagons 1
Figure 1. Two sample task cards

What is a Task Centre?

Schools which develop task centres usually build up a collection of tasks, which are usually stored in a Task Centre or Problem Solving Task Centre. In many cases, schools establish a single room where all tasks are stored, and different classes are timetabled for regular sessions (e.g., once per week) in the room. Alternatively, but less commonly, teachers bring a sample of the tasks into class for use with students. In both situations, teachers choose to either focus on a particular mathematical content area in a given session (choosing tasks for students which relate to this topic) or systematically move students through the tasks, not particularly through a given content area in a given session. The Curriculum Corporation's Task Centre Project, has supplied tasks for over 400 schools in establishing their task centres. Of these, 71 are in the United States, 6 in New Zealand, and 3 in the United Kingdom. Of these, close to half are primary schools, the remainder being high schools, middle schools, regional centres, or universities responsible for preservice and inservice programs for mathematics teachers. Doug Williams, the Project Officer, reported that in around half of these cases, the Curriculum Corporation had provided a one-day intensive inservice program, in order for staff to familiarise themselves with the nature and purpose of the tasks. More detail on this program is given in a later section. Estimates by "key players" of the number of task centres with no particular connection to the Curriculum Corporation vary from around 50 to 400. No data are available to clearly establish this figure. During a task centre session, students typically work in pairs, with a given task taking anything from 5 to 30 minutes, depending on the level of complexity and the students' degree of understanding. Teachers usually change the pairs every few weeks, some taking the opportunity to pair stronger and weaker students, or to put students of similar capability together on occasions. One teacher commented that changes were necessary because "they get into a rut, get used to each other, and if one is not working as well as the other, they will leave the workload to that second person" (GL, 14/9/94). Many teachers begin a task centre session with a whole-group task (sometimes called a "clinic"), providing the opportunity for students to see and to value a wide range of problem solving strategies. The bibliography following this paper includes a large number of papers where authors who have a major involvement in Task Centres describe how their task centres "work", and the many issues involved in establishing and maintaining a task centre. In this paper, however, the focus is on the perceived benefits of the task centres for teacher professional development and collegiality.

Method

The Sample

Using the Curriculum Corporation data base of task centres which have been established around Australia, a sample of thirteen was drawn for this study. These schools and task centres were chosen to represent a variety of grade levels, states and types of uses of the tasks. All respondents had been using tasks for a minimum of one year, with more than half the respondents having used tasks for at least five years. This range of experience enabled the focus of the study to be on both early attempts to use the tasks, while also drawing upon the considerable experience of other respondents. Table 1 gives a breakdown of the various schools and teachers involved in the study, as well as the experience of the respondents with task centres. In Australia, primary schools generally cover grades K-6 or K-7; and secondary schools cover grades 7-12 or 8-12. From the table, it is clear that the sample includes four schools who had recently completed their first year of the use of the tasks. This group had the potential to provide current data on the challenges (and benefits) faced by those using the tasks for the first time.

Methodology

Given the many demands on teachers' time, it was decided by the study team that recorded telephone interviews which could be later transcribed would only require minimal time commitment by teachers, while providing useful data. Having had the methodology explained, all teachers in the study agreed to participate in the telephone interviews, and were aware that these conversations would be recorded. An initial contact was made by phone, during which the purpose of the interview was explained, permission for involvement given, and a subsequent appointment for an extended interview was made. The interviews were all conducted by Margarita Pavlou and were semi-structured, with the basic framework of the interview following the outline given in Appendix 1. We use the term "semi-structured" to indicate that the interviewer frequently asked follow-up questions, in response to the teachers' statements.

Table 1
School Type, Experience with Task Centres, Use of Tasks of Respondents in the Study

As the interview was in progress, Ms Pavlou took brief notes, and then later the study team listened to all interviews, deciding on those parts of each interview that would be totally transcribed. These were then transcribed. Although the interview protocol included 23 questions, the study was particularly focused on the individual and collective benefits to the professional growth of teachers, and so questions 13-17 were of particular interest, given their focus on the advantages and disadvantages to teachers of the use of the tasks. Some data are presented on the perceived benefits to students, as many teachers found it difficult to separate benefits to themselves from benefits to students. Given the role of the profession, this is understandable! Although not discussed in this paper, there are also data on other important areas, including the variety of ways in which the tasks are used in schools, integration of the task centre with the regular mathematics program, the involvement of parents, and assessment, and these data could also be analysed at a later stage.

Results

Perceived Benefits to Students

A common response by teachers was that students were generally highly motivated by the use of the tasks. The students appreciated the level of activity as a pleasant change from worksheets and more conventional teaching, and some teachers observed improvement in students' self-esteem as a result of the tasks. Several teachers were also pleased that the tasks presented mathematics as broader and more integrated than they had been able to demonstrate previously. Some teachers commented that with the tasks, students were quite often using mathematics "without realising it". Readers may be divided on the point of whether this should be regarded positively or negatively. They also were pleased that students were developing a range of problem solving strategies and a recognition that these were all of value. Teachers valued the opportunity to have students working in pairs, so that they could learn from each other. The variety in difficulty level of the tasks was appreciated by teachers, as they found that they could give weaker students certain tasks, while having appropriate challenges for the more able students. The opportunity for "hands-on" activity was mentioned by several teachers as a benefit to students, particularly as they could see students valuing the use of concrete materials, something not always evident at secondary school level. One teacher commented on these tasks as providing "a good vehicle for variety in learning styles" (RB, 14/9/94). One teacher, experienced in the use of tasks in both schools and university settings, emphasised the role of the use of the tasks in challenging notions of what it means "to do mathematics" and the importance of persistence with mathematical tasks (AM, 28/3/95). She spoke of a pair of primary students who were seen by their class teacher as very strong mathematically, but for whom work on the tasks caused considerable initial frustration:

They were frustrated because they saw mathematics as a very closed, one-answer thing. I'm not saying their attitudes changed immediately, but over the period of the term, . . . they started to be more willing to take a little bit of time, realising that they weren't going to get an answer straight away. (AM, 28/3/95) Teachers also mentioned that the various ways in which students were encouraged to reflect on their work on the tasks in written form were important in students connecting mathematical ideas (see also, McDonough, 1984). There is a considerable variety in such "journals", but questions such as "the problem in my own words", "what strategies I tried", "what went wrong and how I fixed it", and "what I learned from this task" are common. Teachers were also asked to identify any disadvantages to students in the use of tasks (Question 14). Few disadvantages were mentioned. One teacher commented on an earlier concern about the time devoted to the use of tasks:

I used to be a bit worried that it's taking one-fifth of the maths program, but that's when I used to worry too much about content, whereas I realise now with experience that it's content and process that go hand-in-hand-you can't really have one without the other if you are to think mathematically.. . . You mightn't cover every content area in the National Statement, but I certainly think the advantages outweigh that. (MY, 12/9/94)

Some students may find it difficult to work in pairs, but some teachers said that they made the decisions on pairing to minimise any inappropriate pairs. The opportunity to talk about mathematics to each other was identified as a benefit of the tasks (see also Lilburn, 1988), as was the situation where some choice of tasks is given to students: "so the kids actually drive it, the kids own it, rather than the teacher driving it, it has to be of some benefit I think" (RB, 14/9/94). On this aspect of choice, another teacher commented on the satisfaction that students displayed when given the chance to choose their own tasks: "the children who are quite able at maths, if it is a challenging task, they've selected a box well, they really get excited about being able to solve it" (GL, 14/9/94). The only other disadvantage to students that teachers mentioned was reading difficulties for young children or some children from non-English speaking backgrounds. In responding to this, teachers sometimes reword or adapt the task for younger children, or read the task to the students. Other teachers deal with the issue of reading difficulties by pairing a stronger reader with a weaker one.

Perceived Benefits to Teachers

Many teachers commented on the benefits that arose from the opportunity to observe students in action as they were using mathematics. Several teachers in primary schools commented that the wide range of content covered by the tasks had led to a re-evaluation of students' strengths and weaknesses. Several students whose mathematical ability had been assessed previously on the basis of their performance on number-related exercises, showed through their work on the tasks that this assessment was too narrow in scope. Teachers gained much information on students' preferred learning styles, as well as their understanding of a range of mathematical content and the processes of reasoning, problem solving, and communication. One teacher commented that the tasks had led to her looking at children differently, becoming more interested in children as individual learners, and therefore becoming much more interested in listening to children's responses (AM, 28/4/95). Not surprisingly, most of the benefits that teachers perceived were benefits to students, but the teachers viewed these as of benefit to themselves, as they aided the teacher's role. In particular, most teachers mentioned the facilitation of group cooperation as a major outcome of the use of problem solving tasks (see also, Richards & Trotter, 1988). The open-ended nature of the tasks was appreciated by teachers, meaning that interested students could take a given problem further, and look for their own directions of investigation. The fact that most tasks could be solved in more than one way and often had more than one solution meant that students could work at their own levels:

Just all the sharing that goes on, the discussion, the fact that they get to make decisions about what they are doing. And with kids being at lots of different ranges in the classroom, the tasks cover lots of different ranges and they get to work where they're at. (JH, 12/10/94)

Teachers also mentioned the chance that the tasks provided for variety for the students, and it reinforced in their minds the positive aspects of hands-on approaches. One teacher described the tasks as "another fantastic tool like the computer for Logo, construction equipment, or calculators", an enjoyable way "to get the maths message across" (GL, 14/9/94). On the same theme, another teacher described it as providing extra ways of looking at mathematics, as it opened lots of doors (RE, 14/9/94). A common theme in secondary teachers' comments was that the task centres were their first attempt to move beyond fairly traditional content and method. As one teacher put it: "They tend to take you out of your comfort zone, to withdraw from that, to try some group work, . . . so essentially it's alternative pedagogy" (RB, 14/9/94). Teachers gave examples of where they took tasks from the task centre and extended them during a whole class discussion, viewing the original tasks as "only the tip of the iceberg" (LN, 11/10/94). The same secondary teacher said that she had taken the pedagogy of the task centre into her regular classroom and was moving away from the "40 exercises approach". In the same vein, a primary teacher commented that using the tasks had taught her a lot about different problem solving strategies, which she then could share with students. She mentioned that her confidence to take risks had grown, and that she was more comfortable with not always knowing the "right answer" (LM, 17/10/94). Hilyear (1981) identified this aspect of teachers' professional growth as a major benefit of task centres. One teacher commented that the experience with the tasks had led her to look for more practical examples and hands-on tasks to enhance particular concepts in the regular classroom, when she had seen the effect of the practicality of the tasks in the task centre (MS, 14/9/94). One more benefit of using the tasks was seen as the enjoyment that they can bring to teaching as well as to the work of students, with teachers commenting that the use of tasks had generated a new interest for them in mathematics. As well as teachers commenting on their own enhanced understanding of children's learning, there were several examples of teachers' own view of mathematics being broadened, as well as their own understanding of particular mathematical content areas. Interestingly, these comments came from teachers across the three levels of schooling- elementary, middle, and high school. One high school teacher claimed a better personal understanding of probability, geometry, and algebra from the use of the tasks (JF, 6/19/95). For example, in algebra, the tasks provided the opportunity to explore algebraic ideas from their early basis in number patterns. He also commented that other staff had gained a better understanding of concepts because they had seen them in the many contexts offered by a number of different tasks. Interestingly, several teachers mentioned a greater understanding of mathematics as "the study or science of patterns" that had emerged from their work on tasks with children and colleagues.

Perceived Benefits to Other Teachers

Respondents were asked to suggest any benefits to the professional development of other teachers that they had observed in their schools. Several teachers commented on attitude changes that they had observed in other teachers to both what was viewed as important in mathematics, and to their enjoyment of the subject. A greater commitment to process as well as content was evident, as was a growing variety of ways of helping children with problems:

Before they would have said 'how on earth can I help this kid?' . . . It is much easier to look at the board, . . . you've got 10 or 12 different ways to tackle the problem, you can find something that is going to help you as a teacher. (MY, 12/9/94) Some teachers commented that colleagues demonstrated a wider variety of teaching skills, possibly due to the experience of working in the task centre situation. As with the respondents, it was clear that for many colleagues, the task centre provided a way into problem solving:

There were some teachers who were very loathed to use problem solving in their classes in any form, . . . to use hands-on materials. They felt very comfortable with the textbook and getting the children to do exercises and rote work, and it seems to free up a number of them to know that you can actually do these things and the students will like it, and they do work-it's liberating for a number of teachers. (MS, 14/9/94) An almost identical comment was made by another secondary teacher (MR, 18/10/94). Several teachers said that whole-staff introductions to the tasks, preferably through a whole-day inservice program were the best way to expose teachers to the tasks initially. Another benefit of the school-wide use of the tasks was that it gave continuity and consistency to mathematics in the school. Schools which made tasks available to parents for use at home, or encouraged parents to work in classrooms during task centre sessions were appreciative of the opportunities that the tasks provided for communication with parents about mathematics teaching and learning. The concept of "risk-taking" arose in this discussion also, as teachers' confidence grew with "giving the centre stage more to the kids than to the teacher" (RB, 14/10/94). In the same way as teachers commented on their own enhanced view of mathematics and level of mathematical content knowledge, several gave examples of similar benefits to colleagues. One secondary teacher (MS, 6/21/95) said that several of her colleagues had previously had "a very restricted range of mathematical ideas, very much text-book oriented, with no ideas of the uses of mathematics," and that the use of tasks had broadened this view of mathematics, including an understanding of the recreational uses of mathematics. One elementary teacher said that collaborative work on the tasks had alerted him to the difficulties that several colleagues had with some areas of mathematics, and the discussion had been mutually helpful (ML, 6/23/95). For example, discussion on a particular task that focused on the relationship between perimeter and area, had exposed various misconceptions which were resolved with the support of colleagues. Without the tasks providing the basis for discussion, these difficulties would have been contained within a single teacher's classroom walls, highlighting again the role of tasks in promoting team work and collaboration. Many other benefits of task centres to both teachers and students are given in McDonough (1991).

Difficulties With Task Centres

Most comments that were offered were related to organisational difficulties, such as keeping track of all the equipment and all the tasks, particularly if they were moved around the school. Teachers also mentioned the challenge of being able to get around to see all children during a task centre session and being familiar with all the tasks so as to provide appropriate guidance. Several teachers indicated that they were still struggling with finding and using appropriate forms of assessment for the work students did on tasks. They were comfortable with observation as an important means of assessment, but unclear on the best ways for both teachers and students to document their progress. A concern mentioned by several teachers was that teachers may regard their one scheduled visit to a task centre as "their problem solving for the week" (MY, 12/9/94). This problem was described by another teacher as the challenge of "integrating task centres with the normal maths program" (RE, 14/9/94). Not surprisingly, the more experienced teachers (in the task centre sense) were more comfortable that they had largely resolved these issues.

Staff Collegiality

Teachers gave several examples of the ways in which the establishment and use of the task centre had led to greater collegiality between staff, particularly in the early stages. In most schools, there had been a whole-school commitment up- front to establish the task centre, and this had created an atmosphere of teamwork: "It certainly is a bit of a talking point. In the staffroom, we often talk about activities, sharing of clinics, . . . in our planning time, and so on" (MY, 12/9/94). Several mentioned that there was much more conversation around the school about mathematics following the establishment of the task centre. Just finding out from each other which tasks were being used meant that staff were more likely to be communicating with each other (MS, 14/9/94). One teacher expressed disappointment that the three out of five teachers who were using the tasks enjoyed a sense of collegiality, while the teachers who made very limited use of the tasks didn't tend to have the same level of encouragement and support (GL, 14/9/94). Interestingly, several schools commented on the high level of collegiality already present in the school prior to the establishment of the task centre. It may be that schools with high levels of collegiality may be the ones that are more likely to take on the task centre concept, given that its success is likely to be enhanced by a spirit of cooperation. One secondary teacher commented that teachers were now "less fearful to talk to one another". At first teachers were worried that they didn't know the answers to all the tasks, but they were now moving away from the idea of having to know all the answers, and feeling "a lot more comfortable with talking about strategies" (LN, 11/10/94). The final word on collegiality comes from a teacher who observed "staff enjoying working on the tasks as much as the kids do, so it adds to the degree of collegiality [through] cooperation and discussion" (MR, 18/10/94). The enthusiastic way in which schools and teachers have embraced the task centre concept is evidenced by the establishment of the Problem Solving Task Centre Network, coordinated by Michael Richards, an experienced user and developer of task centres, and one of the respondents in this study. The Network produces a regular newsletter, which enables different task centre staff to share with and to learn from each other, building the level of collegiality across schools.

Some Additional Data

Schools which commence their establishment of a task centre by using an initial set of tasks from the Curriculum Corporation in Australia are strongly encouraged to involve all teachers in a full-day inservice program. These days are generally led by someone quite experienced in the use of problem solving tasks and task centres. During such a day, teachers have the opportunity to work through many of the tasks, creating their own coding systems for content and difficulty level of each task. They also make "Teacher's Notes" on each task, suggesting possible extensions of the tasks, hints for presentation, and any other notes that they think would be helpful for their colleagues. Teachers also learn about about many issues that arise in establishing and maintaining a task centre. A sample of 170 evaluation sheets from 13 such inservice days provided useful, additional data. Of course, these data were obtained from teachers just about to embark on establishing a task centre, and therefore can be considered as "early impressions", but nevertheless many of the themes discussed above were evident in these evaluation forms. The evaluation sheets were overwhelmingly positive about both the task centre concept and the need for such an introductory program. In one question, teachers were asked to reflect on how their teaching may change as a result of their experience on that day. Many commented on the way in which using the tasks with colleagues under the guidance of a skilled facilitator reinforced in their minds the need to allow students "to find their own solutions or attempted solutions before providing assistance"; and that "to ask the right question is better than providing the answers". Other teachers commented on how the discussion on the day was helpful with general classroom organisation, as well as in their likely use of the tasks, with particular appreciation for the opportunity to consider how the tasks can be integrated into the "regular" mathematics curriculum. Many teachers appreciated the feeling of ownership and teamwork that emerged over the course of the day, in some cases commenting on the expectation that such collegiality was likely to continue, with the tasks providing the focus of many future conversations.

Conclusion

Although problem solving task centres require considerable teamwork and management skills on the part of all teachers involved in their use, the data from this study indicate that their use is viewed most positively by teachers who have had experience with them. The development of problem solving strategies by both students and teachers, a recognition of multiple solutions and solution paths for problems, a climate of "risk-taking" on the part of teachers and students, a broadened view of mathematics content, what it means to do mathematics, enhanced teacher content knowledge, and a spirit of collegiality have emerged from this study as the major benefits to schools which make the decision to establish a task centre in their school.

Acknowledgments

We gratefully acknowledge the willing participation of the thirteen participants in this study. We also acknowledge the detailed comments of Doug Williams and Andrea McDonough on an earlier draft of this paper.

Bibliography

Byrne, J. S., & Zeplin, D. (1990). A Problem-solving approach: Brunswick maths task centre. Victoria: Ministry of Education.

Henry, B. (1991). Task centre activities with (a) SMILE. In J. O'Reilly & S. Wettenhall (Eds.), Mathematics: Inclusive, dynamic, exciting, active, stimulating (pp. 202-205). Parkville, Victoria: Mathematical Association of Victoria.

Hilyear, D. (1980). Problem solving in upper primary and lower secondary school. In P. Williamson (Ed.), Learn to love mathematics (pp. 202-208). Parkville, Victoria: Mathematical Association of Victoria.

Hilyear, D. (1981). More on the maths task centre. In A. Rogerson (Ed.), Maths, myths and realities (pp. 181-185). Parkville, Victoria: Mathematical Association of Victoria.

Jasper, K., & Hodgson, B. (1992). Taking geometry to task. In M. Horne & M. Supple (Eds.), Mathematics: Meeting the challenge (pp. 212-215). Brunswick, Victoria: Mathematical Association of Victoria.

Lilburn, P. (1988). Making maths meaningful with a task centre. In D. Firth (Ed.), Maths counts-who cares? (pp. 50-51). Parkville, Victoria: Mathematical Association of Victoria.

McDonough, A. (1983). Problem solving for years 4 to 7. In D. Blane (Ed.), The essentials of mathematics education (pp. 419-429). Parkville, Victoria: Mathematical Association of Victoria. McDonough,

A. (1984). Fun maths in boxes. In A. Maurer (Ed.), Conflicts in mathematics education (pp. 60-70). Parkville, Victoria: Mathematical Association of Victoria.

McDonough, A. (1991). Problem solving: The mathematics task approach. Journal of Science and Mathematics Education in Southeast Asia, 14(1), 33-38.

Palmer, R. (1989). Setting up a maths task centre. In B. Doig (Ed.), Everyone counts (pp. 146-150). Parkville, Victoria: Mathematical Association of Victoria.

Rawson, P., & Lilburn, P. (1987). Teaching problem solving techniques with the task centre. In W. B. Caughey (Ed.), From now to the future (pp. 95-97). Parkville, Victoria: Mathematical Association of Victoria.

Richards, M., & Trotter, J. (1988). Problem solving task centres. In D. Firth (Ed.), Maths counts-who cares? (pp. 52-53). Parkville, Victoria: Mathematical Association of Victoria.

Richards, M., & de Mestre, N. (1993). The spread of problem solving task centres. In J. Mousley & M. Rice (Eds.), Mathematics: Of primary importance (pp. 307-311). Brunswick, Victoria: Mathematical Association of Victoria.

Trotter, J., & Suter, R. (1987). A task centre on a shoestring budget. In W. B. Caughey (Ed.), From now to the future (pp. 98-100). Parkville, Victoria: Mathematical Association of Victoria.

Williams, D. (1993). The Task Centre project. In J. Mousley & M. Rice (Eds.), Mathematics: Of primary importance (pp. 300-306). Brunswick, Victoria: Mathematical Association of Victoria.

Appendix-Interview Protocol for Telephone Interviews on Task Centres

Name__________________________ School________________________________

We are conducting these phone interviews to gain information on the variety of different ways in which task centre are used in Australia, and the benefits of their use. Thanks so much for agreeing to talk to us.

1. How long have you personally been involved with the use of problem solving task centres from a task centre: -at your current school? -at any other schools?

2. How long had your current school had a task centre? What led to its establishment?

3. Do you have a separate room set aside for the tasks? If "no", please explain.

4. Is there a teacher who has a time allotment given to look after the task centre?

5. How many teachers at your school make regular use of the tasks? (What is the total number of teachers who teach maths at the school?)

6. Have you had the assistance of any "outsiders" in setting up or in the current operation of the task centre?

7. Out of the set of tasks, can you estimate: - the number of commercially-purchased tasks? - the number of tasks you have made yourselves (whether drawn from commercial sources or your own ideas)?

8. Please describe how you use the tasks (i.e., describe a typical session when the tasks are being used). Please elaborate as much as possible.

9. How does the use of the tasks relate to the "regular" maths program?

10. What records do you keep of students' work on tasks?

11. How do you assess students' work on the tasks?

12. Do you involve parents at all with the use of the tasks? Please outline their involvement.

13. Please comment on the benefits that you see for students in working with the tasks? In particular, please comment on: - the maths content they learn? - mathematical processes (i.e., things like problem solving, communication, reasoning, mathematical connections)? - disposition (i.e., attitudes, persistence, motivation)?

14. What disadvantages (if any) are there om the use of the tasks: - for teachers? - for students?

15. What benefits (if any) do you see personally to your teaching from using the tasks?

16. What benefits have you seen in other teachers' professional development in using the tasks?

17. Has the task centre led to greater collegiality between staff (more regular meetings, sharing experiences etc.) Please explain.

18. (Primary schools only) How do you adapt the task for the needs of young children or poor readers?

19. What problems (if any) are you or your school "struggling" with concerning the use of the tasks at your school?

20. How are you tackling these issues?

21. Has the use of the tasks assisted your own understanding of mathematics?

22. Has the use of tasks assisted your colleagues' understanding of mathematics?

22. What other approaches to problem solving have you tried? Please explain whether these occurred prior to the task centres? After the task centre?

23. If a school was considering starting its own task centre, what advice would you give to them based on your own experience?

24. Do you have any other comments on the use of the task centres in schools?