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
We are indebted to the Mathematical Association of Victoria for keeping this history on their site from 1996 until 2008. |
|
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.
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.
|
Figure 1
Click photos to see their cameos.
|
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.
| In this paper the focus is on the perceived benefits of the task centres for teacher professional development and collegiality. |
|
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
Respondent/ Type of
School
Task Centre Experience in years |
System of Task Use in
Schools |
| EE Secondary 10 (in two
schools) |
Tasks
hang on moveable frame |
| MY Primary 7 (in two
schools) |
Separate
task centre room |
| ML Primary 1 |
Stored in
mathematics resource room, with other materials |
| JF
Secondary 2 |
Separate
task centre room |
| MS
Secondary 1 |
Each
teacher has 15 tasks at a time; these are rotated |
| GL
Primary 5 (in two schools) |
Stored in
library, rotated through the school |
| RE
Secondary 1 |
Rotated
from room to room |
| JH
Primary 4 |
Two sets
(senior room and junior room |
| RB
Secondary 1 |
Stored in
mathematics laboratory |
| LN
Secondary 9 |
Stored in
separate task centre room |
| LM
Primary 5 |
Stored in
separate task centre room |
| MR
Secondary 13 |
Stored in
small collections near classrooms |
AM
University (K-12 preservice & inservice)
16 (in school and
university) |
Stored in
mathematics resource room;
selection taken for use with
students
|
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: |
|
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. |
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
| 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. |
|
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.
|
|
... task centres were their first attempt to move beyond fairly traditional content and method ... viewing the original tasks as 'only the tip of the iceberg' ... confidence to take risks had grown ... more comfortable with not always knowing the 'right answer' ... use of tasks had generated a new interest for them in mathematics ... several examples of teachers' own view of mathematics being broadened. |
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 (strategy) 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).
|
|
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. |
Difficulties With Task Centres
| ...the challenge of 'integrating task centres with the normal maths program'. |
|
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.
|
|
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. |
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.
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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?
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