Anglia Ruskin University

1
??????? ???????? ?? ?????? ????? ?????? ???????
?????? ???????? ???? ?????? ???????
?"? ???? ?'???? Anglia Ruskin
University
2
??? ?????

• ???
• ????? ?????
• ?????? ???????
• ??? ???????
• ????? ????? ???? ?????
• ?????? ???????
• ?????

3
???? ?????? ????????

• ??? ??????? ???????? ?? ????? ???? ????? ?????
  ???????? ???? ???? ??? ??????? ???????
• ??? ?????? ?? ?????? ????
• ??? ????? ?? ??????-????? ?? ???? ????????
  ?????? ??????? ??"??

4
?? ?? Wolcott (1994) The biases of our careers,
our personalities, and our situations constitute
essential starting places for our research
attention (p. 408).
The personal costs of trying new innovations are
often high they innovations require that one
believes that they will ultimately bear fruit and
be worth the personal investment (House, quoted
in Fullan, 2001, p. 36).
5
?????? ???????
6
??? ??????? Theoretical Perspectives
a. Beliefs, philosophy and practice in
mathematics education
b. Change processes in school mathematics
c. Factors affecting the implementation of
reforms in school mathematics
d. Self-esteem and behaviour
7
Figure 1 The relations between beliefs,
paradigms and reforms.
8
Table 3 The differences between INSET and CPD.
(Adapted from Ponte, 2001 Metcalfe, 1999
Clarke, 1997).
9
????? ????
Lave and Wenger's (1991) theory of communities of
practice see learning as a process of
apprenticeship that involves participation
10
Social constructivism which is traced back to
Vygotsky, who focused on the roles of society in
the development of an individual, is connected to
learning in a community of practice as defined by
Lave and Wenger (1991) in their Social Practice
Theory (SPT).
Tharp and Gallimore (1988) present learning as a
movement from assisted performance to unassisted
performance (Based on Vygotsky's (1978) ZPD (Zone
of Proximal Development).
11
Figure 6 Structure of the study of reforms in
education through sociocultural framework (based
on Stein Brown, 1997185).
12
Self-esteem a personal sense of worth
??????????? ??????? It is the single most
significant key to our behaviour (Branden, 1969
Gergen Marecek, 1976 Sherman Christian,
1999 Blascovich Tomaka, 1991 Pajares, 1992).
13
Teacher's preparedness for reform
Figure 10 Affective and cognitive elements
effecting teacher's self-esteem and preparedness
for reform
14
Guba and Lincoln (1989) point out the
dissimilarities between constructivism in
mathematics, which demands proofs, and
constructivism in research, where there are
assertions-without-proof that are logically and
intuitively derived from observations and data
(pp. 115/6).
Gallagher, D.J. (1995) 'In Search of the Rightful
Role of Method Reflections on Conducting a
Qualitative Dissertation'. In Tiller, T.,
Sparkes, A., Karhus, S. and Dowling Naess, F.
(Eds.) The Qualitative Challenge. Reflections on
Educational Research. Norway Caspar Forlag,
pp.17-36.
15
?????????? ??????????
According to hermeneutics, meaning is always
conditioned. The researcher's outlook is dynamic,
and changes during the research through exposure
to other people's points of view, or through
reading. The process of understanding the whole
picture involves going back and forth from the
general picture to its components and history and
vice versa. In educational and social research,
like this one, in which I am both the head of the
project and the researcher, it is always one
subjective individual (the researcher) attempting
to interpret the interpretations of other
subjective individuals (the subjects of the
research, the teachers in the project). This is
the essence of hermeneutics (Smith, 1995 Dargish
Sabar, 2001).
16
Figure 16 The research paradigms
17
??? ????
18
(No Transcript)
19
Figure 20 A description of the analysis process
20
Fullan (2001) differentiates between
restructuring, which can be done by
authorisation, and reculturing, which deals with
how teachers come to question and change their
beliefs, and as a consequence, their practices.
He claims that reculturing is what is needed
these days, and that it proves to be much more
difficult than anticipated (p.34).
21
???????? ????? ??
????? ???????? ?? ?????? ?????
????? ??????? ?? ??????? ???????? ?? ?????
??????? (?????? ???? ?? ??????)
????? ????? ?????? ????? ?? ?????? ???????? ??
??????
22
????? ????
A facilitator At first most of the team meetings
dealt with mathematics technical things
mathematical content of the syllabus and such
the motivation was not from within, from the
classroom, but because I brought them up. As time
went by the doses changed, and more mathematical
content that grew out of the lessons came up
(I-F-EV13).
HoD We are talking mathematics (I-T-MA1)
I felt an improvement in teamwork. Teachers
collaborated in writing examination papers and
planning criteria for assessment we wrote
open-ended tasks together and more Yes - there
is an improvement. The mere fact that we meet
once a week and listen to one another, deal with
common problems There is great improvement in
teamwork. We now discuss themes that have not
been discussed before (Q-370-T AH).
23
The team is united, we don't work individually
any more but as a group (Q-370-T T). teachers
hear what their peers do in their classrooms and
they adopt the ideas(Q-371-F ZL). The team
sessions strengthened the ties between us
(Q-371-T A, AH).
24
????? ??????????? ?????? ?? ????????? ??
Community of practice (Wenger, 1998)
Mutual engagment
Negotiated enterprises
Repertoire of negotiable resources
25
??????? ?????? ????? ????? ????
????? ?????? ?????
?????? ?????? ??????
????????? ??? ????
????? ????? ??????
26
????? ???????? ???????? ?? ??????
????? ?????
The facilitator contributed a lot to the school
and the team. She was involved in everything, and
led us to real co-operation we have very good
relations she makes sure not to undermine my
position (M)
She taught us how to organise our work,
strengthened us in our negotiations with the
administration, united the team professionally
and socially and helped us in our everyday chores
(AH) (Q-370-HD).
27
We had a very good facilitator. We really enjoyed
working with her. Truly, we loved working with
her. I am practically sure that the whole thing
depends on the personality of the facilitator. If
somebody else was doing it, it may have turned
out not as good and people would have stopped
coming to the meetings. She, with her
personality, and the materials that she brought,
and the 'anti-pressure' that she transmitted - it
was very nice (I-T-LN3).
????? ???????
There are feelings of uncertainty it is
difficult to create motivation and collegiality
when the teachers feel they know it all. How do I
'recruit' them to implement, to work to schedule?
How do I deal with opposition? How do I create a
need to learn? (MFH-371-2408).
28
I am challenged. This project involves teamwork
that leads to a process of change, allows
participation in this process, it is creative,
includes intensive fieldwork I might improve my
personal communication skills. It facilitates
joint planning and joint learning. It is
fascinating to be part of a new, developing
project (MFH-371-2408).
???? ???????? ???? ???? ????"? It is very
important that a team will be exposed to external
knowledge and experience, especially in the
provinces. This can be done through the
facilitator (I-F-EV214).
29
???? ???? ?????? I feel that the thing I want to
do most now, is to go to another team, any
'no-team', and lead them through the same process
that we had here I wonder if I am able to do
this. I feel so good with what happened here that
I think it is a shame that it would stay only
here. Today I believe that we shall continue like
that forever. It won't change. It is part of us.
No wonder it was called the implementation
project. It is the same as brushing your teeth
every morning - you can't do without it
(I-T-TR3).
30
???? ????
The success of the project depends, first and
foremost, on the co-operation of the team,
co-operation with peers and co-operation with the
facilitator. To achieve that, you need to build
confidence, a long and difficult process
(Q-371-F NL).
If only we had the time to teach mathematics at
ease then learning through discovery is the best
way to learn, the best (I-T-MA3).
31
I believe that most teachers do these things but
in a small way. I have used the "what if not?"
method in my top class this year, and it worked
out very well. But lack of time suffocates me! I
have to cover the syllabus, and we are not
allowed enough time as it is. It is very
important to teach through discovery, but how can
we do it? In the middle-school, there it can be
done more easily. They have a syllabus to cover,
but they are not judged on it as we are (I-T-TR3).
32
???? ????? ??????
Mathematics is an area of knowledge, a culture
too it involves the teaching of thinking tools,
especially where the connections between
different fields are concernedOnly when I can
answer all their pupils' questions - the clever
and the stupid ones - I know that I really
understand Deep understanding comes with
teaching (I-T-LN3).
See, a teacher goes to seminars and comes across
many different approaches, or 'fashions' and
than she should put them to a test do they suit
me? Because maybe it does not agree with my
character or views, and the worst is if one
cannot change with it but, see, the person
should enjoy trying new things, and not be
frightened of failure. If she is not frightened
of failure, why shouldn't she try? I cannot say
that I'll implement it, it depends I don't
believe in forcing a teacher to adopt a practice
that does not suit her (I-T-LN3).
33
????? ????
I don't know I started because I was encouraged.
Naomi and the principal were present at my trial
lesson, and the fact that I got the job made me
feel that I was good. The truth is, I worked very
hard, devoted all my time to preparation and
learning, went to seminars, and worked a lot at
home. In the first two years I never went to bed
before 1AM I put in a lot in order to increase
my confidence in class. But it also came with
time (I-T-TR1).
For me, the main contribution of PIRM is that now
I feel that I can be a HoD managing the team and
leading in mathematics teaching My self-esteem
has improved (MWA-T-372 FG-T-372).
34
It seems that what I have in me - I have. Full
stop. It only had to be discovered. There is
ability and potential that may have been subdued
once, it may be connected to low self-esteem So
maybe, I wanted to say to myself OK you are all
right, and you would be appreciated if you were
good at mathematics. Maybe something like that
went through my mind Yes, it is connected to a
higher self-esteem (I-T-LN1).
35
????? ???????
????? ???????
The problems emerged at the beginning of the
school year. All the teachers, and the HoD,
taught on Thursday the day of the week that the
facilitator was at the school without any break,
so there was no time for meetings with teachers
of HoD (Q-371-F).
On the one hand, the school's administration is
interested in achievements and the improvement of
processes but it does not allow the facilitator
any freedom and forces its opinions without
discussion or warning (Q-370-F-AN).
36
????? ??????
I expect the administrators to adopt the
decisions made by the team. In special cases when
they can't, they should explain their reasons and
open a discussion with the team. I expect the
administrators to refrain from putting hurdles in
our way by making pedagogical decisions that
concern the teaching of mathematics. I expect
the administrators to support us (FR-370-T-2912).
37
I feel that we are going downhill After all,
everything begins and ends with rules and
borderlines as far as discipline is concerned.
When I started in this school, there was chaos.
Had it not been changed, I would have left. But a
process started and things improved in the
middle-school. This year I feel a regression. If
this continues, I am leaving. I can't believe
that the problems cannot be solved. I believe it
can be done differently This is in the hands of
the administrators. It has a major impact on
everything that happens in the school I have
been in this school for five years now, and this
is the third administration already (I-M-AT1)
38
?????? ????????
Accountability
We still have to cover the syllabus, because of
the matriculation examinations you cannot use
innovative methods because you won't make it
(I-M-AT1).
39
????? ???? ???? ????
I can see that part of the process was the
ability of the teachers to raise problems, their
professional problems, to discuss them with me
and with their peers I mean, this is also
something that did not exist before, and then
developed I think it worked when teachers saw
their colleagues bringing their problems to the
surface, and realised that there is no
boomerang-reaction. I reckon that a person who
experienced supervision at some stage, it took
him some time to believe that he is not going to
be judged on his questions (I-F-EV12).
40
????? ????? ???? ???? ????? ???????? ???????
Good assistance requires that the person
assisting and the person being assisted are
working for the same goal. Sometimes mutual goals
can be established at the start of the
relationship more often they emerge (Stein
Brown, 1997175).
41
??????
?????? ????? ?? ????? ??????? ?????. ????? ?????
????? ?? ????. ??? ????? ??? ????????
Although we spent a lot of time discussing ways
to start teaching new topics, and building tasks
and worksheets, and debating how to ask
questions I did not see a revolution in
classroom practices as a result (I-F-EV119).
42
????? ??????? ????????, ?? ??? ?????? ???????
In sum, the operation of PIRM in the school is
very successful. It seems that in spite of the
technical and organisational problems, the
teachers both contribute and are enriched. It
seems safe to assume that activities in the
spirit of PIRM will continue in this school when
the project ends (REY-371-OH).
43
??????? ????????, ??????? ?????????
44
????? ??????? ?? ??? ??????
????? ????
????
??????
????? ????? ???????
????? ??????
???
??? ????? ?? ??????
????? ???-????
????? ?????? ????? ???????
?????? ????????
??????? ???????
?????? ???? ??????
????? ????? ?? ??? ??? ?????
45
(No Transcript)
46
??????? ???????? ???????? (Sociocultural) ??
??????????? ??????.
?????? ???????? ????????? (External and
contextual) ?????? ????? ?????, ?? ???? ??? ??
????? ????.
?????? ??????????? - ?????? ???????.
47
The theory of educational change is a theory of
unanswerable questions No one knows for sure
what is best. We are engaged in a theory of
probing and understanding the meaning of multiple
dilemmas in attempting to decide what to do
(Fullan, 2001110).