A PROGRAMME OF SUSTAINABLE PROFESSIONAL
DEVELOPMENT FOR MATHEMATICS TEACHERS: DESIGN AND
PRACTICE
Teresa Smart and Celia Hoyles
Abstract
A shortage of well-qualified mathematics teachers means that fewer
students have their interest in mathematics stimulated, so fewer
continue their study in higher education. Where are the
mathematicians and mathematics teachers of tomorrow? Breaking
this downward spiral requires improving the subject knowledge and
enthusiasm of existing teachers, in a way that is linked to improved
pupil engagement and motivation. To do this, the London
Mathematics Centre (LMC) based at the Institute of Education,
London, is piloting a 10-day programme of professional
development for secondary mathematics teachers in London
schools. The programme aims to create a trajectory that gives
teachers sufficient mathematics confidence to move towards taking
ownership of their teaching by designing materials informed by and
responding to the needs of their pupils. Interview and observation
data are being collected to test both the change in teaching attitudes
and approach and the response of the students.
Teresa Smart and Celia Hoyles
London Mathematics Centre (LMC)
The Institute of Education
Teresa Smart is director of the London Mathematics Centre
t.smart@ioe.ac.uk
Professor Celia Hoyles is chair of the London Mathematics Centre and Dean
of Research and Consultancy at the Institute of Education.
c.hoyles@ioe.ac.uk
The London Mathematics Centre is a three-year project funded by the Gatsby
Charitable Foundation
A PROGRAMME OF SUSTAINABLE PROFESSIONAL
DEVELOPMENT FOR MATHEMATICS TEACHERS: DESIGN AND
PRACTICE, Teresa Smart and Celia Hoyles
Abstract
A shortage of well-qualified mathematics teachers means that fewer
students have their interest in mathematics stimulated, so fewer
continue their study in higher education. Where are the
mathematicians and mathematics teachers of tomorrow? Breaking
this downward spiral requires improving the subject knowledge and
enthusiasm of existing teachers, in a way that is linked to improved
pupil engagement and motivation. To do this, the London
Mathematics Centre (LMC) based at the Institute of Education,
London, is piloting a 10-day programme of professional
development for secondary mathematics teachers in London
schools. The programme aims to create a trajectory that gives
teachers sufficient mathematics confidence to move towards taking
ownership of their teaching by designing materials informed by and
responding to the needs of their pupils. Interview and observation
data are being collected to test both the change in teaching attitudes
and approach and the response of the students.
Background
A shortage of mathematics teachers in England has become more acute in
the last four years, with many students being taught by teachers with little
specialist knowledge (OU/NAMA/KC, 2002; Smith, 2004). The Advisory
Committee on Mathematics Education (ACME) highlighted this growing
crisis and linked it to the steady decline in students continuing their study of
mathematics after compulsory schooling (ACME 2002). There is no simple
correlation between the ‘amount’ of subject knowledge mastered and the
quality of teaching, but a teacher’s confidence and enthusiasm for
mathematics, alongside an appreciation of how students learn, make it more
likely that a teacher can stimulate student engagement in exploring the subject.
A mathematically confident educator will teach for relational rather than
instrumental learning (Skemp, 1976). As well as a clear need to improve the
specialist knowledge of many existing teachers of mathematics, there is also a
need to provide opportunities for those with specialist knowledge to rekindle
their enthusiasm for the subject. Both ACME (2002) and the Smith Inquiry
(Smith, 2004) reviewed the evidence and called for all teachers of
mathematics to have an entitlement to a programme of continuous subjectspecific professional development.
The London Mathematics Centre (LMC)
In June 2004, the LMC launched a 10-day a pilot professional development
programme for twenty-three mathematics teachers from sixteen schools. The
design of the pilot was informed by the evidence that sustained and
collaborative professional development has a positive impact on teaching and
learning (EPPI-Centre, 2003; Joyce & Showers, 2002). The 10-day
programme was planned in collaboration with the users and set out to integrate
teachers’ own learning of mathematics with developing an enhanced
understanding of mathematics pedagogy. Extending teachers’ mathematics is a
given even for those with a strong mathematics background. ACME (2002) reenforced what had already had been noted in the USA, that in all programmes
of professional development, teachers need to build the ‘three kinds of
knowledge [that] are crucial for teaching school mathematics: knowledge of
mathematics, knowledge of students, and knowledge of instructional
practices.’ (National Research Council, 2001 p.370).
The ten days of the programme are divided into six face-to-face tutored
sessions and four mentored school-based days. This sustained period of
professional development encourages teachers to adopt a reflective approach
to their practice when they try out in the classroom what they have been
learning at the University.
The LMC programme builds on these ideas with several additional features
identified from prior research and experience of successful professional
development for teachers of mathematics:
1. Teachers should be engaged from the start in investigating
mathematics for its own sake – prior to any consideration of
classroom activity. This was found to be the crucial factor in successful
take up in the Microworld Project (Hoyles, Noss & Sutherland, 1991).
2. Starting points for mathematical investigation are based on prior
research or development work and are carefully designed around a
mathematical theme or a ‘deep’ idea such as ‘generalising’ or ‘proof’.
The research-informed activities aim to challenge teachers by
presenting new perspectives on known mathematics or by extending
mathematical knowledge with new ideas. Jaworski, a confident
mathematician, acknowledged how a classroom discussion while
working in a ‘co-learner partnership’ with teachers ‘allowed me to gain
new perspectives of relationships [between quadratic functions and
equations] and hence to enhance my own knowledge’ (2001, p.313).
3. Though teachers at first explore mathematics following pre-planned
starting points, an essential part of the programme is that teachers
design their own activities. In the design process, teachers work
collaboratively in networks or ‘communities of practice’ (National
Research Council, 2001 p.397).
4. As well as planning for impact in classrooms, the programme is
designed from the outset for sustainability after the programme has
ended.
The Programme consists of face-to-face classes taking full days at the
University, each built around a mathematical theme, followed by work in
schools. The programme provides a trajectory to lead the teachers from being
users of prepared curriculum resources to becoming confident mathematicians
who design materials to use their mathematical knowledge and their
knowledge of students’ learning.
University days
Each University day follows the same format. A speaker introduces the
theme providing some mathematical starting points for further investigation,
modelling the process with some examples. In order to improve their students’
mathematical knowledge, teachers need to be guided to learning some new
mathematics for themselves.
Knowing mathematics for teaching also entails more than knowing mathematics
for oneself. Teachers certainly need to be able to understand concepts correctly and
perform procedures accurately, but they also must be able to understand the
conceptual foundations of that knowledge. In the course of their work as teachers,
they must understand mathematics in ways that allow them to explain and unpack
ideas in ways not needed in ordinary adult life. (National Research Council, 2001
p.371).
The teachers engage in exploration of ‘new’ mathematics or new
perspectives on mathematics by working in small groups on a mathematical
inquiry based on one of the starting points offered by the speaker. ‘New’ may
mean doing ‘old’ mathematics in a new way because it is modelled with ICT,
which is integrated into each theme. In this respect, LMC uses ICT as
suggested by Laborde (2001) ‘as a catalyst for teachers to restructure their
mathematics’. The following uses have been made: spreadsheets to explore
variables and functions and to model applications of mathematics, dynamic
geometry to engage in construction and geometrical reasoning, and statistics
packages to explore data sets and trends. In each case, teachers are provided
with research-informed materials and work in small groups negotiating how to
best adapt these material for use in their own classrooms.
As well as using ICT throughout the programme we also use examples of
student responses to reasoning on proof drawn from the Longitudinal Proof
Project (Hoyles and Küchemann, 2002) as a catalyst for designing activities. A
number of teachers on the LMC Programme have opted to become ‘teacher
researchers’ in a follow-up study1 devising activities based around the student
responses, aiming to develop further student reasoning and quality of
explanations.
Follow-up study ‘Developing Research-informed Materials in Mathematical Reasoning
for Teachers’ (Küchemann & Hoyles)
1
Support in the classroom
Between the university days, the teachers try the materials in their own
classrooms. They work along with colleagues and create demonstration
lessons for collective critique and revise them in the light of the experience
and discussion.
The teachers then are asked to design and pilot their own mathematical
teaching sequences. We know this is a hard step to take but one that is
essential, as teaching from prepared materials without adaptation does not
adequately respond to the needs and diversity of a student cohort (Ball, 2000).
Laborde (2001) has documented this process for a team of teachers writing
activities that will fully integrate the use of a dynamic geometry package to
support pupils’ mathematics learning. Laborde noted that bringing technology
into a mathematics classroom creates a ‘perturbation’ (p.87) in the
teaching/learning process which causes teachers to examine and vocalise their
beliefs on mathematics and how it should be taught. Teachers must challenge
and change their beliefs but find this process difficult. The LMC programme
provides support through the organisation of networks or ‘communities of
practice’ working together on the same activity. The network will collectively
decide what to try and will work on the responses in an iterative cycle. The
aim is that networks will continue to function after the end of the programme,
and that teacher leaders will emerge, who will contribute to the programme’s
plans to scale-up in the future. As Ball reports ‘the most effective professional
development model is thought to involve follow-up activities, usually in the
form of long-term support, coaching in teachers’ classrooms, or ongoing
interactions with colleagues’ (Ball, 1996, pp 501-502).
Ongoing work
The LMC programme is at a pilot stage and will be monitored by analysis
of data derived from interviews with the participants and their head teachers,
from observation of their classrooms and from the final presentation of their
collective reflections. We can report that already the teachers are reflecting on
their practice as a result of their encountering new perspectives and the need,
as Jaworski (1998) notes, to ‘address “hard” and “difficult” questions about
their teaching’. As an older teacher with a traditional approach to teaching
remarked:
At the first session, we were asked if we agreed with this hypothesis – ‘A
mathematics lesson without the opportunity for pupils to generalise is not a
mathematics lesson’. I keep thinking about that statement, it is so new to me and
trying to achieve this is what will change my practice.
Another teacher, reflecting on what he had learnt from trialling some of the
materials from the Proof Project (Küchemann & Hoyles) said:
I was convinced that a proof is only a proof if it has algebra in it. Now I am not
totally certain after I have seen the pupils talking about proof.
At the ICMI Study Group, we will present some of these analyses involving
descriptions of the different trajectories along which teachers developed from
the common starting point to their work in classrooms.
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