This project essentially started in September 1995, although it was conceived and some preliminary work done during the previous 6 months. It relates directly to the recommendations made for mathematics teaching and learning by Professors Werner Blum and David Burghes at the first Gatsby Seminar on Mathematics Education. These recommendations have been expanded and refined and the latest version is given in Appendix 1. This work also builds on the feasibility study undertaken during 1994/95 into the provision of mathematics courses related to initiatives stated in the Technology Enhancement Program (TEP). This study showed that mathematics teachers would be keen to use applications in coursework and teaching provided appropriate guidance and support was available. Teachers were also concerned that the revised National Curriculum did not spell out clearly what was required and they felt that more specific schemes of work were needed.

Given the impact that this initiative has made in such a short period, it seems appropriate to provide an interim report outlining what has been achieved and signalling the challenges ahead.

1 PROJECT SCHOOLS

A brief outline of our recommendations and what we hope to achieve with Y10 and Y11 cohorts in our demonstration project was sent to about 400 schools (mostly TEP schools but with the addition of Kassel Project schools and other schools in the South West). Invitations were given to attend initial informatory meetings which were held in London, Leeds and Exeter.

Representatives from about 120 schools attended these meetings (held on Saturdays in October and November, 1995) and these were invited to apply to become project schools. There were three distinct categories of schools:

• Pilot Schools in which most recommendations would be implemented. There would be two categories, namely
  • inner pilot schools whose pupils enter our new framework for GCSE assessment (if approved);
  • outer pilot schools which continue with their usual GCSE assessment.
• Associate Schools in which particular (but not all) recommendations would be implemented.

We have been both excited and overwhelmed by the response. We now have over 90 schools who have volunteered to become project schools (see Appendix 2) of which over 70 have applied to become full pilot schools.

The schools are of all types:

• l.e.a. comprehensives,
• grant maintained,
• city technology colleges,
• independent,

We had originally expected to work with about 15 to 20 schools but we do not wish to diminish the enthusiasm shown by mathematics teachers and hope that in some way we will be able to work with all the volunteer schools, although we will keep to our suggested number of inner pilot schools.

2 DEVELOPMENT GROUPS

As the potential scale of the project increased, we felt it important to capitalise on the available expertise from our project schools. We are achieving this by having regular meetings of interested teachers, with working groups formed to pursue particular aspects of the project:

• Schemes of Work
• Applications / Coursework
• Texts
• Assessment Framework
• Low Attainers
• Teacher Support
• IT and Mathematics.

It is crucial that what we develop is both feasible and appropriate for school mathematics departments and the close involvement of experienced teachers will help us meet this objective.

3 RESOURCES

Our original plan envisaged the development of

• schemes of work
• applications for coursework

but early in the project, and after a thorough review of available resources, particularly the three texts used most in schools (SMP, Holderness, Vickers), it was felt important that comprehensive resources were produced for teaching in Y10 and Y11.

Our emphasis on whole class teaching and raising expectations led us to propose a resources framework consisting of

• pupils' texts
• practice books
• teacher support.

Details of the content of these are given in Appendix 3.

The Schemes of Work group has designed the framework for differentiated ability groups, based on Key Stage 3 results and with the stated aim of achieving enhanced attainment by the end of Key Stage 4. This is summarised in the table below.

The Teacher Support working group has begun the task of providing starting points to be recommended for use by teachers in introducing topics. The work of the group will be extended over the next few months by asking all our group members to provide ideas and suggestions. The team will be further strengthened by using a number of consultants who will both moderate the work and provide material. This will supplement the work started by the Applications/Coursework working group. We will also be considering in some depth how applications from our industrial funding partners (Esso, The Post Office, British Steel and Singapore Airlines) can best be used.

4 ASSESSMENT

Our suggested new framework for GCSE, namely

• two compulsory basic papers (for which grades up to and including Grade C can be awarded),
• an optional extension paper (for Grades B, A and A*, provided Grade C has been obtained on the basic papers),

has been well received by teachers. It provides

• motivation for the weakest candidates since, unlike other schemes, Grade C can be obtained on the basic papers;
• less confusion and greater fairness since each grade can be obtained in only one distinct way (this was recommended in the recent LMS report on the problems in mathematics teaching).

We are currently negotiating with NEAB and SCAA in order to provide a pilot GCSE although this was initially turned down by SCAA.

Other issues being considered by our working group on assessment include:

• one of the basic papers being non-calculator,
• the extension paper consisting of two parts - the first containing shorter questions up to the level of Grade B, with the second part containing less structured but more challenging questions for the award of Grades A and A*,
• a simpler system of grading coursework so that its possible effect on the grade awarded is moderated.

5 LOW ACHIEVERS

In addition to students who fail to reach even the lowest GCSE grade, we have the problem of candidates who reach only Grades F and G. These grades have little currency and whatever advice is given to such candidates Grades F and G are regarded as failures by the outside world (and hence by the students themselves). We strongly feel that we would like to offer some form of positive achievement for the mathematical skills which have been achieved rather than recording failures, and an outline proposal has been developed by our working group.

We are currently considering existing frameworks which could be used, including the Welsh Board's Certificate of Education: Mathematical Achievement.

6 INFORMATION TECHNOLOGY : Integrated Learning Systems

The role of new technology in helping to deliver the mathematics curriculum will be carefully considered. Advice about how best to use, for example, graphics calculators and spreadsheets will be given in the teacher support material.

We are also keen to exploit the potential which a dedicated maths lab. of networked computers has, provided that suitable software can be developed. We have considered two such systems (currently being evaluated by NCET):

• Global Maths
• Successmaker.

Both give an indication of what could be achieved but are far from the ideal. In summary, we would like to see the development of software, dedicated to enhancing mathematics, that

• is complementary to our paper-based material;
• provides a management system able to
  • assess the ability level of the user,
  • provide suitable demonstration, testing and tutorial material for particular topics,
  • move the users onwards when a particular topic has clearly been mastered.
• provides individual student worksheets on topics;
• provides an appropriate reporting system for both users and teachers.

All this is possible but it would require considerable investment both in software development and, ideally, in helping some of our schools to purchase the dedicated network of machines needed to bring this dream to reality.

One further aspect that we are keen to exploit is the possible use of the internet to provide an economical and quick method of communication. We have, for example, established web pages for MEP. Most schools will be connected to the internet in the next few years and another exciting option that could be made available is for the central team at CIMT to provide highly topical and relevant applications based on the news items of the day. This facility would be of use to both teachers and pupils.

7 INSERVICE

The substantial increase in the number of volunteer schools does pose a real problem for inservice support. We have said that any teacher involved in teaching Y10 or Y11 classes in the project must participate in at least one day of inservice before next September. Continuing support will also be necessary throughout the project.

The inservice courses for these teachers to introduce them to our philosophy and provide the necessary support and encouragement will be directed by David Burghes. The schools have been grouped into 11 regions:

with about 5-6 schools in each region. Subject to funding we plan to appoint part-time regional inservice consultants who will be responsible for ongoing support during the project.

One of the main purposes of the first inservice courses is to promote the use of whole class teaching, particularly following the Hungarian approach. It is important that we are able to illustrate exactly what we mean and we are developing videos of good practice for use on these courses, in part funded by OFSTED. The videos, of course, would have a wider use in the years to come.

Our regional inservice set-up would also provide opportunities for mounting short courses for interested mathematics teachers outside the project, and indeed for other Gatsby funded mathematics projects.

8 FUNDING

Our main funding has been provided by

and we are very grateful for their support and encouragement. We are also grateful for the support and encouragement given by our industrial backers,

The project has now expanded far beyond its original aims in that we now hope to be able to

• extend support to about 100 schools, but limiting our inner pilot schools to the originally planned 15-20;
• develop full teaching materials (instead of just the teacher support);
• extend our project to the low achievers, providing both course material and an appropriate qualification;
• produce videos of good practice in whole-class, interactive, mathematics teaching (as seen particularly in Hungary) for use on our inservice courses;
• exploit the potential of recent IT developments to provide motivation, revision and consolidation in order to enhance mathematical progress.

If we are to remain a successful, competitive nation on the world stage we must ensure that future generations are given the required mathematical skills and knowledge. Raising mathematical expectations and helping pupils and teachers to achieve them is at the heart of this project.

Mathematics Curriculum

• Topics to be given a more systematic in-depth treatment, with far less jumping around from topic to topic.
• Clearly stated schemes of work for each year and differentiated ability ranges.
• More emphasis on practical numeracy, particularly for pupils who will not be continuing their mathematical studies beyond 16+.
• More use of relevant applications, both for coursework and for motivation with new topics and concepts.

Mathematics Teaching

• Emphasis on a clear, precise description of the basic idea or concept being taught, with worked examples and applications where appropriate.
• Correct, precise, orderly, spoken and written mathematics to be used at all times.
• Limited, controlled and effective use of calculators.
• Greater emphasis on whole class interactive teaching, with less individualised work during lessons, but more whole class progression.
• Homework to be used as a key component of learning.
• Individual pupil mistakes to be used as teaching points for the whole class.

Mathematics Assessment

• Regular testing (including mental tests) linked to schemes of work.
• Modified tiering arrangements for GCSE, with
  • all candidates taking two papers for awards up to and including grade C; and
  • an optional extension paper for award of higher grades.
• Coursework carefully controlled.
• Encouragement to enter candidates for GCSE Statistics.