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EXTRACTS FROM CURRENT NEWSLETTER - July 2002 No 10.
Conflict in Reception?
National Numeracy Strategy has now issued a guidance pack Mathematical Activities for the Foundation Stage that includes booklets that aim to help practitioners to plan activities that are linked to the Stepping Stones of the QCA/DfES Curriculum Guidance for the Foundation Stage. For Each Early Years goal there are suggestions for large and small group activities and for some �planned play and cooking activities� but the printed examples are very restricted. It is essential that young children have a far broader experience than is implied in this guidance. For example, there is no mention within the activities of the use of stories or singing rhymes that aid learning the counting numbers in order or ideas of more and less, or the sorting and pattern making activities that build towards the generalizations that are the basis of mathematical thinking. There is a danger of an implication that these are not part of the mathematical learning that should be included in the daily mathematics lesson.
The examples of �planned play and cooking activities� are all adult directed and have a strange notion of what constitutes play. There are no examples of the independent child orientated play that is an essential part of early learning. The video does shows examples of role play and one example of a game but most of the activities there is an adult leader who does most of the talking.
This pack is for guidance but should come with a serious warning. The contents will need a great deal of mediation and augmentation by those of you presenting training�it will be very important to plan and present in consultation with your Early Years adviser.
The NNS materials for ITT tutors Teaching Mathematics in Reception and Year 1 (DfES 0501/2002) includes a useful section and research articles on the importance of play in learning mathematics�a pity these are not available to LEAs.
Secondary Specialist Shortage
There is some acknowledgement of a shortage of secondary mathematics teachers with training places being increased to 1,940. "New pools of recruitment" are being sought by the TTA. For example there is a plan to pilot paid courses (�150/week) for up to 6 months for career changers with mathematics backgrounds to up-date their mathematics knowledge prior to PGCE. It has been suggested that teaching needs to recruit 37% of each year�s mathematics graduates. Training bursaries and �golden hellos� are having some effect, but with applications for mathematics degrees down and pupils dropping out after AS level the situation is not likely to improve greatly in the near future.
Government ministers are saying that a secondary curriculum and staffing survey (the last was in Nov 96) will be conducted in a sample of 500 schools this year (answer to Parliamentary Question 7/02/02). A report from the Liberal Democrats (sponsored by SHA and NAHT) based on information from 54 schools suggests that 1 in 7 secondary mathematics lessons are taught by teachers unqualified in the subject. Presumably the most qualified are teaching at GCSE and A level which begs the question how many KS3 pupils are being taught by unqualified staff? The potential problem is further aggravated by the use of inexperienced staff and those who have the necessary qualifications but have a limited range of teaching styles or pedagogical knowledge.
The NAMA survey now has information from over 1150 teachers from 152 schools in 12 LEAs which should give a clearer picture of tuition mismatch and take up of Continuing Professional Development. The data is now being processed and a draft report is expected to be ready by September. The finalised report will be made available on the CME and NAMA web-sites. A second CME one-day conference is planned for 6th January
Update from QCA
Meet the mathematics team - Current responsibilities
Jack Abramsky Principal Officer GCSE, A/AS, FSMQs, Algebra and Geometry
Caroline Attewell Principal Officer KS2, G&T;, creativity, website exemplification
Rachel Bickerton Support Officer Adult numeracy, creativity, post-16 review
Richard Browne Principal Officer KS3, AS and A level, GCSE, post-16
John Fenton Team Manager Manager of the support team, post-16 review
Paul Findlow Principal Officer Basic and Key Skills, secondary and post 16
Neil Kay Admin Assistant Office assistant for the whole team
Gabrielle Lynch Support Officer External events organiser, Algebra and geometry
Paulette McKoy Secretary Personal Assistant to the Principal Manager
Alice Onion Principal Manager Monitoring, overview, cross Key Stage comparability
Tahir Sadiq Support Officer Links Strategies and Subject Associations
Pam Wyllie Principal Officer KS1, Early Years, ICT, Standards Reports KS1-3, SEN
Changes to SATs etc
A letter has been sent to all headteachers outlining changes to statutory tests for 2003 onwards. Further guidance will be sent next term and there will be examples on the web-site. The changes in mathematics are:
- Some marks will be awarded for all three strands of Using & Applying Mathematics i.e.: Problem solving, communicating, reasoning at each Key Stage.
- There will be separate papers at KS1 for level 2 and level 3
- There will be no extension papers.
Optional tests
- Optional tests for years 3, 4 and 5 are being rewritten. There will be papers targeted at a range of levels in year 3 and 4 to match KS1.
- Y7 progress test will be purpose-designed (L3-4).
- Optional tests for KS3 to be made available from 2004 Y7 (L4-6), Y8 (L4 -7).
Other information
- KS2 remains a pair of papers at levels 3 to 5, no tiering
- TThere are to be no starred awards
National Curriculum in Action
The QCA National Curriculum in Action website illustrates standards of pupils' work at different ages and key stages. The site will continue to develop as more pupils' work and extra features are added. The site builds on the 'Consistency in Teacher Assessment and Expectations' series of booklets produced by the School Curriculum and Assessment Authority (SCAA) between 1995 and 1997. New work is being collected for all subjects and will be added to the site from September.
The website is for teachers and senior managers working in schools. Others may find it helpful, for example inspectors, advisers and consultants. The site has the means to build up an individualised portfolio. To view the site, go to www.ncaction.org.uk.
Curriculum development
- Algebra and geometry at key stages 3 and 4
This is a three-year project to strengthen algebra and geometry key stages 3 and 4. It is now in its final year. Analysis and research has been undertaken into current practices in England, best practice internationally and the requirements of higher education institutions and employers. The study of international comparisons, and problems and pedagogy will be published (purchasable) in September 2002. The geometry work has two strands: formal geometry and proof, and ICT. There will be a report on the whole project to the DfES in March 2003 which may include recommendations to the statutory curriculum. Other outcomes are likely to be advice and support for schools so they can develop and strengthen the place of algebra and geometry within the delivered mathematics curriculum. Work progresses in liaison with the Key Stage 3 National Strategy.
Developments across subjects
- Promoting creativity
This project considers ways of promoting pupils' creativity in the national curriculum. As well as reviewing the research and literature on developing creativity and looking at work in other countries, the project involves a practical investigation of what effective teachers do to develop creativity.
A trial generic pack will be sent to school in September. There will also be subject specific exemplifications � the mathematics group is being chaired by John Mason [email protected]. In subsequent years the work will encompass other subjects and explore issues of progression and expectations. Materials to help schools promote creativity and innovation may also be provided through QCA's website.
- Inclusion
Respect for all: valuing diversity and challenging racism through the curriculum
Respect for all has been circulated for consultation to organisations, LEAs and schools. QCA is now completing the final draft with partner organisations. Guidance is website based and supports inclusion in primary and secondary schools: http://www.qca.org.uk/ca/inclusion/respect_for_all/
Examples of work for gifted and talented pupils will soon be available on http://www.nc.uk.net/gt/mathematics/examples.htm
World Class tests are available for gifted 9 and 13 year olds. Visit http://www.worldclassarena.orgfor details.
ICT.
Cameos and case studies are being developed in each subject to illustrate classroom practice using ICT. In mathematics this might include for example use of, small programs, databases, dynamic geometry, independent learning systems, internet and programming.
GCSE Update
A 2-tier pilot will run in 2003 & 2004 with OCR involving up to 3000 students. The 2 tiers are: Foundation tier G-C: Higher tier D-A* This improves on the current system by providing access to grade C for all students. The overlap grades C and D will be examined using the same questions.
Post 16
A review of post-16 mathematics is considering all mathematics courses and qualifications, including GCSE retakes, Application of Number, Free Standing Mathematics Qualifications, AS Use of Mathematics, AS and A level Mathematics, Further Mathematics and the Advanced Extension Award. A full report will be written for the DfES and findings will feed into QCA Curriculum Monitoring report. AS and A level criteria for mathematics are being revised. A new draft will be sent out for consultation in the autumn term. This will go to all stakeholder organisations and to a controlled sample of schools and colleges. New specifications will be available autumn 2003 for first teaching from September 2004.
Monitoring the Curriculum
QCA has the key role of keeping the curriculum under review. This includes not only the statutory curriculum, but also the curriculum as delivered in institutions. QCA seeks evidence and views on all aspects mathematics education. Research findings, Ofsted reports etc are included with monitoring information. All findings and evidence are compiled into an annual report. Monitoring outcomes are used to inform future work on development, support and guidance. This includes the dissemination of good practice. If you have evidence or views that you would like considered in our monitoring do send it in to QCA. Also let QCA know when you come across good practice examples, that could usefully be disseminated. E-mail addresses of the team are all of the form [email protected]
JMC
http://mcs.open.ac.uk/jmc/
ARE YOU DOING RESEARCH IN MATHEMATICS?
The Joint Mathematical Council is very interested in the work being undertaken by teachers in researching school/classroom practice to improve the teaching of mathematics as part of the BPRS scheme. JMC is keen to support the work in two ways.
Firstly, there is a need to use research evidence to improve our knowledge of how children learn and teachers can teach to optimise learning. It is important that the knowledge gained by individual researchers is made available to curriculum planners; government sponsored bodies such as the QCA or the NNS and also fellow teachers. JMC would, therefore, like to make contact with you so that we can build a database of the work undertaken and to which colleagues can refer when considering their own practice or when planning their own research.
Secondly JMC would like to help to put practitioners working in similar areas in contact with each other so they can form a network to provide critical support and encouragement.
NNS
Guidance for teaching gifted and talented pupils is a website of guidance for teachers, coordinators and others involved in teaching gifted and talented pupils. It appears in the Inclusion area of the national curriculum website http:// www.nc.uk.net/gt. The site includes specific guidance for each national curriculum subject, as well as links to useful resources. The mathematics examples are still under development.
CONSULTATION RESPONSES
- ACME Consultation on Continuing Professional Development
ACME is conducting a project to review mathematics for the following groups:
1. Primary mathematics co-ordinators
2. Other primary school teachers
3. Secondary mathematics specialists, heads of mathematics, aspiring heads of mathematics
4. Secondary non-specialists � defined as those teaching mathematics whose main specialism is not mathematics or a closely aligned discipline.
In the light of the above groups we were asked to respond to the following questions:
- How important do you consider the role of CPD in relation to each of the groups defined above?
= CPD is vital in order to ensure that mathematics is taught in such a way that learners of all ages are motivated to continue with their mathematics education. The form that the CPD takes will vary according to the subject knowledge, confidence, stage in career and past experience of mathematics. It is not directly linked to the level of mathematics qualification of the teacher. CPD is not only to do with subject knowledge but also pedagogy, leadership and management. Significant groups that should be included are head teachers, curriculum deputies and strategy managers. There is also the issue of CPD for NNS consultants and consultants for the mathematics strand of the KS3 Strategy
- What CPD has been, or is now available, for mathematics teachers under the four headings given above and how widely available is it? Do you consider the current provision sufficient?
= The current provision is focused on the implementation of the NNS at key stages 1 and 2 � although there are now training materials for the foundation stage � and the mathematics strand of the KS3 strategy. This is a cascade model of training and although participants welcome the training and the evaluations of the training are high, there is a significant lack of impact at classroom and school level on the standards of teaching and learning. This training can take a narrow view of developing mathematics teaching and learning. The DFEE designated five, ten and twenty day courses that were run with accreditation from HE or linked with HE appear to have had more impact in terms of improving teaching and learning.
Most advisory services are stretched to capacity to provide the training entitlement that the standards fund requires to be delivered. This leads to a very narrow approach. Even if schools have the ability and capacity to send teachers to other courses these tend to echo the national strategies provision. Understandably schools are reluctant to be seen to be deviating from the Frameworks. Many schools are unaware of the serious concerns voiced by those in the mathematics research community and mathematics educators about the strategies. The OISE materials raise significant issues about the sustainability of the NNS and it will be interesting to see the external evaluation of the KS3 strategy.
The availability of training varies across the country. In some authorities schools have refused to allow their teachers to attend training due to problems with supply cover. Other schools have sent as many teachers as possible to training. Particularly in secondary schools heads of departments have been surprised that their mathematics teachers have demanded their entitlement to training. In my experience the teachers in the department below second in department have not been offered any CPD since taking up their post. The head of mathematics or second in department have attended those courses that have been offered.
Until the provision of the 5-day NNS course many primary teachers had gone out of their way to avoid any CPD to do with mathematics teaching. The attendance at 5,10,20 day was usually limited to mathematics co-ordinators, aspiring mathematics co-ordinators, heads of mathematics or aspiring heads of mathematics. Primary head teachers tend to restrict CPD funding to courses that directly address school development needs rather than personal development ones.
- What are the most effective types of CPD modes of delivery? You may have views as to the most effective number, distribution and timing of sessions (in-school/evenings/weekends/holidays? Spread over time or more concentrated?) and/or how CPD is best delivered (e.g. visiting AST/LMT, face to face, on-line etc)
= The demonstration lessons given by primary teachers as part of the NNS were one of the significant factors in helping schools to implement the Strategy in the primary sector. However, demonstration lessons can in themselves cause intransigence, for example where the teacher is not convinced that s/he can regularly prepare sufficiently good activities, or control the class when working in a different way. Another approach, used by some 10/20 day courses, is to facilitate teacher exchanges � two teachers jointly plan, deliver and evaluate a lesson in each others classroom.
The same level of attendance at demonstration lessons is not evident by secondary schools. It is felt this ties in with the previous submission that heads of mathematics do not recognize the CPD needs of teachers in their departments, compounded by the effect of the serious shortage of mathematics teachers to cover classes. Some teachers with �good� mathematics backgrounds are unaware of different approaches to teaching mathematics. Do not have the knowledge or skills to engage low attainers. There is initial evidence from the NAMA survey that teachers appear to be understating their need for CPD, for example, teachers �happy to teach �A� level� with �A� level as their own highest mathematics qualification. Evidence from primary 10/20 day courses and OU PGCE students also reveals that many primary teachers do not recognise the need to have confident subject knowledge beyond the level at which they teach the subject.
Cascade training is not effective unless time is spent helping those who have attended the courses to develop the skills of delivery and time is given to allow them to do this when they return to school. Typically a 1 day training is cascaded in 5-10 minutes. Effective 10/20 day primary co-ordinator courses included sessions and activities designed to help course members work with colleagues. The cascade model is training that is transfer of information in time rather than development of good practice over time.
CPD needs to happen in quality time. Many teachers are prepared to attend courses at weekends, after school and in holiday time. There are serious equal opportunities issues here as well as the implications for overburdening individuals � both course participants and trainers!
An alternative is supported distance learning with locally based groups. For example:
In the 1980�s LEAs sponsored primary and secondary teachers and advisory teachers to do The Open University (OU) ME courses such as EM235 Developing Mathematical Thinking. The OU now only runs a Master�s course (ME822 Researching Mathematics Classrooms � uptake 75/year 25% of ME masters nationally). The Associate course/undergraduate programme gradually declined to nil during the 1990�s due to the small number of students taking courses. Informal market research revealed this was due to teachers not having the time (NC introduction, Ofsted, NNS), encouragement or funding to enrol on these courses. Some LEAs continued to run �10-day� courses using OU distance learning materials accredited under the OU certificate of professional development.
In the late 1980s DFES funded the OU materials "Project Update Mathematics" for secondary teachers including the series "Preparing to teach". Some LEAs ran courses based on these materials. The OU Centre for Mathematics Education (CME) is currently developing a Diploma programme. The first course ME624 (in 2 parts 1 week residential, 1+ term distanced) is under production funded by Esmee Fairburn Foundation.
University College, Chichester run Diploma/Certificates in Advanced Educational Studies (ME). These are run in conjunction with LEAs (for example Dorset) and combine NNS courses in accreditation.
- Do you have evidence of the effectiveness of different patterns of CPD, especially in terms of improved student learning or teacher retention?
= TThere is some anecdotal evidence from Learning Schools Programme that on-line support is NOT effective.
Effective CPD, which improves practice and has long lasting effect. has the following features:
Initial 2/3 days �kick start� (evenings free to think not marking/preparing)
Drip feed support/sessions over two terms
Active support required from head teacher/HoD � (plus another colleague from same school even more effective (Northants))
High quality support materials (including distance learning) designed for use during and post course that include: examples of developing programmes of study and activities that have progression and are challenging, �how to work with colleagues� for example overcoming intransigence� etc.
�Homework� � requirement e.g. undertake action research work in class and/or with colleagues and then to present findings orally and/or in writing�.
Opportunity for work to be accredited
A block of time, for example 5 days in a row, is not as effective as �drip feed� in the long term. Teachers need time between sessions to think, talk to colleagues, try things out and overcome the �baggage� they bring with them to CPD labelled mathematics.
NAMA RESPONSE TO "14-19: EXTENDING OPPORTUNITIES, RAISING STANDARDS"
GENERAL
NAMA welcomes the opportunity to respond to the government proposals in the green paper 14-19: extending opportunities, raising standards.
As with other recent consultations, we consider requesting yes/no responses to the specific questions to be over simplistic. A five-point scale would be more helpful and perhaps more informative e.g. strongly in favour, broadly in favour but with reservation, neutral, broadly against but with some agreement, strongly against.
Many NAMA members have link adviser and inspector roles so our response addresses the broad education issues and as well as areas that relate to mathematics. NAMA also wishes to endorse the ACME response.
RESPONSE SUMMARY
We welcome the vision of the 21st century requiring an education system that meets the needs and aspirations of society and the individual.
Some consideration is given to supporting teachers and schools in meeting the proposals but we feel that there is insufficient attention to the resources, including time, that will be required to implement the spirit as well as the letter of the proposals, for example individual learning plans.
We also welcome the proposals that are designed to engage young people in the study of modern languages and science but would like to see similar proposals for mathematics, perhaps by extending the FSMU ideas to the younger age range.
There is a shortage in mathematically knowledgeable teachers. In order to engage the disaffected and challenge the more able we consider that there needs to be an extensive programme of Continuing Professional Development (not merely training in requirements) so that mathematics teaching can become exciting and interesting for all young people. The Free Standing Mathematics Units offer a way forward but again, without adequate CPD take-up is likely to be limited.
There needs to be collaborative learning opportunities within classroom setting as well as collaborative teaching between institutions.
The concentration on external qualifications and standards (as measured by test results) seems to us to militate against engaging young people in education in its broadest sense.
To varying degrees many young people feel alienated from their families, schools, communities and society (and not just the academically less able). Teachers and others working with young people need the resources and encouragement to develop approaches that enable such young people to feel that they are part of a learning society, and that they have valued contributions to make to their local communities (class, school, locality).
We strongly agree the challenges to be faced. In particular the implication of �education with character�. The notion of a �decent education� is not just measured by examination qualifications. There is a great need for young people�s achievements to be recognised by society beyond merely having �pieces of paper�. Young people in full range of academic ability need a broad education for a place in society.
How does the 14-19 stage correspond with the proposal that KS3 will reduce by a year and become 11-13? How will transition and development of KS3 work be managed? Some of the material associated with KS3 Strategy gives exemplars of schools that, effectively, have a 2 year KS3 for more able students.
INVESTIGATING HOW TEACHERS MIGHT USE ICT TO PROMOTE PUPILS' CREATIVITY ACROSS THE CURRICULUM
The following is a record of Mathematics Group discussion on how teachers might:
Recognise pupils' creative thinking and behaviour when they are using ICT in the context of the subject/ aspect of the curriculum
Use ICT to promote pupils' creative thinking and behaviour
Use ICT to promote a creative learning environment
Interpretation of task and responses:
It was agreed that the teacher is the principal factor, and that a suitable classroom atmosphere has to exist before any of the following strategies can successfully support a culture of creativity.
What is Creativity? What does it look like? How do we know it when we see it?
Stimulated curiosity that leads a pupil to pose their own problems�and choose their own path towards a solution. For example: a pupil sees a shape or pattern and tries to replicate it in Logo
How do we promote creativity? What is the teacher's role?
* Introducing the exploration of a new area beginning with a situation, not a specific task, letting pupil discussion lead towards a problem(s) of interest, with negotiated relevance.
* Modelling an enquiry style of learning:
* Asking open questions: For example: "Can you give me some more information about...? etc".
* Fostering the "What if?" attitude.
* Allowing pursuit of the initial question to be replaced by a new direction if that occurs.
* Encouraging pupils to take risks with possible solutions.
* Not attaching any stigma to wrong answers.
* Saying "I don't know", leaving room for students to explore the area of unknowing.
* Allowing the sharing of ideas with others. For example "make a square and a rhombus to have the same area" where pupils in different locations share ideas.
* Guiding the above process so that it is productive, judging when closure helps and when a new direction is needed.
* Recognising that a pupil's arriving at a 'classic' solution of a problem, which they have not encountered before, is as creative as a pupil thinking of a novel solution.
* Recognising that all learning involves creativity if pupils construct their own meanings.
* Allowing pupils' ownership of the ideas generating process - the above suggestions help to foster this.
* Recognising the importance of Geometric Construction and other spatial intellectual experiences in order to include the wide variety of learning styles among pupils.
* Question arising in the course of discussion: "if effective teachers set clear learning objectives how do teachers encourage creativity and still operate effectively?" Is there a tension between establishing clear learning objectives and fostering creativity in mathematics?
There was a feeling in the group that openness, which fosters creativity, is not valued. That there is a perceived pressure to hit closed objectives, particularly in mathematics using the national frameworks.
The place of ICT in mathematical creativity
* ICT is not central to the issue, but can provide a very important environment.
* ICT can change the pupil's attitude to taking risks or being wrong through simple and neutral feedback. A pupil can form a tentative view, make an initial decision, and examine the effect.
* Thus ICT shows the consequences of a choice or decision. For example in defining the procedure (Logo), setting the construction rule (dynamic geometry), or building the formula (spreadsheet).
* ICT can offer alternative routes into a problem E.g.: "Room Doubling" (Nrich) could use a spreadsheet to explore number patterns. The spreadsheet allows quick generation of numerical results, giving pupils a better chance to see relationships - it may give them more to notice and attempt to account for.
* ICT offers many stimulating environments, for example: new ways to display and share ideas, promoting discussion around the computer, or between pupils in different locations
What is helpful in the learning environment?
Creating:
* a rich stimulating environment where children can display their creative characteristics
* an atmosphere of question posing and openness to the variety in directions taken towards solutions.
* Having available a variety of resources/tools which students can access with confidence.
Notes recorded by Graeme Brown ([email protected])
Revised by David Wright (Becta) ([email protected])
Using and Applying Mathematics Items in End of Key Stage Tests
Jeffrey Goodwin
Mathematics Test Development Team, QCA
End of key stage tests have always had a Using and Applying Mathematics (UAM) demand. Three years ago, Brian Seager, the key stage 3 lead chief marker, was asked to undertake an audit of key stage 2 and 3 tests to establish the areas of Attainment Target 1 that were implicit in the items. The demand was apparent in a large number of questions.
The 2000 National Curriculum starts each Programme of Study with the relevant aspects of UAM, thus giving a high profile to this most important area of mathematics. With an implicit demand and a higher profile for UAM it was right to be more explicit about pupils� AT1 attainment within the end of key stage tests.
From 2003, approximately one eighth of the marks for each test at all three key stages will be identified as having a UAM aspect to be assessed; that is not to say that there is no UAM demand in the other questions.
The marks will be for parts of questions which need UAM to get a correct answer, and for parts of questions where UAM is being assessed directly, the most common form of which is an "explain" question. As it is not possible to use and apply mathematics without some mathematical content, all UAM marks will contribute to the content balance of each test.
Pupils should not see a change to the look of the test papers. It is not intended at this stage to make questions longer or to ask for different modes of answer. However, there will be a noticeable change within some questions where the amount of support given to the pupil is reduced to increase the need for UAM. The intention is not to change the overall demand of the test; any slight variation will be dealt with, as now, through the level setting process to maintain year on year consistency. A letter has already been sent to schools with an explanation of the change and sample questions for each key stage. Further sample questions will be sent to schools in the autumn.
We recognise that not all aspects of Using and Applying Mathematics can be covered in a test paper. To aid teacher assessment, we are developing UAM tasks which will be published on the QCA web-site in 2004.
Best Practice in Problem Solving
An Ofsted invitation conference designed to share best practice in problem solving, communication and reasoning in primary mathematics took place at Brunel University on March 20th 2002.
Problem solving allows children to engage in the processes of mathematics. In particular it is a means of stimulating children�s curiosity and catching their attention. Problems can facilitate the learning of new concepts, provide a vehicle for transferring concepts and skills to new situations or present a meaningful device for practising computational skills.
The following are the points that delegates felt were pertinent to the effective implementation of problem solving, reasoning and communication in mathematics:
- ensure that starting points are accessible to the children. In the planning of problem solving work, focus on intended outcomes rather than activities.
- Each child should have a goal to achieve with equal value placed on their work, despite ability;
- the problems chosen need to build on children�s own interests and their own ideas and questions;
- problem solving is a two way process. It tests the applications of learnt skills but also can initiate new learning;
- consider what you need to teach the children to do when faced with problems. In particular, model solving one or two problems using a framework for problem solving and how to break down a multi-step problem into its various parts;
- a group of children working together on a problem make more progress than individuals working separately. Collaborative working enables children to spark ideas from one another and to discuss thoughts and hypotheses;
- different methods of grouping children should be employed including grouping by ability and by friendship groups;
- well chosen problems provide pleasure and satisfaction as new situations are explored. Problems also allow children to encounter difficulties; a significant part of the problem solving process is to find ways of over-coming these. A great deal can be learned from unsuccessful attempts, providing teachers build strategies that children can employ when they become stuck;
- it is important to build a climate which encourages children to share their work with teachers and with each other. Much of this will be through talk and discussion.
- problem solving task allow children to find their own perfectly acceptable ways of presenting written work. Where necessary, children can be helped to simplify overly complex and long-winded written recording through showing them more conventional forms;
- it is a good idea to allow children to decide for themselves what resources and equipment to use to solve problems. Providing equipment is often restricting � as children become experienced at problem solving they also become confident about choosing equipment. It is, however, important to build competence and confidence and this means making suggestions such as "would xxxx be of use?" or in putting out a carefully selected range of equipment from which children can make a reasoned choice;
- children need the experience of evaluating their own work. The teacher can help this by sharing the learning goals with them and then using carefully framed questions to guide children to make their own judgements about the strategies they have used and the work they have produced;
- during plenary sessions, review together one or two questions, possibly the most difficult, taking the children through the problem solving framework, discussing different methods used to solve problems and commenting on the appropriateness and efficiency of the methods chosen. Alternatively, allow children to work with a different pair or group to discuss whether there is agreement about answers and to explore the range of mathematics used to solve the problems.
The full report is available from: http://www.ofsted.gov.uk/public/docs02/subjectsconference/subjectconf.htm
Announcement:
National Day Conference, January 6th 2003
Shortage of Mathematics Teachers - What progress?
Background to the conference
National concerns about the shortage of qualified teachers of mathematics led the Open University's Centre for Mathematics Education (CME) to host a conference in October 2001 entitled 'Key Stage 3 mathematics teachers: the current situation, initiatives and visions'. http://mcs.open.ac.uk/cme/conference/index.html
Following this conference, a national survey of the situation across LEAs was set up by CME, the National Association of Mathematics Advisors (NAMA) and King's College London. Additionally, other initiatives have been undertaken, including the development of courses and materials to support non-specialists teaching mathematics and developments in on-line delivery
of mathematics.
The theme of this second CME national day conference is 'reviewing progress'. The day will start at 10am with coffee and registration, and end with tea at 3.30pm.The programme is planned to include:
Margaret Brown, King's College London
John Howson, Education Data Surveys
A report about the National Survey
A presentation from Advisory Committee on Mathematics Education (ACME)
Papers with the theme 'Solutions' - descriptions of work in progress or suggestions for future work.
Discussion
Planning future action
Call for Papers
You are invited to submit an abstract of about 100 words for a paper for discussion during the afternoon. Please submit the abstract by 30th September 2002. The abstracts will be reviewed by members of CME and a small number will be accepted for inclusion in the programme.
If the abstract is accepted, please
* Submit the paper by 30th November 2002.
* Do not exceed 8 pages A4 in Times Roman 12pt, including references.
Accepted papers will be published on the CME website, http://mcs.open.ac.uk/cme/, made available to delegates on the day and published in the proceedings.
The papers from the 2001 conference are available on
http://mcs.open.ac.uk/cme/conference/papers.html
Hard copy of the proceedings can be ordered from
http://mcs.open.ac.uk/cme/conference/proceed.html
Registration
Registration will be available on-line or by post from 1st November 2002. The cost will be �15 to include refreshments and a copy of the proceedings. To register your interest, please email Tracy Johns, CME secretary on [email protected]
FUTURE DATES:
REGIONAL MEETINGS
Thursday 7 November 2002 1.30-4.30 pm in Havering
Tuesday 25 February 2003 1.30-4.30 pm in Harlow in Essex
Wednesday 21 May 2003 10.00 � 4.00 pm in Wheathampsted in Herts.
South West Maths Advisers
Meetings are held every term - next meeting will be on Sept 10th at the Holway Centre. Please contact either Trevor West ([email protected]) or Pete Griffin ([email protected]) for further details.
We are hoping to change the format our meetings from now on in order to include an element of professional debate and INSET as well as the helpful networking and sharing of business items that we all find so helpful.
To this end our Spring term meeting on Jan 7th 2003 will be a whole day affair and consist of a morning session run by Richard Dunne on the theme of "Direct Teaching versus Child-Centred learning: Is there a conflict?" and an afternoon of sharing news and views from across our region. This meeting will be held at Great Moor House in Exeter. Contact Pete Griffin for further details.
We are in contact with Mike Askew (Lecturer in Mathematics Education, King's College, London) and hope to invite him along to a future meeting - possibly May 6th, 2003.
North West
On the move ...
Adrian Koskie�s successor at Bury is Brian Roadnight, currently head of mathematics at Woodhey High school, Bury
John Hall retired at Easter as Adviser for Sefton for many years. He is replaced by Lesley Lee, formerly Adviser in Liverpool.
John Nolan takes over as Adviser in Liverpool
Martin Little moves from Wirral to NNS
Martin Golds has moved from Adviser in Wigan to be Adviser in St. Helens
The Soap Bubble Geometry Contest with Professor Frank Morgan (Williams College, USA)
What shape would you make 2 adjacent sheep pens so as to minimise the total
amount of fencing required?
How do you find the shortest length of road joining 2 cities?
These are both problems that the bubbles in your bath can solve! Can you?
Professor Morgan will give demonstrations, explanations prizes and the latest maths news on soap bubbles.
Wednesday 14 August 2002
17.00 - 18.00
Isaac Newton Institute for Mathematical Sciences
20 Clarkson Road
Cambridge
CB3 0EH
The event is free, but entry is by ticket only. For ticket reservations please contact Sara Wilkinson on 01223 335983 or e-mail
[email protected]
Further details are available on http://www.newton.cam.ac.uk/soap.html
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