Either Choose three small integers, positive or negative. Place these integers in the boxes in the expression below in all possible orders and multiply the brackets in each case: (x + ) ( x + ) = Now add up all your answers and factorise the result if you can. Or Let f(x) = sqrt(a cubic in x). Sketch y = |f(x)|
A bit about ACME An independent committee, established in January 2002 • To enable an effective and constructive partnership between Government and the mathematics community • To inform and advise the DfE and BIS in order to assist in its drive to raise standards and promote mathematics at all levels within education • To provide advice to government agencies and other key stakeholders
The Chair A “user of mathematics” • Professor Steve Sparks FRS • Volcanologist and risks • Joined ACME in January ★
One year ago this month The Bew Review ACME Response to the Education Select Committtee Inquiry into 16-19 participation in education and training ★
Mathematical Needs Reports A and B • Published June 2011 • Presented at workshops and seminars at various conferences • Looking outside the mathematics community
MNB: What mathematical proficiency entails: • procedural recall, accuracy and fluency in familiar routines • to develop procedural, conceptual and utilitarian aspects of mathematics together • the ability to interpret and use representations • a range of mathematical knowledge and experience • strategies for problem-solving and hypothesis-testing, including working with current digital technology • mathematical reasoning • appreciation of the purpose and usefulness of mathematics, and willingness to use it Need to develop all these aspects
What learners need in lessons: • to read, talk and interpret mathematical text • to get a sense of achievement • to use feedback from tasks and results • to have good-quality explanations (images, representations, language, analogies, models, illustration) • to have explanations that incorporate past knowledge, including familiar images, notations and mathematical ideas • teachers who understand the need to avoid unhelpful conceptions from particular examples, images and language • to base new learning on earlier understandings • teachers who push the boundaries of conceptual understanding
Cognitive needs: • to become aware of, familiar with, and fluent in connections in mathematics • to accumulate mathematical ideas • to have multiple experiences of mathematical ideas • time to develop the mathematical confidence to tackle unfamiliar tasks • to recognize the common ideas of mathematics • to know how to listen to mathematical explanations ★
And then things got really busy • National Curriculum Review • Early entry to GCSE • Primary arithmetic • Initial teacher education strategy • ... ★
GCSE early and multiple entry – an update • Nick Gibb responded to ACME’s position statement • The Department said they would look at reasons for early entry, and • Whether early entry is undermining progression • DfE has published a statistical study on the impact of early entry – detrimental to overall performance
National Curriculum review – a brief update • Responded to the Call for Evidence • Contributed to working groups • Individuals heavily involved through July/August, and again since January • Offered to facilitate pre-consultation discussion with the community • September – November/December a quiet time • Expert panel report – response
And after the summer, things got busier • Non-Government reports • Mind the Gap • Maths Task Force Report • BIS gets involved • HE white paper • Select Committees • Attracting, training and retaining the best teachers • How should examinations for 15-19 year olds be run?
ACME response to Expert Panel • Welcome split of Key Stage 2 • Do not recommend year-by-year primary curriculum • no evidence • Welcome more specialist teaching in primary • but it’s up to schools to determine deployment, and more support/training is needed • Cautious about Key Stage 3 / 4 split • would need eg linked pair GCSE and mechanisms to counter early entry • Agrees levels should be removed • but, support is needed during transition ★
But are we having any impact or influence? Early entry • Yes, but Government needs to take further steps National Curriculum • Process and content • Primary Best Practice seminar Key Stage 2 assessment • Disappointing • Mathematical Needs • Definitely
MNA: Bridging the maths gap The number of people entering higher education each year who would benefit from recent experience of post-GCSE mathematics 330,000 The number of such people supplied by the school/college system 125,000
Mathematical Needs of the Workplace • How has the jobs profile changed in recent years? • What general mathematical skills are needed by those in employment? • What are the particular mathematical needs for particular areas of employment?
Key findings from the workplace • To be effective employees need to have studied mathematics at a higher level than they will actually use in the workplace • Many employees have difficulty in applying the mathematics they know • Employees have difficulty in communicating mathematical ideas • Many people lack basic skills in mathematics (and literacy)
What mathematics does the workplace say is needed? • Statistics • Mathematical modelling • Problem-solving • Use of software packages and coping with problems • Performance indicators and the use of ratios • Risk
What can students choose today? – post-GCSE qualifications • A-level Mathematics • A-level Further Mathematics • A-level Use of Mathematics • Free standing mathematics qualifications (FSMQs) • Cambridge Pre-U • The International Baccalaureate Diploma • … a variety of mathematics is implicit in many vocational courses, but content is often ill-defined and not rigorously assessed.
Mathematical Needs of Higher Education • What are the course entry requirements in mathematics? • What mathematics does a course need if it is to achieve international standard? • What mathematics (including statistics) do students need if they are to be successful in their university course? ★
Push and pull • ACME recommends: • Universities should make clear the level and extent of mathematics encountered within each of their degree programmes. ★
Increasing participation Who are these students? < GCSE Grade C A-level • Not to scale! ★
Increasing participation • Probably have Grade C or B at GCSE (and maybe grade A) • Probably not studying A-levels in physics (or chemistry) • They may (or may not) be studying A-levels and planning to go to HE. • What do they need? ★
Increasing participation • ACME is preparing an options paper for the summer • Who is it for? • What size and shape? • What would it contain? • Who would teach it?
Moving forwards • Making it happen • Mathematical Needs A + Post-16 pathways • Pre-16 qualifications/pathways • The profession • Joining up initial teacher education and CPD: what, when and how? • Mathematical Needs B
Keeping up-to-date ACME Conference • 10 July 2012 ACME Membership • Advert out ACME Outer Circle • End of the summer News and Events • Website • Newsletter