Mathematics 14-19 Functional Mathematics Tom Roper, School of Education, University of Leeds

Mathematics 14-19 The Smith Report Set up to investigate problems in post-14 mathematics education and, Found many problems associated with the provision of mathematics for the 14-19 age group, Recommended that various bodies be commissioned by QCA to investigate new and different pathways in mathematics, Two contractors were chosen by QCA following a tendering process.

What is the next pair of numbers in this sequence? Mathematics 14-19 5, 7 11, 13 17, 19 29, 31 41, 43 What is the next pair of numbers in this sequence?

Functional Mathematics: What is it? Why is it called into being? How is it to be realised? How is it to be assessed? How does it fit with GCSE 1?

Why is it called into being? Mathematics 14-19 Why is it called into being? Need for a high skills economy, Which implies a highly skilled work force, Dissatisfaction of employers with the current output of schools, Lack of trust in the grade C of GCSE mathematics.

Mathematics 14-19 What is it? Term coined by Tomlinson, Defined initially by the contractors in Phase 1, Developed by QCA through consultation with the mathematics and mathematics education community, Now defined by the functional skills standards: mathematics on the QCA website, What are the standards?

Mathematics 14-19 What is it? The standards define what a student should be able to do in order to achieve functional mathematics at various levels as defined by the national qualifications framework: Entry Level ( Levels 1, 2 and 3) Level 1 (Equivalent to GCSE grades G to D) Level 2 (Equivalent to GCSE grade C and above) Level 3 (Equivalent to A-level – not yet defined) Available at http://www.qca.org.uk/qca_6069.aspx

Primitive Pythagorean Triples Mathematics 14-19 Primitive Pythagorean Triples 3 4 5 5 12 13 7 24 25 15 17 9 40 41 11 60 61 12 35 37 Based upon the data above what conjectures, hypotheses, questions, observations can you make? E.g. does every triple have an element divisible by 5?

Mathematics 14-19 What is it? Processes are defined as: Representing: making sense of situations and representing them, Analysing: Processing and using mathematics, Interpreting: Interpreting and communicating the results of the analysis

Mathematics 14-19 What is it? The levels are differentiated not only by content but by: Complexity, Familiarity, Technical demand, Independence. Content goes up to level 6 national curriculum for level 2.

Mathematics 14-19 How is it to be realised? We conceived of it as two components: Competence – can you do basic mathematics to a required degree of mastery? Functionality – can you use this basic mathematics in a given context?

Mathematics 14-19 How is it to be assessed? AQA and OCR are trialling/piloting assessments. AQA – test of competence and test of functionality, the latter depends upon a variety of contexts and has some questions that use prior data sheets OCR – a test which takes a single context and develops questions from this context through increasing the amount of information and complexity of the situation.

How does it fit with GCSE 1? Mathematics 14-19 How does it fit with GCSE 1? QCA has ruled that functional mathematics must be independent of GCSE yet be examined within GCSE since the standards will be incorporated into the national curriculum and hence into GCSE specifications. But, in order to prove that a student has met the standards it will be examined separately as a stand-alone qualification. It is still not clear whether or not you must pass functional mathematics at level 2 in order to get GCSE Maths at grade C but the odds are that this will be the case.

What did Pythagoras say? Mathematics 14-19 What did Pythagoras say? What is the statement of the theorem of Pythagoras?

Mathematics 14-19 GCSE 2 What is it? What did Smith recommend? Who will take it? How does it fit with GCSE 1 and A-level?

Mathematics 14-19 Smith said: The Inquiry recommends that, at the earliest possible opportunity, consideration should be given by QCA and its regulatory partners to re-designating GCSE Mathematics, appropriately modified if necessary, to merit a double award at level 2. (Recommendation 4.2) The Inquiry recommends that QCA and its regulatory partners should be funded to develop an extension curriculum and assessment framework for more able pupils at Key Stages 3 and 4. The extension curriculum should be firmly \rooted in the material of the current Programmes of study, but pupils should be presented with greater challenges. (Recommendation 4.5)

Mathematics 14-19 A-level What is missing at the moment? Sustained problem solving? Proof? Standards debate

Mathematics 14-19 How fast can you walk?