GCSE Mathematics Retake For Vocational Students GCSE .

indicate that the relevant mathematical understanding is best developed through theuse of problem solving techniques and a consideration of mathematics in context.The report also highlighted the importance of tailoring mathematics content to the needs ofvocational students and of maintaining the rigour and currency of GCSE Mathematics.Finally, there are those students who don’t gain a grade C at GCSE (just under halfof the cohort of all 16 year-olds). As a result of the Wolf Report, this latter group willcontinue to study towards GCSE mathematics if they are on a school or collegecourse. For this group, it is important to identify ways to tailor the traditional GCSEmathematics pathway to the needs of this group that are rigorous, engaging forstudents, provide sufficient breadth and are valued by employers.4.Some emerging concerns about GCSE retake for vocational students4.1ConcernsTo prepare this report, MEI has asked teachers from the FE sector about the experience ofteaching GCSE Mathematics retake courses to vocational students. Some concerns haveemerged from these discussions; they are noted here as possible barriers to enablingvocational students to succeed in GCSE Mathematics. There are teachers who have some experience of teaching Functional Skills; will theirmathematics be good enough to teach GCSE? How can areas of mathematics which are not in Functional Skills, such as geometry,be made relevant for vocational students? Many students who go into FE at age 16 without GCSE Mathematics are neitheremotionally nor academically prepared to retake it. What is to prevent colleges from offering only a Functional Skills qualification, evenfor students who are capable of gaining a grade C at GCSE before they are 19? There is a tension between trying to teach the whole of GCSE in a year anddeveloping the understanding and mastery of basic mathematics that students willneed as employees and for everyday life.Malcolm Swan 8, writing some years ago about retaking GCSE in FE, confirmed thatteachers felt a tension between covering content and developing student understanding.The primary objective for both teachers and students appears to be utilitarian – toachieve a grade C in the GCSE examinations. Obtaining a conceptualunderstanding of mathematics is only a secondary objective, at least for thetransmission teachers. These two objectives sometimes appear to be in conflict inthe teacher’s mind (eg, when considering the issue of coverage). While each teacherclearly wants to spend time helping students to develop meaning, there remains aninner anxiety that, unless students are given adequate opportunity to becomeacquainted (even superficially) with all of the syllabus, they will be disadvantaged inthe examination.8Collaborative Learning in Mathematics, Swan, 20065

4.2Addressing the concernsThe NCETM post-16 CPD enhancement programme, which was developed earlier this yearand piloted with over 20 further education colleges, has been designed to focus on thoseelements of mathematical subject content and subject pedagogy that enable teachers ofnumeracy and functional skills from the further education sector to begin the process ofbecoming expert teachers of GCSE Mathematics. This programme will be made availableacross the sector.As a result of the new requirements, a number of further education colleges haveapproached MEI to lead professional development to address the needs of tutors new toteaching GCSE Mathematics. In response, MEI has developed a new programme;Strategies for teaching resit GCSE Mathematics. This course is designed to address thevery specific needs of teaching post-16 learners working towards re-sitting GCSEMathematics. Early feedback has shown that this course is being very positively received byboth tutors and college leadership.Some FE providers have tried using vocational contexts in teaching GCSE Mathematics tovocational students. Examples are given in the next section.Emerging findings from a study of the experience of vocational students with FunctionalMathematics show it is possible to change the negative attitudes and lack of confidence withwhich some students enter FE. 9The transition from school to Further Education provides an opportunity for change instudents who may have previously experienced failure with mathematics. The earlyindications of this research are that students bring a legacy from school but it ispossible to provide an environment in which student beliefs and attitudes can bereshaped, useful mathematical skills for the future can be developed and studentscan gain the confidence to use them.9From failure to functionality: a study of the experience of vocational students with functionalmathematics in Further Education, Dalby, BSRLM proceedings, Nov 20126

5.Teaching GCSE Mathematics to vocational students5.1Using vocational contexts at Abingdon and Whitney CollegeA 2010/11 LSIS STEM case study 10 of effective practice at Abingdon and Witney Collegeidentified the problem of motivating vocational students as follows.We have noticed that the motivation of many of the students for maths is low, webelieve this is partly due to them finding it difficult when they were at school; theyhave almost all taken the exam recently and not achieved a C grade. However, wealso felt that one of the key problems in motivation levels was that they did not seethe relevance of the maths they were doing to their chosen vocational courses. Evenif students did recognise that the GCSE maths is of some importance to them, thisrecognition was not enough to maintain their motivation for a year-long course.One group of science students at the college were also taught mathematics by their scienceteacher who incorporated contexts from the science course into the teaching ofmathematics. Other vocational groups had material which linked to their vocational courseincorporated into their mathematics lessons. Abingdon and Witney College reported on theimpact of the changes as follows.We will continue with this approach as it has shown some promise, although it is hardto get linked vocational material for all subjects, so it is likely to take time to build upthese materials.Perhaps the clearest message from the case study is that having a maths lecturerwho also teaches in the vocational area is a distinct advantage for the students. Thatsaid there does seem to be an improvement in the motivation of students when anon-vocational maths lecturer tries to make the maths they are studying morerelevant, but this is a difficult task.10Abingdon and Witney College: Vocational Context for Mathematics, LSIS STEM, 2010/117

5.2Wirral Metropolitan College: good practice in GCSE MathematicsWirral Metropolitan College is a medium sized general Further Education College. At thecollege, the practice for the past few years has been to encourage vocational students toretake GCSE Mathematics if they do not already have grade C or better. Wirral MetropolitanCollege does not offer A levels.Students undergo a short diagnostic assessment which, together with their previous grade,enables the college to decide whether to offer them a place on a Functional Mathematics orGCSE course. Students have typically sat GCSE Mathematics at school more than once anda small, but substantial, minority have not attended school in either year 10 or year 11 orboth.To support students to succeed the college has developed the following key features in itsmathematics teaching.1. Each student completes a short diagnostic assessment which is built aroundcommon misconceptions in number, percentages, decimals, fractions and proportion.This informs schemes of work and lesson plans for the first weeks.2. Induction activities focus on career goals, the mathematics required for vocationalsuccess and getting to know students’ aspirations and previous experience oflearning mathematics.3. Frequent formative assessment enables tutors and learners to focus on whatstudents need to learn; there is insufficient time to re-teach the whole GCSE course.4. Early intervention (by week 5) and additional support (drop-in at the Maths Café)when learners aren’t making progress together with close links with vocational tutorsfor further support.5. Teaching mathematics through active learning, problem solving, addressing keymisconceptions and encouraging cooperative learning and peer support in theclassroom.6. Contextualising problems to the vocational areas which students come fromwhenever possible. Where logistics allow, groups for allied curriculum areas aretimetabled together e.g. Health & Social Care with Childhood Studies; Constructionwith Engineering.Pass rates for Wirral Metropolitan College are above national benchmarks 11. Studentsexpected to succeed in GCSE Mathematics this year come from a number of curriculumareas: Art & Design, Health & Social Care, Construction, Sport Science, Business, Cateringand Hair and Beauty.The college celebrates student success both on a small scale in class and on a larger scaleat their annual awards. They always nominate a Student of the Year from the 16-18 year oldvocational GCSE Mathematics students.116.2 % above benchmark in 2011/12.8

5.3Wirral Metropolitan College: contextualising mathematics for students fromCatering and Hair and BeautyTutors at the college feel that it is important to introduce, as early as possible, the intrinsicunderpinning role that mathematics plays in vocational areas. The example that follows isfrom two vocational areas: Catering and Hair and Beauty.In the induction for new students, tutors asked the catering students to make minestronesoup for three people using a recipe for two people. The activity involved weighing,measuring, cutting vegetables into specific shapes, calculating time etc.The students also had to divide a batch of dough into seven equal sized rolls by firstestimating and then using some trial and error.During their induction, the beauty students made face masks, aromatherapy oils and bathbombs with detailed and specific ratios.The activities were followed up with a discussion about the mathematics that was involved intheir chosen area and each student wrote his/her own individual learning plan detailing, notonly the things he/she needed to learn, but also the topics he/she would want to learn. As aresult the students were more engaged with the need to have a competent and confidentrelationship with mathematics. During lessons, care was also taken to consistently draw onreal life examples from the vocational areas to reinforce the link.This positive attitude towards maths needs to be fully embraced and supported by thevocational tutors, many of whom still need to exorcise their own mathematics demons. Twovocational tutors (a beauty therapy lecturer and a catering lecturer) took and passed GCSEMathematics in one of the college’s adult evening classes. They have become ambassadorsand have encouraged and spurred their own vocational learners on to not give up and tosuccessfully retake GCSE Mathematics.Having a strong link with the vocational tutors helps to reinforce the network of supportneeded to enable a student to succeed. Where there are issues of attendance or lack ofindependent work, the vocational tutor will also step in and provide the necessary support toaddress these.Note: The mathematics induction programmes for Catering and Hair and Beauty weredeveloped as part of an LSIS STEM Funded Action Research Project. The learningmaterials, ILPs and materials used in the CPD process are available fromheather.aspinwall@wmc.ac.uk9

6.The use of context in teaching mathematicsContexts are often used in the teaching of mathematics. Different ways in which contextscan be used in mathematics teaching are listed below.a. A realistic problem for students to solve, using skills they have already acquired.b. A realistic problem for students to solve in order to motivate and facilitate the learningof new skills.c. A realistic context to enable the students to see the point of the mathematics they arelearning.d. A realistic context to help students make sense of abstract mathematics.e. A pseudo-context which looks as though it refers to real-life at first sight but does not.These ways of using contexts in mathematics need not be mutually exclusive but someresources, and teachers, focus more on some of them than on others. The approaches areoutlined and exemplified below.6.1Realistic problems on which to practise skillsMany mathematics texts include such problems, often at the end of an exercise. This tendsto reinforce the impression that working in a real context is more difficult than working withabstract mathematical techniques and is only for able students who finish all the other work.An example problem which could occur at the end of a section about locusThe diagram below shows the plan view of a display stand at an art exhibition.Scale: 2 cm to 1 mA fence will be put around the display stand to stop visitors getting too close.The fence will everywhere be exactly 1.5 m from the edge of the display stand.Draw the fence accurately on the scale diagram.10

6.2Realistic problems to learn new skillsThere has been an increased interest in problem based learning recently, at university aswell as at school level. Students start with a problem; they may already know some of themathematics needed to solve it and will also need to learn new mathematics. In addition tolearning mathematical techniques, students also develop problem solving skills by workingon such tasks.An example problem to enable students to learn new skillsThe image below is from a resource produced by the Royal Statistical Society Centre forStatistical Education to exemplify the teaching of statistical problem solving at GCSE level.Source: Problem Solving Approach www.rsscse.org.uk, extracted 18/07/201311

6.3Realistic contexts for motivationIn the example below, the rest of the worksheet (for carpentry students) is about working outareas of different shapes and makes no further reference to the context; the purpose of thecontext is to let students know why they are learning the mathematics.An example of a realistic context for motivationCrown copyright 2006, DfES Key Skills Support Programme12

6.4Realistic contexts to facilitate understandingThe purpose of the context in the example below is to build students’ understanding of ratio.The context is one which many students find familiar but it is capable of being generalisedinto a model for dividing in a given ratio by means of sketching a rectangle, dividing it intoparts and attaching a value to each part.An example of a context to facilitate understandingMaking Sense of Maths, Hodder, Paul Dickinson, Stella Dudzic, Frank Eade, SteveGough, Sue HoughA team from Manchester Metropolitan University have recently been trialling some of theMaking Sense of Maths resources with post-16 GCSE retake students. Emerging findingsare that some students welcome the new approaches to learning mathematics which theyhave previously failed to understand but that the resources need to be adapted for the FEcontext.13

6.5Pseudo-contextsThe question below illustrates a type of question which is only seen in mathematics lessonsor quizzes.An example of a mathematics question using a pseudocontextBill is three times as old as Ben.In two years, Bill will be twice as old as Ben.How old are Bill and Ben now?Some people enjoy puzzles like these but most of them will probably pass GCSEMathematics at the first go.Olive et al, writing in Mathematics Education and Technology: Rethinking the Terrain 12 saythe followingThese “pseudo-contexts” can actually make mathematics more difficult to learn(especially for lower socio-economic group students), as they give children conflictingmessages about whether unintended contextual and experiential factors should beignored or drawn into play. By oversimplifying the intellectual demands required tomathematize and interpret problems, and by trivializing the contribution ofmathematics to solving real problems, the perception of mathematics as a subjectwith limited use outside of school is reinforced.7.Contextualising GCSE Mathematics content7.1Context and pedagogyThere can be a perception that working in context can make it more difficult for students tounderstand the mathematics but the experience of teachers who have worked withvocational students by using meaningful contexts suggests otherwise. However, it isimportant to choose contexts carefully – contexts which are motivating and interesting forsome students will bore others. It is also important for teachers to know what learning thecontext is intended to facilitate; this will enable them to communicate appropriately withlearners and to maximise the learning opportunities.7.2Context in Functional MathematicsFunctional Mathematics questions are set in a realistic context so it is natural for teacherspreparing students to sit Functional Mathematics tests to teach mathematics in context.However, it is by no means straightforward for teachers to source high quality teachingmaterials set in suitable contexts. The Wolf report 13 describes the problem as follows.The idea is that English and mathematics (and IT) should be ‘embedded’ in real lifeexamples that are related to the vocational course that someone is studying and to12Mathematics Education and Technology: Rethinking the Terrain: The 17th ICMI Study, Springer,Ed: Hoyles and Lagrange, 201013Review of Vocational Education- the Wolf Report, 201114

‘real life’. This is actually very difficult to do, because it demands that the teacher ofthe subject knows a great deal about a wide range of contexts, and can develop highquality materials for each.Some of the best pedagogy achieves it, but as a recipe for a mass system it is highlyambitious and demanding. The alternative to having specialist teachers grapple withmultiple contexts is to ‘embed’ the teaching in the vocational classes. That way, aswe have discovered in a number of previous occasions, they embed to the point ofvanishing.Vocational teachers know about vocational subjects. They are not maths or Englishteachers. And if teaching maths and English were so easy that they could just beslipped into other lessons as an extra, why would so many young people bestruggling with the subjects a

GCSE Mathematics retake for vocational students . GCSE teaching from 2015 . 1. Introduction . MEI was commissioned by the DfE to look at the proposed content of the new GCSE Mathematics for teaching from September 2015 in relation to the needs of post-16 students who have not achieved GCSE Ma