Document Sample

Widening Participation in Mathematics Project report Version 3 22 November 2010 www.ncetm.org.uk Contents Executive summary .............................................................................................................................................................................. 2 National trends ...................................................................................................................................................................................... 6 Case study schools and colleges...................................................................................................................................................... 8 Project initiation and support ........................................................................................................................................................ 11 Patterns of intervention ................................................................................................................................................................... 14 Measures of success .......................................................................................................................................................................... 15 Recommendations ............................................................................................................................................................................ 16 References ............................................................................................................................................................................................ 18 Appendix .............................................................................................................................................................................................. 19 Bishop Challoner Catholic College ............................................................................................................................................... 19 Bridlington School ............................................................................................................................................................................. 21 Chesterton Community College ................................................................................................................................................... 24 Childwall Sports College .................................................................................................................................................................. 27 Long Road Sixth Form College ...................................................................................................................................................... 30 Marshland High School .................................................................................................................................................................... 34 Plymstock School ............................................................................................................................................................................... 37 West Anglia, College of .................................................................................................................................................................... 42 Harris Academies, London .............................................................................................................................................................. 44 Page 1 of 44 Widening Participation in Mathematics Executive summary This report describes the outcomes of a set of case studies in which participants sought to increase the number of learners progressing to mathematics at AS or A2 level post 16, having achieved at most a grade B at GCSE. These case studies were commissioned by the National Centre for Excellence in the Teaching of Mathematics (NCETM) as part of an exploration of how schools and colleges might contribute to the improvement of these transition rates nationally. Context The context of the case studies is a series of papers published in the last decade that focussed on the relatively poor participation rate in mathematics at Advanced Level (References, page 18). These documents identified a number of contributory factors, of which the low participation rates of girls and of young people achieving a grade B or less at GCSE were particularly significant. The report produced for the then DCSF by the NCETM Factors influencing progression to A Level mathematics (2008) identified a range of strategies used by schools with the highest transfer rates nationally in mathematics from GCSE to A Level. The common thread identified by the report was the way in which these schools sought to attend to the important aspects of managing the teaching of mathematics and to do them all well. They were: • high quality teaching throughout the secondary phase • clearly demonstrated enthusiasm and passion for mathematics • professional planning and managing of the several elements that between them make for effective teaching and learning of mathematics • high expectations of pupils’ learning of mathematics • effective pupil monitoring and assessment regimes • a positive whole-school attitude towards mathematics as a subject • good inter-personal teacher-pupil relationships. In particular, it is clear from the evidence that pursuing single strategies in isolation is unlikely to have a significant impact on participation rates. Ten case study schools and colleges were selected to provide a small but varied selection of educational establishments that between them offer a set of very different experiences of providing mathematical education. Interventions A number of potential interventions were suggested to case study participants as part of the project’s initiation phase. These interventions had previously been documented in, for example, Robinson (2007) and NCETM (2008). Each of the case study schools and colleges chose one or more interventions that they believed would have an impact on progression rates, based on perceived similarities between their own circumstances and those in the previously researched schools. The most common interventions or change programmes that case study schools and colleges sought to make were: • interviewing and surveying students to gain an insight into their attitudes to mathematics and their reasons for choosing or not choosing the subject at A Level • professional development for teachers of mathematics on active learning approaches such as those promoted by the NCETM; • taster or interest-raising sessions for potential students, with an emphasis on the accessibility of the subject • using Year 12 and 13 students as positive role models, as speakers or in a formal mentoring scheme Page 2 of 44 Widening Participation in Mathematics • awareness and interest-raising through special activities such as visits to mathematics events and venues with mathematical significance • mathematics clubs and drop-in sessions designed or re-designed to attract a broader range of students and not just the most able • working with local universities to provide enrichment and encouragement. Learning experiences from the project Having emphasised the differences between the case study schools and colleges and their chosen change programmes and interventions, there were nevertheless some common characteristics in the kinds of learning experiences that participants reported as a result of their participation in this project. Chief amongst these were the confirmations of previous research; in particular: No single solution There is no single “magic bullet” that can be used to address the issue of low rates of transition for B-grade learners. Many case study participants were aware of how the different interventions they were making tended to support each other – or to be weak in their implementation because other improvement measures were not in place to help embed the outcomes. Attitudes matter The school’s attitudes to mathematics – its cultural norms and assumptions about the subject and about how it should be discussed and presented – have an important impact on progression. Several of the case studies sought to develop ways of raising the status of the subject in the eyes of pupils, either as a career choice or as an important and valued intellectual discipline. The options trap In all schools mathematics is an automatic choice at the selecting options stage, typically in Year 9. Because it is a non-negotiable choice, mathematics is rarely given any profile at this stage and an important opportunity to raise its significance for young people’s futures is lost. Lack of learning continuity As well as the selection of options in Year 9, there are other critical stages in young people’s lives, depending on the particular system of schooling they find themselves in. The transfers into secondary, typically into Year 7, as well as the move to a college, if there is one at the end of Year 11, are very important stages. Several case study schools and colleges experienced a loss of information about pupils at moments of transition, especially from school to college. One of the case studies involved a college seeking to establish a strong and early relationship with pupils at feeder schools in advance of transfer. This should have been unexceptional, but was actually significant because of how rarely this appears to happen in practice. National issues In addition, two issues emerged that have national significance. Even though the case studies represent a very small sample, the two emerging themes described below nevertheless ring true, and the case studies direct our attention to them because of the consistency with which these issues were present across the majority of participant establishments. Maintaining quality before and after transition There are big differences between schools, sixth form colleges and colleges of further education. These establishments still effectively operate under different funding regimes and the power to effect change within them continues to be located in different parts of the education system. The recent launch of the Young People’s Learning Agency (YLPA 1 ) presents an opportunity to improve the ways in which 1 http://www.ypla.gov.uk/ Page 3 of 44 Widening Participation in Mathematics mathematics teaching is monitored and supported before and after transition across these three different kinds of educational institution. Whilst it is not the whole story, the consistency of the quality of teaching and learning of mathematics across both sides of the transition at age 16 was identified as an important factor. It was seen as significant both in students opting to continue the study of mathematics after 16 and in the successful completion of AS or A2 courses of study. Several of the case study schools and colleges recognised that they needed to improve the overall quality of teaching in general and in post-16 in particular. They identified gaps in their teachers’ knowledge of recent developments in the pedagogy of mathematics and sought to deal with this by providing continuing professional development designed to bring teachers up to date. This, of course, supports what is already known about the need to continue to raise standards of mathematics teaching. However, it also points to the importance of ensuring that if pupils experience good quality teaching at GCSE they must also experience good quality teaching at A Level if they are to remain positive about the subject and speak well of it to their younger peers. These issues are particularly important where students change institutions on completion of KS4. Maintaining quality is also about ensuring there is an appropriate relationship between GCSE and AS/A Level curricula. In some of the case studies, older students would report to their younger peers that they had difficulties with the transition. The schools or colleges involved could do little if anything about the curriculum and sought instead to address these messages. Long Road Sixth Form College, however, actually changed the curriculum by piloting Use of Mathematics AS/A Level. Collecting data One of the weaknesses identified by the project was the limited availability of hard data. Despite participating schools and colleges being asked to ensure they had reliable initial benchmark data on pupil progression, hardly any such data had been routinely collected. In the case of 11-16 schools and colleges data on progression was difficult to garner, both locally and nationally. Attempts were made to collect the data through National Data Services. However, even in the 11-18 schools such data was not forthcoming. The simple reason appears to be that the schools in the sample did routinely collect and analyse data to shape selection processes for entry to post-16 study, but they did not track learner performance in GCE, after transition, in relation to previous GCSE performance. Anecdotal evidence suggests this is a general problem rather than a mathematics-specific one. In the case of partner establishments with pupils transferring at age 16, there is considerable collaboration effort needed if progression data is to be captured reliably. In 11-18 schools there is clearly a need for a strategic focus by mathematics teams on capturing and using progression data. Implications There are clear implications from these case studies and from previous work on transfer to A Level. More than anything else, schools and colleges need to become aware that in order to achieve the kind of transfer rates that are appropriate for a leading OECD country, they need to focus on seeking to do well all those key activities (such as those listed on page 2 above) that make up the daily, weekly, termly and annual work of a mathematics team. This will, of course, bring with it all kinds of positive outcomes and benefits. Additionally, along with those will also come an increasing self-confidence in young people in their own ability to take mathematics further. In order to be able to do things well, mathematics teams need reliable and timely data and information about the progression profiles of their pupils, about their attitudes to mathematics and how these affect their decision to progress with the subject. Some of these data should be collected routinely by the school or college, but more affective data such as pupil attitudes may need building in to teaching and learning. In order to support the mathematics team, the school or college needs to take a strategic approach to the ways in which it speaks about, promotes and makes visible its commitment to mathematics, not just as a subject but as a life-long learning habit. It is not enough that the teaching of mathematics to GCSE or the teaching at A Level should promote high quality learning. This quality must also be a golden thread that connects the pre- and post-16 experience of the subject. In addition, therefore, to continuing professional development (CPD) that promotes good Page 4 of 44 Widening Participation in Mathematics teaching and learning, there is also a need for CPD targeted both at mathematics teachers and at school and college managers about what makes for effective transition and how to manage this. The establishment of the YPLA creates an opportunity to really tackle the relationship between providers of GCSE and A Level mathematics. The goal, whether from school to college or within an 11-18 school, is to establish a symbiotic relationship that makes for an almost seamless transition between pre-and post-16, with young people getting the same positive messages about mathematics, the same high quality of provision and the same expectations that they can and will succeed at this subject which is an essential life skill for the citizens of a modern developed economy. Page 5 of 44 Widening Participation in Mathematics National trends Whilst there have been some significant swings in engagement over the last 20 years, the national trend in recent years has been for the number of students who are studying A Level mathematics to increase. Despite this, the number of pupils progressing to A Level has not reached the peaks achieved in earlier years: Year Mathematics Percentage Entries change 2005 46,034 +0% 2006 49,805 +8.2% 2007 53,331 +7.1% 2008 59,105 +10.8% 2009** 66,552 +12.6% ** data not available for 2010 until November. (Source: Rises in A Level mathematics – Some Preliminary Thoughts by ACME, October 2009) The previous government set a target of 80,000 entries to A Level mathematics to be achieved by 2014. How realistic this target is depends on the number of students achieving GCSE at the appropriate level. The most recent data available shows that 224,712 students achieved GCSE A*-C in the year 2006-7 and of these 152,571 achieved A*, A or B. The target of 80,000 therefore seems achievable. However, of these students only 41,299 were entered for A Level. The number of students who achieved grades A and A* totalled 74,360, so even if all these students progressed to A Level the target would not be achieved. This underlines the importance of encouraging the 78,211 students who achieved a grade B GCSE mathematics to consider progressing to A Level. To meet the proposed target on present numbers, a large proportion of the grade B students need to take up A Level mathematics as well as a greater proportion of students achieving a grade A* and A . The current position based on exam entries for 2008 and 2009 is shown in the table below: Year 2009 2008 Progressed from mathematics GCSE Grade B to mathematics AS Level 1,669 1,673 Progressed from mathematics GCSE Grade B to mathematics A Level 4,815 4,724 Total number of students who progressed to AS or A Level 6,484 6,397 Total number of students who progressed to AS or A Level 6,484 6,397 It became clear at the national workshop for this project, that some schools and colleges would have difficulties in gathering historical GCSE data linked to transfers to A Level. This was particularly difficult for the 11-16 schools present, who seemed to have limited access to data about progression. It was agreed in these cases, to use the resources of National Data Services (NDS) to find relevant data. The NDS data for the 11-16 schools were not generally available to classroom teachers but were compiled for those who took part in this project. The data were compiled by using GCSE results and relating them to AS and A Level entry. The data were therefore historical and related the GCSE grades of students who had been entered for AS and A Level a year ago and whose GCSE grade was achieved one or two years earlier. In practice, the picture was complicated by the fact that the AS entries are not made in some circumstances until the summer term of the first year or, in some circumstances, December of the following year or not at all. (In the science area there is some evidence that up to one third of centres may not certificate AS qualifications.) Page 6 of 44 Widening Participation in Mathematics This provided some help in tracking progression and the data were the best available through NDS. In the future, changes to examination processes will require post-16 providers to register all AS students during the first term, so this should improve the system and data should in future include those students who are currently never accredited with completing AS studies – usually those with less than C grades. If the data tables had been generally available then they could have been used in a number of ways. For example, the tables show that 152,571 students achieved a grade A*-B in 2006-7 and can therefore give an indication of the number of potential students who might progress to A Level. The fact that 41,299 students were entered for A Level in 2009 indicates a progression rate of 27%. The comparable progression rate when A Level and AS Level entries are combined is 30%. Using the same measure of eligibility, one of the schools who took part in the project, Chesterton Community College, achieved a progression rate to A Level of 36% and to AS and A Level combined of 47%, both of which are considerably above the national percentage. The teachers were unaware of their positive achievement until they took part in the project. Similarly, Marshland High School, another 11-16 school that took part in the project, had 31 students who achieved a grade B or above at GCSE. Of these students, ten went on to complete an A Level course. This indicates a progression rate of 32%, which again is above the national rate. This could be welcome news for a National Challenge school. A number of schools and colleges are asking for grade B or above at GCSE in order to enter AS Level mathematics. However, the data tables from the NDS and the case study reports indicate that there are a number of grade C students and grade D students who progress. Making these data available may have an impact on these requirements for admission. An analysis of the data available for science seems to coincide with the findings for mathematics. In compiling the science data the explanations and idiosyncrasies of schools and colleges reflected those in the mathematics case studies. For example, there are students in one of the case study schools who take Additional Mathematics and get better grades than in their GCSE. The same issue was identified with science students taking Additional Science. However, further work is needed to see if either of these affects progression. Page 7 of 44 Widening Participation in Mathematics Case study schools and colleges Selection of case studies Ten schools and colleges were selected for the case studies. The main criterion for selection was to get a wide range of institutions with very different characters of mathematics provision and covering the majority of phase or sector structures common in England. While a small number had particularly good transfer rates from GCSE to A Level, others did not. Some of the establishments were selected because of particularly interesting individual features that were felt might offer some useful insights. For example, the proportion of pupils who previously took GCSE mathematics and achieved Grade B at Childwall Sports College was 56% but only 8% of pupils gaining a B grade at GCSE in 2007/8 took A Level mathematics. Another school, Chesterton Community College, was selected because it illustrates the challenges associated with mathematical pathways from 11-16 phase schools, where the local progression route is to a sixth form college. Some of the schools were identified nationally by DCSF(now DfE) as having high numbers of students achieving grade B in mathematics but with less than 25% of these progressing to A Level. Of the 18 schools identified in this way, four volunteered to take part in the project. However, these were all 11-18 schools and while this made identification of transition data easier it did not provide a focus on 11-16 schools and colleges. A selection of colleges and 11-16 schools were included for comparison purposes. The College of West Anglia was selected as an FE College to see if this was the route that students used who gained grade B or grade C and wanted to progress to AS Level. Marshland High School was used as an example of an 11-16 school whose students did not have a single route for progression: students from this school could choose to study AS mathematics at any of one of four 11-18 schools in the area or the local FE College (College of West Anglia). They were included to provide an example of the data generally available to an 11-16 school and to examine the efforts of such a school in encouraging progression amongst their students. Chesterton Community College was chosen as an example of an 11-16 school whose students’ had relatively few progression routes. The majority of students transfer to one of two local sixth form colleges, one of which is Long Road Sixth Form College. They were intended to be a contrast with Marshland to examine the different experiences of 11-16 schools. Long Road was included to provide evidence about the role of sixth form colleges in recruitment of students on to AS mathematics. Subsequently, they also became a case study in the role of the Use of Mathematics A Level pilot. Harris Academy was included as an 11-16 school that was hoping to establish a sixth form and thus provide an additional option for their pupils.. The circumstances of each case study, then, are sufficiently different from each other to provide a marked variety of experience. This is a particular strength of this study. Bishop Challoner Catholic College, Birmingham Bishop Challoner is a Voluntary Aided 11-19 comprehensive school in the Kings Heath area of Birmingham. Their intervention was focussed primarily on increasing the number of girls progressing to A Level in the belief that this would also increase the number of students with B grades progressing. They used a combination of university visits and additional mathematics sessions to increase interest in mathematics. They also used girls who were studying mathematics in Years 12 and 13 as role models for the students lower down the school. In 2009, the school had 55 students studying A Level, 32 studying AS and 23 studying A2; in 2010 they have 66 students studying A Level, 41 in Year 12 and 25 in A2. Bridlington School, Bridlington Bridlington School Sports College is an 11-18 comprehensive in West Yorkshire with a little under 1,000 students. The DCSF data showed that 51% of students achieved a grade B at GCSE and that of those students eligible at KS5 only 15% chose to study A Level mathematics. There seemed to be a large group of students with the Page 8 of 44 Widening Participation in Mathematics potential to continue to study mathematics. In the initial plan, the school had intended to invite outside speakers to talk to potential mathematics students and arrange trips for students to universities to increase motivation to progress. In fact, the results of an early survey disclosed important barriers to progression in the attitude of learners. The mathematics team addressed these problems first and made changes to teaching and learning. Once these changes had taken place invited speakers were used to increase motivation to progress. In 2009, 39% students who gained GCSE Grades A*- B progressed, which was an improvement on previous years; but in 2010, after the changes described in the case study, 52% of students who gained grades A* - B progressed. Chesterton Community College, Cambridgeshire Chesterton Community College is an 11-16 school in the centre of Cambridge. The head of mathematics is a shared post between two women teachers. Girls and boys are taught in separate groups for some sets for Years 10 and 11. The school has well-documented evidence to show that this approach works for them and has increased their success rates at GCSE. The school conducted a survey and focus group discussion with students about what motivated them to want to progress to AS Level. Their choice of career and degree aspirations were important motivators so the school introduced the students to career websites and created a careers notice board. Former students returned to the school to help to motivate students to progress. Using statistics compiled for this project, Chesterton had the highest rate of progression of all the schools that took part. The historical data showed that 47% of students who gained grades A*-B progressed, compared with a national proportion of 30%. The result of taking part in the project suggested an improvement of this figure for the school to 65%, with 52 from 80 students progressing to study mathematics. Childwall School, Liverpool Childwall Sports College is a large inner city 11-19 secondary school with a comprehensive intake and has approximately 1,300 students. This school focused its intervention on using the time between the end of GCSEs and the start of the summer break to introduce the students to topics they would encounter at AS Level. The activities they used were based on those in Improving Learning in Mathematics. In the first year, the introductory programme lasted for two days in each of two weeks. The recruitment rate to AS in this school was 48% for 2010, which was above the rate of recruitment for A*-B that had been achieved previously. However, the key measure of success for this centre was the increase in the number of students who progressed to AS, which during the life of the project went from three to 22. Long Road Sixth Form College, Cambridge Long Road Sixth Form College in Cambridge is one of two sixth form colleges in the area. It has an intake of over 2,000 students per year. Students in the area generally compare well against the national average for five GCSE A* to C. The college has introduced a series of taster days to introduce potential students to the courses that are on offer there. This is particularly important because the college now offers Use of Mathematics, which had increased the number of students studying mathematics, perhaps because it had a wider appeal. It is worth noting, however, that the introduction of Use of Mathematics has had no impact on the numbers taking A Level. The majority of students gaining a grade B GCSE now appear to take this option. Marshland High School Marshland High School is an 11-16 comprehensive in Norfolk. Students may progress from this school to the college of West Anglia (an FE college) or one of eight 11-18 schools in the area. The school gained specialist status for science in September 2005, but prior to the beginning of this project, it was designated a National Challenge school. At the school’s inspection in May 2009 it was given a Notice to Improve. The school used a combination of a mathematics club and entry into Additional Mathematics as a way of boosting students’ self-esteem in relation to mathematics. Although it was possible to calculate a progression rate for this school based on 2009 entries, it was more difficult to calculate a rate for the current year due to the number of possible routes that students could take. There is a need for more work to be Page 9 of 44 Widening Participation in Mathematics completed with schools in this situation to give feedback about the effect of their encouragement of students to progress. Plymstock School, Devon Plymstock School is a comprehensive 11-18 school with 1,700 students. It is a specialist sports college. They used differentiated learning for the taster sessions they staged for Year 11 and catered for the needs of grade B students to bridge into AS Level. They also used real world applications of mathematics within the Year 11 and AS mathematics schemes of work to relate mathematics to a career pathway. As a result of the changes made at the school the recruitment to AS Level mathematics had increased from 39 to 58, and the number of students who progressed with a grade B had increased from 12 to 23. The students with grade B GCSE now accounted for 40% of the AS mathematics intake. College of West Anglia, Kings Lynn College of West Anglia is a post-16 FE college in Norfolk. There are a number of 11-19 schools in the immediate area but the college continues to offer and recruit to A Level mathematics and Further Mathematics. Twenty-six schools provide students for the college. The college concentrated on raising interest in and enjoyment of mathematics with a specific focus on its “Launch Pad” website and event sponsored by Norfolk LEA. The event featured LA advisers, teachers from the college, invited presenters and teachers from local schools. The recruitment for 2010 showed that there had been an increase in the number of students with grade B or grade C at GCSE who were studying at AS Level. Harris Academy London There are a number of schools in this consortium who are just beginning to offer A Level mathematics. The academy planned to contact former pupils to offer role models of students who had progressed with mathematics. They also planned to complete a questionnaire survey of the whole consortium to find out what would motivate students to progress. Page 10 of 44 Widening Participation in Mathematics Project initiation and support Throughout the project the case study schools and clusters were supported by an NCETM regional coordinator. On 15 July 2010 the project participants were invited to a national workshop in London. More than half of the case study schools and colleges were able to send representatives and this enabled participants to compare activities and hear progress reports from each other. It became clear at the national workshop that schools and colleges would have some difficulty in gathering historical GCSE data linked to transfers to A Level. This would be the case especially for schools that take pupils up to age 16 and therefore have limited access to transfer data. It was agreed that in these cases Julian Clark, senior adviser to the Secondary National Strategy, would use the resources of NDS to find relevant data. Suggestions for identifying interventions All case study participants were encouraged to read the NCETM report participation to DCSF on widening Factors influencing progression to A Level mathematics (2008). They were also provided with suggestions for the ways in which they might identify appropriate interventions. These suggestions are summarised below. Gathering data about progression Analysing data about progression to A Level mathematics: • highlights issues about recruitment • sets the scene for the discussions that follow • sets a baseline for measuring success of any intervention • brings the issue of progression of students with grade B in GCSE mathematics to the attention of staff and encourages debate • highlights the points where data is missing e.g. with progression data for staff in 11-16 schools there is possibly a need to establish informal means to get data on progression. Discussion of progression amongst mathematics staff Discussion of progression issues within the mathematics team is as an opportunity to raise awareness, especially about the recruitment of GCSE mathematics grade B students on to A Level mathematics programmes. In particular, it is worth considering what factors teachers think are influencing student choice of subject at A Level. Interviewing students Interview Year 12/13 students to discuss the factors that influenced their choice of A Level subjects. Share the interview results with the mathematics team in order to: • make them aware of the reasons students give for rejecting or selecting mathematics as an option at level 3 • Identify significant factors in the students’ choice of A Level subjects to inform a strategy of making mathematics more attractive to future students, especially those with target grade B at GCSE. Interview Year 11 students to discuss the factors that influence their choice of A Level subjects. Share the interview results with the mathematics team to raise awareness and identify selection factors, and how approaches to teaching and learning might be influenced. The interview can also be an opportunity to present the advantages of studying mathematics. Interview Year 10 students to discuss the factors that are currently influencing their choice of A Level subjects. Again, share the interview results with mathematics team. The interview can also be used as an opportunity to counter the negative images of mathematics and accentuate the positive value of studying the subject. Page 11 of 44 Widening Participation in Mathematics Student survey conducted for the project A small-scale survey was conducted for the project. 165 students of AS Level mathematics were asked to give their reasons for choosing the subject. They were also asked to prioritise those reasons. The graph below shows the percentage of all students and those who achieved grades B or C at GCSE that gave the highest priorities to the reasons offered in the survey. This was provided to participants as a suggested starting point for discussions of the reasons students choose A Level mathematics and to encourage them to consider conducting a similar survey in their school or college. Suggested interventions in relation to career choice Case study schools and colleges were also invited to consider a number of careers-related interventions they might make: • Teachers of mathematics could use the opportunities during their lessons to emphasise the careers that an AS- or A Level qualification leads to. Surveys of students such as the one described briefly above have shown that teachers are more significant than parents for influencing progression into mathematics. • Set up a mathematics careers notice board and website. • Highlight the career pathways for a specialist mathematician to make the subject relevant to career choice. Posters that advertise careers not normally associated with mathematics are also useful. Images from FutureMorph and Mathscareers can be used to advertise these websites. These highlight the importance of mathematics as a general qualification that supports many career pathways. • Use invited speakers to emphasise the value and usefulness of mathematics in the workplace. • Visit the local university to emphasise the usefulness of mathematics in degree studies. Not necessarily degrees in mathematics. Other suggested interventions Further suggestions to case study schools included: • Use existing students to report their experiences of AS mathematics to Year 11 students. Page 12 of 44 Widening Participation in Mathematics • Prepare bridging work for grade B students to complete, perhaps over the summer, to support fluency in algebra in preparation for AS mathematics. • Hold taster sessions after GCSEs are complete but before the summer holidays begin, to encourage an image of mathematics as an enjoyable subject to study. • Have other appropriate pathways available for students with grade B, e.g. Use of Mathematics as well as A Level mathematics. Page 13 of 44 Widening Participation in Mathematics Patterns of intervention The schools and colleges participating in this project were given a free hand to develop interventions that they believed would work in their specific context. They had, however, been given a steer through the project initiation process and most of them chose one or more of the suggested interventions. The interventions used by case study participants fell into the following categories: • Interviewing and surveying students to gain an insight into their attitudes to mathematics and their reasons for choosing or not choosing the subject at A Level (five cases) • Professional development for mathematics teachers on active learning approaches to teaching mathematics, such as those promoted by the NCETM (three cases) • Taster or interest-raising sessions for potential students with an emphasis on the accessibility of the subject (three cases) • Using Year 12 and 13 students as positive role models as speakers or in a formal mentoring scheme (three cases) • Awareness and interest-raising through special events and activities such as visits to mathematics- relevant venues (two cases) • Mathematics clubs and drop-in sessions designed or re-designed to attract a broader range of students and not just the most able (two cases) • Working with local universities to provide enrichment and encouragement (two cases) • Entering students for Additional Mathematics GCSE, including those predicted grades below A in mathematics GCE (one case) • Including more material on real-world applications of mathematics into GCE teaching (one case) • Creating positive messages about mathematics through such things as posters, displays of work and assembly input (one case) • Identifying a specific target group for progression to A Level mathematics that includes students likely to get a grade B at GCSE and working with them specifically (one case). These are described in more detail in the appendices. All case study participants used more than one intervention. As a research project this made it difficult to disentangle the benefits of specific interventions. However, as examples of action research these case studies exemplified the creative nature of the process and in most cases engaged the whole mathematics team. In many cases, this was a journey of discovery that led to some challenging realisations for the teachers involved, especially about what informs students’ decision-making about progression. Page 14 of 44 Widening Participation in Mathematics Measures of success It proved remarkably difficult for project schools to collect the kind of hard evidence about progression that would support the proposition that their intervention had been successful. However, there was good deal of soft evidence in the form of improved student attitudes and a greater focus of interest by the schools in their grade B students. The table below indicates the evidence that was available: Participant Nature of evidence Bishop Challoner Catholic In 2009 the school had 55 students studying A Level – 32 studying AS and College, Birmingham 23 studying A2; in 2010 they have 66 students studying A Level, 41 in Year 12 and 25 in A2. Bridlington School, 12 out of 31 students with grade B going on to A Level (of which seven out Bridlington of 16 are girls). Three students with grade B at GCSE were studying A Level in one year so that they could take up Further Mathematics next year. Chesterton Community No hard data but a decision to focus on students with grade B at GCSE by College, Cambridgeshire the 16+ establishment to which students from the school progressed. Childwall School, Liverpool 12 out of 33 students with grade B progressing to A Level (nine out of 19 were girls). Long Road Sixth Form Large increase in Use of Mathematics AS (mostly grade B at GCSE) with no College, Cambridge corresponding fall off in numbers of AS mathematics students. Marshland High School Increasing number of students with grade B at GCSE with corresponding increase of those going on to A Level. Plymstock School, Devon 50% of boys and 11% of girls with grade B at GCSE opting to progress to A Level. West Anglia, College of, Increase from nine out of 22 students with grade B or C at GCSE Kings Lynn mathematics taking A Level, to 13 out of 22 Wisbech School [No report received] Harris Academy Identification of student attitudes and its impact on planning the development of sixth form mathematics provision. The schools and colleges in these case studies appear to have a significant poverty of information about their students’ progression profiles in mathematics. If the situation evidenced here is a common phenomenon across all schools and colleges this would be a matter of significant concern. It is also clear that many mathematics teachers within these establishments need more opportunities for professional development in such areas as the active learning approaches to mathematics promoted by the National Centre. Page 15 of 44 Widening Participation in Mathematics Recommendations This study has confirmed a number of promising interventions and change programmes that have the potential to make a difference to the numbers of young people with grade B in mathematics progressing to A Level. Recommendations to schools In the light of the NCETM report to DCSF on widening participation, Factors influencing progression to A Level mathematics (2008), it is important that schools and colleges seek to make a number of interventions and do not rely on just one to improve progression rates to A Level. All of the interventions suggested to and used by the case study participants appear to have had at least some measure of success and there is evidence from the 2008 report that they are more likely to be effective in combination. In particular, the gathering of students’ views on mathematics and their reasons for choosing or not choosing to progress in the subject has been especially illuminating for case study participants. However, it is clear that schools and colleges have relatively poor information about the progression profiles of their students in mathematics. It is also clear that many teachers of mathematics still have little knowledge of current developments in mathematics teaching. It is therefore recommended that schools and colleges: • place a priority on collecting, analysing and acting upon data about the grade profile of student progression in mathematics • ensure that all teachers of mathematics are up to date with current developments in teaching and learning by, for example, active engagement with the NCETM • develop ways of regularly collecting students’ views about mathematics and especially about their reasons for choosing or not choosing to progress to A Level • seek to work collaboratively to manage effective transition to A Level • consider at least two of the interventions listed in the “Patterns of Intervention” section above (page 14), if they are not already doing them. Issues for consideration by the National Mathematics CPD Committee or by other infrastructure organisations supporting increased transition to A Level It is clear from these case studies that more needs to be done to engage teachers in the quality of teaching and learning of mathematics that is promoted by the National Centre and other organisations and professional development providers who have similar roles. The solution to the problem of promoting transition is multi-faceted with no one approach offering a high degree of success by itself. The most important elements of the solution appear to be: • high quality teaching throughout the secondary phase leading up to GCSE • enthusiasm and passion for mathematics • professional planning and managing of the several elements that between them make for effective teaching and learning of mathematics • aspirations and ethos demonstrated by the school or college • a whole school attitude to recognising the learning of mathematics as a lifelong journey. One other critical factor in successful outcomes following transition is that the nature and quality of the teaching and learning must be maintained during the programme of A Level study following transfer. The implication for the FE sector is the need to recruit, retain and develop mathematics teachers of the highest calibre. Page 16 of 44 Widening Participation in Mathematics Therefore, the key issue is managing the transition to A Level both through effective teaching and learning and through collaborative CPD between teachers pre- and post-16. Key to the ability to effect change is the availability and timeliness of the data and its usefulness. A great deal of work is being done in this area at present. It is particularly important that where the transition at 16 involves a change of learning centre – such as from an 11-16 school to a sixth form centre or an FE college – there must be effective and transparent ways for the two establishments to have dialogue about the most effective ways to manage successful mathematical journeys leading to good mathematics outcomes for students. Making data available to 11-16 schools in a form that they can use to gauge their success at progression is particularly important. This is an area currently being explored by the Department for Business, Innovation and Skills. The list below contains relatively easy interventions identified by the case study schools and colleges. They promote good engagement with mathematics and when applied at or near the transition period can be very powerful in persuading students about future pathways. They are: • running taster sessions that incorporate active learning approaches to mathematics as a way to increase GCSE to A Level conversion • emphasising the importance of mathematics as a progression route to higher education and employment outside mathematics, thus giving a relevance to the need to progress • emphasising the relevance of mathematics to many careers is a great “pull” for progression; use of a mathematics careers notice board and the web sites helps but the best ambassador appears to be the mathematics teacher. • surveying students and responding to their opinions, leading to a positive atmosphere and hence a negotiated progression • staff taking part in any intervention, making them question the progression factors, canvass student opinion and challenge their received opinions • having a number of appropriate pathways for progression available in order to enhance progression e.g. AS Level and AS Use of Mathematics allows more students to access the subject • tackling the gender issue – the gender issue and mathematics grade B is very complex but we found that this can open up the debate about progression and then motivate change for the good. Whilst the project has focused on grade B and above, there are students who achieve grade C who wish to progress to A Level, and other studies (notably the pilot for Improving Learning in Mathematics) have shown that more active approaches are inclusive of all students. However, there is pressure on teachers to achieve high success rates and this can lead to rigid entry criteria which exclude students below grade B. The issue to be addressed is not whether these are good or worthwhile activities, but how to disseminate with clarity this guidance and information to schools and to colleges, and to ensure that the messages are embedded and then sustained over many years, The National Centre has a key role to play in this and indeed has been very successful in promoting appropriate help and guidance. This has been made difficult in the past by the different funding streams and regulatory regimes that were in place for providers of 16-19 education. The creation of YPLA creates an opportunity to seek to develop a symbiotic relationship between pre- and post-16 providers. In the area of mathematics, a key common goal would be to establish effective and high quality teaching of the subject. In support of this goal, there is a need for some specialist professional development provision that will address the challenges of educating teachers in the skill of ensuring effective transition at 16. Careful thought needs to be given as to who should take responsibility for ensuring that such a programme exists and that it is coordinated nationally, is of high quality and is effective. Page 17 of 44 Widening Participation in Mathematics References Kowszun, J. (2004) “This Innumerate Isle” Times Educational Supplement 17 Sept 2004 Nardi, E. and Steward, S. (2003) “Is Mathematics T.I.R.E.D? A Profile of Quiet Disaffection in the Secondary Mathematics Classroom” British Educational Research Journal June, vol. 29, no. 3, pp. 345 366 NCETM (2008) Factors influencing progression to A Level mathematics [https://www.ncetm.org.uk/enquiry/10114] Ofsted (2006) Evaluating mathematics provision for 14-19-year-olds [HMI 2611] QCA (2007) Evaluation of participation in GCE mathematics [QCA/07/3388] Robinson, D. (2007) Post 16 participation in mathematics Specialist Schools and Academies Trust Smith, A. (2004) “Making mathematics count. The report of Professor Adrian Smith’s inquiry into post-14 mathematics education” London: DFES Page 18 of 44 Widening Participation in Mathematics Appendix This appendix provides detailed reports from nine of the ten case study schools and colleges. Bishop Challoner Catholic College Bishop Challoner is a Voluntary Aided 11-19 comprehensive school in the Kings Heath area of Birmingham and describes itself as “an integral part of the Catholic Community”. Its pass rate at GCSE mathematics A* - C, was 75% in 2009 and 77% in 2010. The school was inspected by Ofsted in March 2009 when it was described as providing “an outstanding education built upon high expectations, the desire to provide young people with an enriching range of opportunities and the readiness to adopt improvements, which address the needs and talents of individual students. ... students feel challenged, confident in their teachers’ expectations of them and secure in taking the risks necessary to make outstanding progress.” In looking for means to increase the uptake of AS mathematics at the school, the mathematics department decided to look at two inter-related themes. Across the A Level programme they looked at ways to increase the number of girls who were studying mathematics, in the belief that this would also increase the number of students with grade B who were studying the subject. This meant that one of the targets they set themselves was that of “increasing the number of female students opting for A Level mathematics study at the end of the 2009/2010 academic year.” This would address the “loss” of girls from mathematics, which happened when those with very good GCSE results had to make a choice at AS Level and, particularly those who wanted to study medicine, did not choose mathematics. There was also a perceived need to make mathematics more attractive to girls generally and so draw into the subject area students from across the acceptable ability range. The mathematics department also set itself “less measurable success criteria”, namely, “a better idea of the importance of mathematics within chosen career paths, a greater awareness of what is involved in further mathematics study and improved confidence and self-belief within the chosen cohort.” The project had very strong management backing, with the head of mathematics, the deputy head of department and a member of the senior management team supporting the project. Interviewing staff and students The project began with the deputy head of department interviewing staff and students to canvass opinion about the potential barriers to the uptake of mathematics at AS Level. This identified that there was a need for more female role models studying mathematics and the need to raise awareness of the uses of mathematics beyond GCSE and AS Level. Perception of mathematics As part of raising awareness, the school established contact with Birmingham University and arranged for students to attend an event that consisted of master classes and lectures in mathematics, physics and engineering. The aim was to create and sustain an interest in mathematics amongst the students so that they would want to continue with their studies. As part of this event, there was a session about the careers to which a mathematics qualification could lead. This was particularly well received by the students and the staff thought that this was one of the most important parts of the day. As part of the same theme of developing awareness, a second trip was organised for a small group of students to visit Bletchley Park. The visit demonstrated the importance of mathematics in the past, but was also related to the importance of encryption systems for modern internet communication. The success of the event has meant that it is planned to be a recurrent visit in future years. The school also organised a visit to the “Take Mathematics Further” event at University of Warwick. The aim of these visits was to change the perception of mathematics as a “dry” subject, to one that was vibrant and had many exciting developments taking place, with connections to many career pathways. Targeting specific students with the potential to progress Page 19 of 44 Widening Participation in Mathematics The head of mathematics used indices that had been compiled earlier in students’ school career, (MABLE and JESSON) along with predicted GCSE grades, to identify a target group of students for progression. The students were encouraged to attend further mathematics sessions which ran after school and were well- attended. Students were encouraged to explore mathematics interactively and the sessions received positive feedback. This has become the mathematics Drop-in Centre which, in 2010, is now part of the enrichment activity programme that takes place after school. Providing positive role models To establish more positive role models, the mathematics department ensured large numbers of female mathematicians in Years 12 and 13 attended the sixth form open evening, to encourage younger students to consider the benefits of taking A Level mathematics The department also created a mentoring scheme using Year 12 mathematics students. The emphasis was on recruiting girls from Year 12, to provide support for Year 10 and 11 students, to act as positive role models. This was included as part of the Year 12’s enrichment programme and the mentors were incorporated into the work of the department by supporting students during lessons. The same students helped the department to select display materials that would emphasise a positive image of women mathematicians. The students who took part in this exercise were often those who were thinking of taking up teaching as a career. Measure of success In 2009, the school had 55 students studying A Level, 32 studying AS and 23 studying A2; in 2010 they have 66 students studying A Level, 41 in Year 12 and 25 in A2. Page 20 of 44 Widening Participation in Mathematics Bridlington School Background Bridlington Sports College is a slightly larger than average 11-18 comprehensive in the East Riding of Yorkshire. The proportion of students with learning difficulties and/or disabilities is well above average and the proportion with statements of special educational need is more than double the national average. Students enter the school with standards which are below, and sometimes well below, the national average but make progress through their school career so that the pass rate for five GCSEs is about the national average. The school offers a traditional sixth form curriculum including mathematics. There were 150 in the Year 11 cohort for 2010 and the GCSE results for the school have been steadily improving. Generally, the teachers were aware that students’ perception of mathematics was that it was not much fun; the department cared about the success of the students but they also expected hard work. As students progressed towards the Year 11 GCSE exams, teachers were aware that the students were less optimistic about their chances of progression. The head of mathematics pointed out at the beginning of the project that the GCSE grade was not always a good indicator for A Level success and good grades at GCSE were no guarantee that students were going to do well. Attitude and approach were as important as ability. At the beginning of the project, 20 students were studying AS mathematics and 15 were expected to complete, most of whom would gain a pass. Ten students were expected to continue to A2. Generally, very few students gain a higher grade in other subjects than their mathematics grade. The head of mathematics found it difficult to identify consistent trends in gender differences for achievement at Key Stage 3 and GCSE in mathematics. However, fewer girls than boys chose AS mathematics. For those that did choose mathematics, there were no marked differences between the achievements of male and female at AS and A Level. The focus of the project was therefore “to encourage more girls and pupils with grade B at GCSE to progress on to A Level mathematics”. The project A series of visits to outside venues and by invited speakers were written into the action plan, because it was assumed that the main issue would be portraying a positive role model for girls. The action plan started with a questionnaire and focus group discussion, with mathematics students in Year 11 and those studying AS Level. The intention was to find out student attitudes and then plan interventions to change them. The questionnaire for both Year 11 and Year 12 included a question about how much the students enjoyed mathematics. The focus group was asked the same question. This simple question created a major change for the project. The staff were shocked at the level of disenchantment shown by the survey, particularly amongst girls. The focus group interview was lead by someone outside the department, who was a woman, and this revealed that the girls in the group displayed low self-esteem where mathematics was concerned. The 26 Year 11 students who were present were asked about their intentions to progress in mathematics with the following results: Number present Number choosing AS mathematics Girls 11 1 Boys 15 6 Total 26 7 This showed that a disappointing number of students were going to progress, only 27%. The department realised that what they had found out here was more significant than the items on their original action plan, so they re-wrote the plan in response to the student’s feedback. As the head of mathematics said, “The survey made us change our practices.” It also had an impact on the class teachers of the Year 11 group and the AS group. They decided that they had to respond to the survey Page 21 of 44 Widening Participation in Mathematics and adopt more varied activities in lessons. The department realised that simply arranging for visits from outside speakers was not going to be enough, so, although they kept these within the action plan, they added professional development activities as well. One of the problems was that traditional teaching approaches were used to deliver A Level lessons, even by teachers who used much more varied styles in Key Stage 3 and 4. Teachers were encouraged to use a greater variety of activity in GCSE classes as well as AS classes. An outside consultant came into the department and ran professional development sessions to make staff aware of active learning approaches to teaching mathematics. The students were surveyed again The outcomes of the new survey suggested that many students now had a positive attitude towards mathematics. Most were enjoying the subject more and there was a “shift” in the student’s perception of how good they were at mathematics. The survey of Year 11 students showed the following: Number present Number choosing AS mathematics Girls 13 4 Boys 14 12 Total 27 16 Four girls and two boys recognised that they had changed their minds about studying AS mathematics. The table of results suggests that more students changed their minds than were willing to admit in public. The key issue for the project was that the staff had responded to the perceived needs of the students and the students had appreciated this. The head of mathematics thought that this perceived response to student need was probably more important than the activities that were used. Although not reflected in the survey, five students were now thinking of tackling Further Mathematics. The changes introduced by the teachers meant that activities were being used more in their mathematics lessons, consequently the staff decided to devote one of their professional development days for training in the use of activities taken from Improving Learning in Mathematics. Videos from the “mathematics in work” series were also used as “starters” at the beginning of some mathematics lessons, to relate the mathematics to real applications. Whilst this was taking place, some of the original action plan was implemented. Outside speakers were invited into the school to talk to students about mathematics. These talks took place in girl-only sessions and the speakers were women who were mathematicians: two were primary school teachers, one was an engineer and a fourth was a lecturer with the Further Mathematics Support Programme. The intention was to give girls confidence and foster the belief that they could be successful at mathematics beyond GCSE. By its very nature, organising the sessions conveyed the message that girls were important to the department. The sessions were not restricted to the top set but included set two as well. The head of mathematics noted that, “Including the girls from set two definitely raised expectations and gave the girls confidence. Three girls in set two got grade As and a fourth was one mark short. This level of success in set two is unparalleled.” As the same person noted, “It was clear from the final survey that attitudes to continuing mathematics had changed during the year.” To continue the theme of encouraging girls to adopt a positive attitude to mathematics, an all girls team was entered for a local mathematics competition. These changes produced the following results and illustrate the improved progression that had taken place within this group: Fraction of students getting this grade Percentage of students getting this Grade Gender going on to study AS Level grade going on to study AS Level A* Boys 1 out of 1 100% Page 22 of 44 Widening Participation in Mathematics Girls No passes at A* Boys 5 out of 5 100% A Girls 4 out of 5 ** 80% ** Boys 7 out of 16 44% B Girls 5 out of 15 33% ** The girl who is not studying A Level, wanted to but could not because of a clash with other subjects. In order to do some mathematics she is doing AS FSMQ over two years. More students are now opting for A Level mathematics; the particularly important point is that the whole of the A and A* grades opted for mathematics. Another indication of renewed motivation was shown by the fact that three grade B students, were studying A Level in a year, so that they could take up Further Mathematics next year. The school intends to continue to organise outside speakers for the top two sets. They will probably be mixed in future rather than single sex and will start in Year 10. Page 23 of 44 Widening Participation in Mathematics Chesterton Community College Chesterton Community College is an 11-16 school in the centre of Cambridge. Its recent GCSE results show that 34% of pupils achieve at least 1 A or A* and that 77% achieve 5 A*-C . The head of mathematics is a shared post between two women teachers and girls and boys are taught in separate groups for some sets for Years 10 and 11. The school has well-documented evidence to show that this approach works for them and has increased their success rates. As an 11-16 school, Chesterton does not have a sixth form, but the majority of pupils who want to study AS mathematics go on to two local sixth form colleges. A local school offers the International Baccalaureate (where one or two students go each year, and so study mathematics beyond GCSE), but as the local FE college no longer offers A Levels, the two sixth form colleges account for practically all progression pathways on to AS mathematics. The project at this school had two separate strands. One was to interview Year 10 and 11 pupils to find out what their main motivations were for choosing or not choosing mathematics as an option after GCSE. When this was known the issues could be addressed and progression encouraged. The other strand concerned the data available to the average classroom teacher in an 11-16 school who wanted to encourage their students to progress. How easy was it for them to get access to progression data and so give good advice to their pupils? Two focus groups of students were interviewed, one in Year 10 and one in Year 11. The results of these interviews showed that pupils were thinking of choosing AS mathematics because they saw themselves as good at the subject, but those that lacked confidence, even if they were in the higher sets, did not seek to progress. In some cases parental encouragement was a factor, but the most important driver was the perceived use of the subject to aid a future career. Mathematics was seen as a good “holding” subject for those who had not made a definite choice of career and essential for those that had chosen careers like engineering. Where the choice of career definitely involved mathematics, then this was a strong pull towards the subject, even if the student’s predicted grade was not encouraging. As one student said, “I want to do engineering but my predicted grade in mathematics is a C, I know I will find it difficult but I still want to do it [AS mathematics].” Where students wanted to do a degree, then they were more likely to want to study mathematics, sometimes to increase their chances to get into a “good” university. The findings are broadly in line with the results of a survey that was conducted with a group of 165 AS students as part of the project. The survey showed that students had chosen to study mathematics because they enjoyed the subject, thought that they were good at it and because it was going to be useful for them in their career or degree. The survey also showed that teachers were a greater influence than parents in encouraging students to choose AS mathematics. The focus group interviews and the survey lead to the use of a mathematics careers notice board. The notice board displayed posters to show that mathematics was useful for a fashion designer, landscape architect, pharmacist, civil engineer and solar physicist. It also advertised the Mathscareers website and Future Morph, a STEM careers website. Staff directed potential mathematics students to look on the websites and at the notice board so that they were aware of the opportunities available to successful mathematicians. The other major factor was enjoyment of and confidence with the subject. One of the sixth form colleges encouraged former pupils to return to their school to give an insight into AS mathematics at the college. The school took advantage of this opportunity when three former students returned to the school to talk about the choices they had made to accompany AS mathematics. One had chosen to study mathematics, further mathematics and physics, another had chosen music, a classical language, a modern language and English and the third was studying the three sciences and mathematics. The importance of the event was underlined by the fact that the whole of Year 11 was invited. Whether or not these measures were successful formed the second part of the project. The difficulty for 11- 16 schools is that the classroom teacher does not have information on progression readily available. In fact, Chesterton did have an indication of intended destination but did not have the complete picture of who had gone where. There was no formal requirement to analyse the data on progression and consequently it was not routinely completed. What was readily to hand was the data on predicted GCSE grades and the Page 24 of 44 Widening Participation in Mathematics data on intended destination, and from this the head of mathematics could produce a prediction of likely progression. This showed the following picture: Predicted grades Female Number Male Number A* 3 A* 19.0 A 15 A 14.0 B 15 B 16.0 C 27 C 25.0 total grade B+ 33 49 82 Total 60 74 134 The two local sixth form colleges required students to have a grade B to take AS Level, so this table shows that there were 82 students with a grade B or better. This table shows those students who had expressed an interest with continuing their mathematics: Want to continue with mathematics Female Male A* 3 A* 14 A 6 A 12 B 3 B 2 C 1 C 1 total grade B+ 12 28 40 Total 13 total 29 42 Hence, 40 students of the 82 who were predicted a grade B or above at GCSE had expressed an interest in continuing – a progression rate of 49%. The sixth form college that encouraged former students to return to their school to promote AS mathematics also supplied Chesterton with information about their students. This was part of the established relationship between the two organisations. The college prided itself on being a high achieving college, with 56.2% of its annual intake studying AS mathematics, representing 550 students. The college was therefore seen as a magnet for able mathematics students. It had also established a procedure that asked the “feeder” schools for a thumb-nail sketch of applicants to the college. These sketches were used to indicate students who might find the AS course difficult or who could be described as “gifted and talented”. This helped to form a close relationship between the school teachers and the college, as did the release from timetabled duties for a member of the mathematics staff to act as a liaison person with the schools. The college did not run taster events but instead relied heavily on this liaison work and the reputation of the college to attract students. A member of staff had produced a set of question sheets that prepared students for AS mathematics and these were distributed to applicants on the understanding that they would be completed before the beginning of the academic year. The revision sheets formed the basis of the induction programme. The feedback from the college showed that 35 students were studying mathematics there. The liason work between the sixth form college and the 11-16 schools seemed to encourage the staff from Chesterton to assume that the route to this particular college was the main one for their mathematics students. However, this college only had 26 students with GCSE grade B, out of a total of 550 studying the subject, so their intake of students was biased towards the higher grades, but the school did not know this. The teachers in Page 25 of 44 Widening Participation in Mathematics Chesterton therefore tended only to receive information about the achievements of their more talented mathematicians. An NCETM Associate worked with the school and the two colleges it fed into, to try to provide data. In fact, 17 students were studying AS mathematics at the other sixth form college, of which eight had a grade B. The majority of the grade Bs, that is five out of the eight, were studying Use of Mathematics. This meant that Chesterton had 52 students studying AS mathematics at one or other of sixth form colleges, which was more than they had estimated. Their progression rate was 52 students out of 80, which was 65%. This analysis suggests that a number of students may have changed their minds about studying AS mathematics and, perhaps in the light of better-than-expected GCSE results, had opted to study the subject. It is also possible that the predicted grades may have under-represented the number of students who achieved grade B or higher, and consequently there was a larger number of students who could potentially study AS Level. For whatever reason, this second channel of mathematics recruitment came as a surprise to the Chesterton teachers. The example illustrates the way that the 11-16 school relied on the receiving organisations to supply data on progression so that they could give good advice and encourage progression. The school is now in touch with both sixth form colleges and in the future ought to receive information on progression from both. The school needed to know the number of students progressing to both colleges so that they knew the importance of each to the progression of their students. In fact, using statistics compiled for this project, Chesterton had the highest rate of progression of all the schools that took part. The historical data showed that 47% of students who gained grades A*-B progressed, compared with a national proportion of 30%. The result of taking part in the project suggested an improvement of this figure for the school to 65%, with 52 from 80 students progressing to study mathematics. However, there were additional factors that may have enhanced the rate of progression in this case. The college that received the students who achieved a high grade had a very high take-up of mathematics; Chesterton Students who went to this college were therefore very likely to progress. The other college that received students with a wider spread of GCSE grades had introduced a curriculum change that may have encouraged more students to take up mathematics. Page 26 of 44 Widening Participation in Mathematics Childwall Sports College Childwall Sports College is a large inner city 11-19 secondary school with a comprehensive intake. There are approximately 1300 pupils including 300 in Years 12 and 13. The school population consists of 58% males and 42% females. In the first year of the project, the mathematics department provided a specific route through GCSE for pupils with the potential to study the subject beyond GCSE. At the end of KS4, following the terminal paper, they ran two courses for pupils that opted for A Level mathematics. They both ran until the end of the term. Refreshments were provided to foster a more relaxed environment for pupils. Graphical calculators were purchased to encourage deeper thinking when investigating graphs. One of the ‘bridging courses’ was aimed at B-grade pupils. It was designed to ensure that the learners had experience of using A* techniques that are utilised in Core 1. The course covered: surds; completing the square; algebraic fractions and co-ordinate geometry. No assumptions were made about the pupils’ ability to access the content, simply that they had not yet accessed the topics. An ‘enrichment course’ was aimed at A/A* grade pupils. It used practical activities based around extending GCSE knowledge to encourage deeper thinking. The topics were drawn together to form a ‘bigger picture’ of how mathematics fits together. The course covered: exploring circles; investigating quadratics; understanding trigonometry; rates of change. The outcomes of the end of term course in the first year were: • momentum was maintained following completion of GCSE • the activities demonstrated to the B-grade pupils that they are able to achieve success at A Level • greater communication was developed between pupils because the practical activities gave them more opportunities to express their ideas to each other • the girls involved in the course agreed that, “girls are better at finding different ways of getting the answer, it was good to be given opportunities to investigate instead of being told how to do something”. The head of mathematics at the time wrote, “The curricular route that we provide through GCSE has resulted in our A Level pupils being able to undertake both Core 1 and Core 2 examinations at the same time in January. This is having a direct impact upon their results and confidence.” Learning conversations show that pupils felt very confident in undertaking the A Level course – pupils reported that they had sampled some of the content without feeling pressured. There are a growing number of girls undertaking A Level mathematics, 45% (nine out of 20) of the cohort are female, in comparison to 18% the previous year. Amy Bersantie, Year 13, said, “I found that I could relate much easier to my female mathematics teacher, this made me feel that I could do it,” she added that, “I am proud to be studying mathematics it makes me feel very intelligent. I know that studying mathematics will give me more opportunities.” Thirty-five per cent of the cohort that year achieved B grades at GCSE, 17 of the 20 students continued to A2, one student failed and the rest achieved grade E and above. Whereas the school had recruited relatively low numbers to its A Level mathematics in previous years – sometimes only three made this option choice – the result of using the taster course was that, their recruitment went up to 20. Two changes then took place in the school. The head of mathematics left to take up a promoted post and the school adopted the idea of a set of taster events across the sixth form. The new head of mathematics was male, very committed to the promotion of students from GCSE to AS Level and adapted the original plan to match his own priorities. The expansion of the taster programme meant that this was now a timetabled event that took place over a two-week period with each subject having four two-hour slots. The previous programme was adapted to keep the topics the same, but there was no distinction between a ‘bridging group’ and an ‘enrichment group’. An Associate visited one of the induction sessions which dealt with manipulating surds. The head of mathematics ran the session, set the scene for the topic in relation to the GCSE and A Level syllabus, Page 27 of 44 Widening Participation in Mathematics emphasising that they were going to tackle some AS questions at the end of the session, hopefully with some degree of success. The teacher had attended some training sessions run by Susan Wall and so was familiar with the Standards Unit materials and the principles of effective teaching and learning summarised in Mathematics Matters. The group therefore tried a quiz, where they had to identify whether or not statements about surds were true or false and an “always equal” or “never equal” exercise where the learners had to insert the correct symbol between two statements. Both exercises explored common misconceptions about surds and learners in pairs or threes engaged in discussion to come to an agreed answer. They used mini-whiteboards to try out ideas. The group then had a look at some exam questions on the topic that had been extracted from past papers. The learners tackled the questions as a small group exercise. The same questions and more were available on the school’s website and the teacher set the challenge to try as many as possible of these questions over the summer break. The session ended with an emphasis that the group had tackled what was probably going to be their first topic on the AS course, and they had all made some progress – the subject was therefore accessible to them at AS Level. Fourteen potential students attended, three were predicted a grade A*, seven had predicted grade A and four had predicted grade B; there was one girl. Five were thinking of studying mathematics because they were good at the subject, 13 thought that it would be a useful qualification to have, six chose mathematics because they wanted to work in the construction industry, possibly as civil engineers or architects, two were thinking of becoming mathematics teachers. Recruitment to the AS mathematics course continued to increase in September 2010. This was helped by an increased GCSE pass rate at grade C and above in mathematics, which went from 43% to 56%. The head of mathematics was particularly pleased with an increase in the number of A* and A grades, which he thought had resulted from an increase in the number of students taking A Level mathematics acting as a “pull” to encourage students to achieve higher grades at GCSE. The school had recruited 22 students in 2010, which were taught in two groups, three students had A*, nine had grade A, nine had grade B and one had grade C. The number of grade Bs had increased from seven to nine over the previous year. Four of the AS students were girls. All the pupils who took part in the taster days had progressed, in particular, the A* pupils had continued their studies at the school at AS Level and were now taking part in a further mathematics group supported by one of the local universities. One student had joined the AS group from another school. Using the “down time” at the end of the GCSE exam period had been so productive that the mathematics department had tried this at the end of the AS exam period. They had brought the AS students into school after they had finished their AS exams and started to teach the next pure mathematics module. This had meant that the syllabus knowledge had been covered relatively early in the new academic year and allowed more time for revision and consolidation. The emphasis that learners placed on the value of mathematics to open up career pathways had become apparent during the project with the result that the head of mathematics was hoping to run a school trip to Salford University to explore this careers angle further. The mathematics department had produced a pamphlet “Why study A Level?” which also emphasised this angle. Clearly the tasters had increased recruitment to AS mathematics. There had been a dramatic, sustained increase in the number of pupils studying AS Level and the number of grade B students studying the subject had increased. The table below shows how many students started taking A Level mathematics in Year 12, broken down by gender and their GCSE mathematics grade. The proportion is shown in each case. Students starting A Level mathematics in September 2010 from Childwall School (Of the 22 starters, 21 were from the school and one from outside. The cohort for the school was 89 boys and 80 girls) Grade Gender Fraction of those with Percentage of those with Page 28 of 44 Widening Participation in Mathematics the grade who went on the grade who went on to A Level to A Level Boys 3/3 100% A* None achieved this Girls grade Boys 4/4 100% A Girls 1/4 25% Boys 9/19 47% B Girls 3/14 21% Boys 1/23 4% C Girls 0/27 0% The table shows that 21 students from 94 progressed, which is a progression rate of 22%. The project used the proportion of students who gained A*-B as a measure of progression. The historical data showed that in the recent past Childwall had a progression rate of 41%, but they now had a progression rate of 48%. The earlier figures had been based on relatively low numbers, so the success of the changes introduced at this school ought to be measured in terms of the increased numbers of students who were now opting to take mathematics. This number had increased from three to 22. Page 29 of 44 Widening Participation in Mathematics Long Road Sixth Form College Long Road Sixth Form College is located in Cambridge, one of two sixth form colleges in the area. It has an intake of over 2,000 students per year. Students in the area generally compare well against the national average for five GCSE A* to C. According to Long Road’s last inspection, 61% achieve five GCSEs at grades A* to C in 2006/7. The college visits the local feeder schools for post-16 progression events, but unlike the neighbouring sixth form college, does not have a system in place to encourage students at the college to visit their former school. Until recently, students applied to the college via the Cambridge Education Partnership, were interviewed and then, if they achieved the required the GCSE grades, would start the course in September. However, for the last two years the college has run a taster event. In the first year, the college contacted the students via their applications but had a poor response, so the head of mathematics repeated the invitation via the student’s parents and the response improved significantly. In the second year, the response from the initial invitation was sufficient to not warrant a second invite and the take-up on all three taster days was substantial, with 155 potential students attending. The feedback from the events was an opportunity for the staff at Long Road to canvas the opinions of students about what they thought was in store for them on the AS mathematics course. Ninety-eight per cent of those who attended thought that the event had helped them to understand what the AS course would entail. Some of the other statements explored other aspects of studying mathematics at AS Level. To the statement: “I feel that GCSE mathematics has prepared me effectively for the AS course” the students’ responses were: Total Percentage Agree 108 70 Disagree 27 17 Strongly Agree 19 12 Strongly Disagree 1 1 Total 155 100 The responses indicate that there were a number of students (17%) who did not think that GCSE was adequate preparation for AS Level, which echoed the comments from some of the teachers who took part in the project. To the statement: “I am studying AS mathematics because I have enjoyed the subject at GCSE level” the students’ responses were: Total Percentage Agree 79 51 Disagree 32 21 Strongly Agree 40 26 Strongly Disagree 4 3 Total 155 100 In the survey of 165 students taking AS mathematics completed for the project, enjoyment of mathematics was a significant reason for studying the subject. This is borne out by these results, but in this sample 36 students actively disagreed with the statement. To the statement: “I think that I will enjoy the subject at AS Level” the students’ responses were: Page 30 of 44 Widening Participation in Mathematics Total Percentage Agree 108 70 Disagree 19 12 Strongly Agree 24 15 Strongly Disagree 4 3 Total 155 100 This showed that the number of students who were expecting not to like AS mathematics was fewer than those who did not like GCSE, which indicates that the sessions had a positive effect on attitude to the subject at a higher level. However, the survey also indicated that the students were expecting to find the subject difficult. To the statement: “I expect to find AS Level mathematics very difficult” the students’ responses were: Total Percentage Agree 76 49 Disagree 32 21 Strongly Agree 41 27 Strongly Disagree 5 3 Total 155 100 The tables indicate that that there were a sizeable number of students who expected to enjoy the subject but knew it would be challenging. An Associate interviewed students during one of the sessions and found that although the students did expect the subject to be challenging they wanted to study it because they thought that it would increase their chances of getting on a good degree course. The presentation given at the taster session emphasised the importance of four key A Levels, of which mathematics was one (the others being English literature, chemistry and history). None of the students interviewed wanted to do a mathematics degree but business studies, psychology and architecture were popular choices. The sessions used mathematical activities that were intended to enhance the student’s algebra skills and encouraged discussion in small groups. The activities were like ones in the Improving Learning in Mathematics pack and concentrated on solving quadratic equations and completing the square. At the end of the session, the students attempted some AS-style questions and then tried some online work that could be accessed over the summer holiday. The same topic sheets were used during the course as a means to increase fluency with a particular subject. Use of Mathematics One important reason for the taster sessions taking place was because the college offered Use of Mathematics alongside A Level mathematics, and the taster session was to help students to make up their minds about which AS was appropriate for them. The opening presentation set the scene by describing AS mathematics as placing algebra in a pure mathematics context while Use of Mathematics tested algebra skills in a more practical context. This introduction was to set the scene for more detailed discussion during an interview or during induction. Page 31 of 44 Widening Participation in Mathematics The importance for this option for the department was that the senior management team at the college had just given its approval for the department to enter the Use of Mathematics Pilot for the full A Level. The head of mathematics saw this as a positive decision that would allow more students to be successful at AS Level. He thought that this was particularly important for students who gained a grade B or grade C at GCSE. He thought that they were more likely to be successful at Use of Mathematics than the more “traditional” AS Level mathematics. The decision about increasing the AS offer had been informed by the experiences of Colchester sixth form college, with whom Long Road had connections as part of a consortium of sixth form colleges that shared professional development days. The sixth form college in Colchester was taking part in the A Level Use of Mathematics pilot and had presented their findings at a consortium event. The following table demonstrated the growth in numbers that they had sustained from using the Use of Mathematics qualification. Year Use of Maths Maths AS Maths Further Statistics Total (Mechanics) Maths 2005 39 244 41 20 35 379 2006 34 223 32 25 31 345 2007 46 290 47 38 48 469 2008 81 271 45 37 54 488 2009 159 286 38 42 60 585 What was apparent was that Use of Mathematics had demonstrated a growth that had not affected significantly the numbers on the “traditional” mathematics course. Colchester also presented an analysis of their AS results related to GCSE grades. This was similar to the chances chart produced for the “traditional” AS Level mathematics and showed that students with grades B and C at GCSE had good chances of gaining an AS in Use of Mathematics. Page 32 of 44 Widening Participation in Mathematics It was by using this evidence that the head of mathematics at Long Road had persuaded the SMT to approve the college to enter the pilot for A Level. However, the qualification was largely unknown to the college’s feeder schools and so the taster days were an important vehicle for the students to understand the AS offer in mathematics. The result has been that in 2010 the Use of Mathematics recruited 67 students, AS mechanics recruited 72 and AS statistics recruited 127. Of the grade Bs recruited by the college on to AS mathematics courses, 18 are studying mechanics, 32 are studying statistics and 54 are studying Use of Mathematics. Page 33 of 44 Widening Participation in Mathematics Marshland High School Marshland High School is an 11-16 comprehensive in Norfolk. It is smaller than the national average, with 830 pupils, and students enter the school with levels of attainment that are broadly average or just below. The school gained specialist status for science in September 2005, but prior to the beginning of this project, it was designated a National Challenge school. At the school’s inspection in May 2009 it was given a Notice to Improve. The outcome of the Inspection and the National Challenge status, meant that the focus of attention of the head of mathematics was on supporting students with a predicted GCSE grade D to achieve a grade C. From the inspection report, the school and the head of mathematics recognised that the school needed to increase the number of students gaining the highest grades. However, the subject leader was also keen to encourage her students to progress and to continue to study mathematics even if they did not achieve A and A*. Marshland is therefore a school in challenging circumstances that chose, much to their credit, to take part in the project. What happened The head of mathematics conducted an attitude survey about progression amongst Year 11 students. The survey showed that students thought of themselves as “not good enough” to get on to an AS mathematics course and that the work would be too hard for them. She felt that this highlighted a low level of aspiration, so she aimed at getting the pupils to believe they could get a grade B in mathematics, to view themselves as successes and so continue to study the subject. This followed up a point that was apparent from the survey of 165 students conducted for the project, which showed that the belief in being “good at mathematics” was the largest single factor in influencing AS students for choosing the subject. As part of the strategy the head of mathematics ran a mathematics club after school as well as increasing the number of students being entered for Additional Mathematics. The mathematics club provided opportunities to show students how the subject could be extended beyond GCSE. It also provided extra support for students who were on the boundary of a GCSE grade, which was particularly important where the boundary was between a grade D and a grade C. The club therefore served a dual purpose. The GCSE mathematics results for the period 2008 to 2010 were as follows: GCSE Grade Number Number Number achieving the achieving the achieving the grade 2008 grade 2009 grade 2010 A* 5 1 1 A 5 4 7 B 9 12 23 C 38 62 60 The significance of these results for progression, was that the schools and colleges in the immediate area preferred a GCSE grade B or above in order to continue. Using this criterion, the potential number of students to progress was 19 in 2008, 17 in 2009 and 31 in 2010. What was also apparent was an increasing number of students gaining grade B. This was important because it increased the pool of students who could potentially progress. However, the attitude survey showed a general lack of confidence, which suggested using a further qualification would show that progression was possible; this was the role for Additional Mathematics. In 2008 the school entered 36 students for Additional Mathematics but this was increased in 2009 to 61 and 107 in 2010. One idea was to increase aspirations by opening up the qualification to a wider range of ability. The questions the students encountered were more open-ended problems than those in the GCSE, so they could get a wider experience of mathematics, gain in confidence and hopefully feel that they could tackle AS mathematics. Page 34 of 44 Widening Participation in Mathematics The results for Additional Mathematics over the period 2008 -2010 are shown below for those that achieved a grade A*-C: Results 2008 Results 2009 Results 2010 A* 4 A* 1 A* 2 A 4 A 10 A 9 B 15 B 15 B 24 C 12 C 19 C 41 Total entries 36 61 107 Each year there were students who gained a better grade at Additional Mathematics than in their GCSE. Analysing this in terms of grade improvement, showed that in 2008, 12 students improved their grades in this way, eight going from grade C at GCSE to grade B at Additional Mathematics, but none going from grade B to grade A. The table below shows an increasing number of students improving their grade, particularly for those going from grade B GCSE to grade A at Additional Mathematics. You would expect such students to progress on to AS mathematics with some degree of success. 2008 2009 2010 Number getting a higher grade on Additional Mathematics than GCSE 12 22 24 Improving from grade C at GCSE to grade B Additional Mathematics 8 8 7 Improving from grade C and B at GCSE to grade A and A* Additional 0 8 14 Mathematics Also, if a minimum of grade C at GCSE is required to study AS Mathematics, then the grade B for Additional Mathematics may indicate that these students had the potential to continue. In which case, there were eight potential AS students in 2008, to add to the 23 in 2008 who gained a grade B and above, giving a possible 31 students who might progress. Using the same criteria would indicate a possible 25 to progress in 2009 and 38 in 2010. This pattern of increasing numbers of potential students to progress accompanied an increasing pass rate at GCSE mathematics at the school, which went from 38% in 2008 to 56% in 2009 and 63% in 2010. To accompany this attempt to foster a positive attitude to progression in mathematics, the mathematics department placed posters all around school, cross referencing mathematics in different subjects. The head of mathematics talked to student about different career pathways and how mathematics was useful for them all. Notice boards were also used to display career pathways for mathematics. At the beginning of the academic year 2010-11, the school was re-inspected. The inspection report noted that “Marshland High is a satisfactory school that is improving. A culture of high aspirations is being embedded successfully by the head teacher, the senior management team and by staff and students alike ... standards, particularly in English and mathematics, are rising rapidly... Attainment of both genders improved in 2009/10 with a notable increase in the standards reached by boys.” Within the report there was, then, some recognition of a measure of success in raising aspirations. The problems arise in tracing what has happened to the students. The head of mathematics’ commented in October 2010 about the destinations of students into mathematics: “No clues where they went, we may find out at prize-giving next half term.” The problem for the school is that their former pupils have previously gone to an FE college and two 11-19 schools in the nearest large town, travelled further afield to an 11-19 school in rural Norfolk, or gone to an 11-19 school in Cambridgeshire. An Associate has tried to help with tracing former students but with limited success. When asked about whether encouraging progression has had a positive effect on success in mathematics, the subject leader said, “Progression discussions have been too recent to have had an effect. [We may see confirmation] possibly in the 2011 GCSE results.” Page 35 of 44 Widening Participation in Mathematics Data produced by the project suggested that the progression rate for Marshland, based on entries for 2009, was 35% compare to the national rate of 30%, which suggests that Marshland’s approach is having some success. However, whether the changes introduced recently in mathematics have made a difference is difficult to evaluate statistically because data on individual progression was not available to the project. There is a need for more work to be completed with schools like this one to give some indication about whether or not their strategies for progression are successful. Page 36 of 44 Widening Participation in Mathematics Plymstock School Key aim: “To improve the number of students going on to study A Level mathematics with a particular focus on girls and students gaining grade B at GCSE mathematics.” To help the school to understand where they were in terms of students opting to take AS Level mathematics, they started the project by determining the proportion of students opting to take AS Level mathematics in September 2009: Students starting AS Level mathematics in September 2009 Boys 2/3 67 % A* Girls 3/4 75 % Boys 16/27 59 % A Girls 6/15 40 % Boys 5/20 25 % B Girls 7/35 20 % This showed that of the 104 students who gained a grade A* - B, 39 progressed, indicating a progression rate of 38%. Data compiled from the national statistics for the 2009 entries indicated a progression rate of 40%, which gives some indication of how representative these figures for Plymstock. The department compared data from previous years, which are illustrated below. This analysis indicated an issue for recruitment because it appears that the proportion of A* and A students from the whole cohort, both male and female, that are taking A Level Mathematics has fallen, when the actual number of students taking A Level mathematics at Plymstock School has remained fairly constant with 35 students in 2007 and 39 students in 2008 and 2009. Although the low numbers in the A* category means that small changes have been a significant influence on the final percentage, nevertheless a trend is apparent. At the same time, the number of grade B students taking the subject has increased, particularly for girls. Grade Sex 2007 2008 2009 Boys 100 % 91 % 67 % A* Girls 100 % 83 % 75 % Boys 79 % 74 % 59 % A Girls 48 % 45 % 40 % Boys 16 % 19 % 25 % B Girls 0% 0% 20 % As part of the project, Plymstock used two main interventions. These were: • Increased differentiation at AS and A2 level. This included setting one AS mathematics group, increasing the resources to incorporate different learning styles, and increasing students’ self- assessment skills. • Increased reference to ‘real world’ applications for A Level topics, which included informing students of real world applications of the mathematics they were learning, ways that these can be researched further by students and relating mathematics to career choices. In particular, they introduced this to a number of students in Year 11, to encourage A Level uptake of mathematics. The mathematics department implemented this strategy in a number of ways. The January report showed that they had completed the following actions: Page 37 of 44 Widening Participation in Mathematics • In the summer of 2009, once they had completed their GCSEs, work was set for students to help them to prepare in depth for the start of the AS mathematics course. In particular, this included many of the algebra tasks that are covered early in the C1 module. This helped students at the lower end of the ability range to develop their skills further and practise more of the basic algebra that would be involved in AS Level. This meant that students started the course with a similar skill set. • Teachers and students have spoken positively about this, although there needs to be more work on closing the gap between GCSE and AS Level, as students still see this gap as significant. One teacher is now considering developing a bridging project for students to complete at the start of the AS Level course. • Self-assessment sheets have been produced for all chapters for the core modules. These need to be used more and discussed in class. Self-assessment at KS3 and KS4 has also been discussed within the whole mathematics department to make sure we are starting to implement these skills as soon as we can for as long as we can! • Members of staff have identified particular students for progression on to AS Level, with particular reference to grade B girls. Many discussions have taken place with students during class time, but particularly during parents’ evening and KS5 options evening. We also asked students currently taking A Level mathematics, both in Years 12 and 13, to speak to students at the options evening. We had many students turn up to help who talked very positively about the subject, but also very truthfully especially when talking about the level of difficulty. The Year 11 students and their parents have said how useful this was and the students were in much more demand for discussions than staff! • Discussions about the project have taken place within the mathematics department, increasing all members’ awareness of AS Level mathematics issues. This has lead to the production of further ideas and work to help towards the project. • A number of posters, relating STEM subjects and mathematics to the real world and careers, have been laminated and are now on permanent display in the mathematics corridor. The intention is to increase the application value of the subject to real life problems. From discussion with the whole mathematics department it is clear that this is something that still needs to be increased for the subject. • A Year 10 mathematics conference at the University of Plymouth has been arranged for our top set Year 10 (grades A*, A and B) to highlight their mathematics work and support taking mathematics beyond GCSE. This will take place in March. The January 2010 update report indicated that, although the number of students taking AS Level mathematics at Plymstock School has remained fairly constant, with 35 students in 2007 and 39 students in 2008 and 2009, initial numbers of students choosing A Level mathematics in 2010 seems to be significantly higher. In the final report the project leader at the school made the following observations: Students’ thoughts “As part of the study we spoke to the Year 11s (after they had made their post-16 choices) and the Year 12s about what had influenced their choices at AS Level. By far the main reasons students chose specific subjects at AS Level, was for their future career or their enjoyment of the subject. (This echoed the results of a survey of 165 students that was completed as part of the project and asked them for the main influences on them choosing mathematics.)” Increased differentiation “After questioning the Year 12 students in 2009, a large proportion of the students thought that the jump from GCSE mathematics to the start of the AS Level mathematics course was very large; significantly larger than in other subjects. To try to decrease this gap, and therefore improve the new Year 12’s confidence and Page 38 of 44 Widening Participation in Mathematics retention rate, the mathematics department set work for students to complete over the summer. This highlighted to the students with a lower predicted GCSE grade, some of the areas that they needed to practice to become fluent. Opportunities were given to students to come in to school and receive help from AS Level mathematics teachers with this work. Students have spoken highly about this as they felt more prepared to start their AS Level work. Teachers have also spoken highly about this and feel that students are more prepared now than in previous years. “In September 2009, one of the groups that had chosen to do AS Level mathematics (approximately 25 students) was set according to their GCSE results. This has helped staff to differentiate the subjects taught, allowing less confident students more time with the teacher and also allowing for more extension activities for students who are fluent with the work. We also set a Year 13 class according to AS results, which has had very positive effects for both students at both ends of the ability range.” Resources “We have produced a number of resources to aid the teaching of mathematics at A Level using different teaching approaches rather than relying on traditional “textbook and exercise” lessons. A number of jigsaw/domino activities have been produced for the core mathematics modules using the TARSIA software. These resources are referenced in the schemes of work, and are available already printed within the department. This has promoted discussion between groups of students.” Self-assessment “We have also produced new self-assessment documents for students to use for each of the modules at A Level (both core and applied). The importance of self-assessment has been discussed in class between staff and students. As staff we have also discussed self assessment across the whole school, particularly at KS3 and KS4 so that we can start building these skills at an earlier age. “A couple of the Year 13 students have also talked to the current Year 12s about what they can do to make sure they achieve their full potential in the subject and to make the course go as smoothly as possible for them.” Real world applications “To increase student’s awareness of the real world applications of mathematics a number of posters have been produced and displayed around the mathematics area. They have also been posted in other areas of the school, showing possible careers that mathematics can lead to as well as the use of mathematics in other subjects. Some of the posters were produced using information from the Mathscareers website (www.mathscareers.org.uk) and some were from the STEM network. “Representatives from a company called ‘Intelligent Counting Limited’ came into the school to speak to a number of students from Years 10 to 13 about how they use mathematics in their company and how other companies use the mathematical data they produce as well. This allowed almost 100 students to think about how mathematics is used in one area of business and produced some positive and high-level thinking from some of the students. This was a successful day and we are looking at continuing this in the future with the possibility of an optician coming to the school to speak to some of the students. “A group of high achieving Year 10 students attended the University of Plymouth to take part in a mathematics conference with other students from around Plymouth. This showed a number of applications of mathematics in the real world looking at Mathematical Modelling in Mechanics, some statistics work with the Royal Statistical Society and a lecture on ‘Bubbles!’. Students were enthused by the day and a number have talked about modules studied at A Level. The day was very positive. Some Year 13 students who have studied mathematics at A Level are going to speak to some of the Year 10 students (aimed at Year 10 girls with predicted grade B) about why they chose mathematics at A Level and how they are planning to use it in the future. All A Level schemes of work now have a column entitled ‘real life’ in them with a number of real life applications of specific topics being given. The new textbooks that the school have bought for S1 and C3 also show in them a number of real world applications and we are working at highlighting these to students.” Page 39 of 44 Widening Participation in Mathematics [Extracts from the final report compiled by the teachers who took part in the project.] September 2010 Cohort Students were targeted in a number of different ways this year to encourage continued study of mathematics at A Level. Staff held discussions with classes during the year about the course, encouraging students to opt for A Level. Mathematics staff spoke to students and parents at parents’ evening to encourage uptake of the subject. Students currently taking A Level mathematics both in Years 12 and 13 talked to students at the options evening with the intention of encouraging take-up of mathematics. Many students turned up to help who all talked very positively about the subject, but also truthfully, especially about the level of difficulty. Both students and parents commented about how useful this was to answer their questions and aid their choices. This resulted in an increased level of interest in A Level mathematics this year. The Year 11s made their choices and it indicated that 57students were thinking of studying A Level mathematics starting in September 2010. Boys 7/7 100 % A* Girls 3/3 100 % Boys 17/30 57 % A Girls 14/29 48 % Boys 13/26 50 % B Girls 3/28 11 % Three other students who had a predicted grade of C, had also opted to study the subject. At the time the head of mathematics noted that, “It is difficult to analyses these numbers properly as these are only taken on current predicted grades. There are a number of students who will achieve differently from their predicted grade as of January 2010. There has been a large increase in the number of students choosing to take further mathematics A Level (currently 10 students compared to last year’s one).” The take-up of mathematics amongst girls with a target grade B was 11%. The head of mathematics’ comment on this was that, “We feel 11% is still a good uptake at this level but could still improve.” The final results of the interventions at the school, shown in the table below, are that the number of students recruited had increased to 58, much as the staff predicted. The table shows that 58 out of the students who gained a grade B or above for GCSE mathematics had progressed. This indicated a progression rate of 47% compared with the previous figure of 38%. There had been a significant increase in the number of grade Bs studying AS mathematics, this had increased from 15 to 23. The proportion of girls studying mathematics had remained static at 40%, however, as the table below shows, the growth in numbers had come from the increased recruitment in students who gained a grade B: GCSE Grade Number in 2009 Fraction of AS Number in 2010 Fraction of AS group with this group with this grade grade A* 5 13% 9 16% A 22 56% 26 45% B 12 31% 23 40% The project leader at the school thought that the success of the project resulted from having “more discussion with students earlier in the year as to them taking up A Level” and “involving current students taking the A Level mathematics course in the recruitment evenings”. She goes on to echo comments from other teachers who have taken part in the project: “We have had more discussion in class with the students targeted grade B to encourage them to uptake mathematics, teachers of A Level have been teaching these Page 40 of 44 Widening Participation in Mathematics classes to increase the awareness of A Level and also comment on the suitability of students for an A Level course.” Fraction of students getting this Percentage of students getting this Grade Gender grade going on to study AS Level grade going on to study AS Level Boys 6/6 100 % A* Girls 3/3 100 % Boys 18/28 64 % A Girls 8/19 42 % Boys 11/29 38 % B Girls 12/39 31 % In terms of the permanent change that the project has made to the school, she also says that, “We are going to continue to use current students to talk about their experiences and the use of A Level mathematics when promoting the course. We have increased the awareness of the use of mathematics in other areas of the school and are going to continue this, as well as the real life mathematics uses in the KS3 curriculum. We are looking at increasing the career aspects of mathematics through speakers and posters this year.” Although the mathematics staff are planning to emphasise the importance of mathematics for career progression, not many of their students will continue on to degrees in mathematics, no more than two or three. Those that are interested in progressing to a degree, are aiming at science and engineering, for which mathematics is directly relevant, or more generally see mathematics as a well-respected subject that will lead on to a variety of degree pathways. Page 41 of 44 Widening Participation in Mathematics West Anglia, College of College of West Anglia (CoWA) is a post-16 FE college in Kings Lynn, Norfolk. There are a number of 11-19 schools in the immediate area but the college continues to offer and recruit to A Level mathematics and further mathematics. Twenty six schools feed into the college, the majority of them in Norfolk. Pupils in the immediate area transfer to post-16 education in a smaller proportion than the regional or national average, with 69.3% moving to full-time post-16 education, compared with the national average of 71.3%. As the schools in the area are a mixture of 11-16 and 11-18 comprehensives, this means that the college is in competition with local 11-19 schools to attract students. The college began the project by surveying the AS students to find out what motivated them to take up the course. The results were incorporated into the survey of 165 students conducted for the project and showed that students had chosen mathematics because they liked the subject, saw themselves as good at it, and needed it for their chosen career or degree. Staff had the opportunity to emphasise these messages when potential students came in to the college for open days, but the bulk of the recruitment in the local schools was conducted by the marketing department who did not promote specific subjects, more the college as a whole. There was therefore limited opportunity to use the results of the survey. One of the key results, however, demonstrated the importance of enjoyment of the subject and this became a theme for an event that took place during the summer months, when the Year 11 students from the “feeder” schools had completed their GCSEs. The aim was to encourage progression in mathematics and Norfolk County Council, in response to the below average progression rates in the area, sponsored the event for which the college played host. A similar event, to motivate students to study mathematics, was held at the University of East Anglia, in Norwich, but, perhaps because it was held in a university, it attracted a different spread of predicted grades, the majority being A and A*, with 14% predicted a grade B, no grade C students attended. The CoWA event attracted a wider audience, with 44% predicted a grade B or C. Despite the competitive environment and because it was sponsored by the local authority, the event did not market the college courses specifically. The students enrolled on the course via a website called “Launch Pad”, which was hosted by the local authority and the students were expected to make their own arrangements to travel to the event and make their own catering arrangements. The local authority paid for the speakers, if this was necessary, and for the teachers who supported the workshops that took place. The Launch Pad event lasted for five days and the ethos was to motivate students and introduce them to new ways of thinking and working in preparation for their new course. The teachers emphasised to learners that mathematics was an enjoyable subject and could be fun, as well as introducing some of the topics that they would meet at AS Level. The students tackled activities similar to those found in Improving Learning in Mathematics and teachers used the principles of effective teaching outlined in Mathematics Matters, both of which were familiar to staff through the subject learning coach programme. Throughout the week the students worked on open-ended tasks using small group work and discussion, which culminated in each group presenting a possible solution to one of the problems they had tackled. This problem solving approach was used to develop some of the skills that they would need for the AS mathematics course. Some of the fun activities involved the mathematics of juggling, the use of students as co-ordinate points who formed shapes according to the dictates of a formula, and analysing the outcomes of successful and unsuccessful bungy jumps using conservation of energy. On another occasion, after learning about the centre of gravity of a system of bodies, the learners then worked in teams to construct these frameworks as a set of “impossible” (which meant in this context surprisingly possible) sets of objects that could be balanced on top of each other. The feedback from the evaluations completed by the students was extremely positive. One of the associates for the project attended both the Launch Pad events and found that the event had generated real enthusiasm for mathematics, regardless of the student’s predicted grades. The nature of the event meant that its success could not be measured by CoWA’s recruitment alone. In 2009 the profile of the group studying AS mathematics was as follows: Page 42 of 44 Widening Participation in Mathematics Fraction of students getting this Percentage of students getting this Grade Gender grade studying AS Level grade studying AS Level Boys 0 0 A* Girls 4/22 18 Boys 6/22 27 A Girls 3/22 13.6 Boys 4/22 18 B Girls 4/22 18 Boys 0 0 C Girls 1/22 4.5 Of the 22 students, eight had achieved grade B. At this time, the entry requirement for the AS mathematics course was a grade C, and this year Launch Pad did not take place. The equivalent statistics for this year are as follows: Fraction of students getting this Percentage of students getting this Grade Gender grade studying AS Level grade studying AS Level Boys 1/22 4.5 A* Girls 1/22 4.5 Boys 6/22 27 A Girls 1/22 4.5 Boys 6/22 27 B Girls 4/22 18 Boys 0 0 C Girls 3/22 13.6 This shows an increase in the number of grade Bs and grade Cs that have opted for the subject. However, for a variety of reasons, the college increased its entry criteria from grade C to grade B at GCSE in order to continue at AS Level. The table shows that girls with grade C have been persistent in wanting to study mathematics and teachers have been sympathetic to that request, which may have been due to participating in the project and staging Launch Pad. Page 43 of 44 Widening Participation in Mathematics Harris Academies, London The Harris Girls’ Academy, East Dulwich, is an 11-18 school for 900 girls which opened as an academy in September 2006. It is one of nine schools in the South London Harris Federation. The academy has been judged by Ofsted to be making ‘Good Progress’ with student progress in the top 25% nationally. It offers a co-educational post-16 curriculum with Harris Boys’ and together they have a capacity for 400 sixth formers. Although they now described themselves as an 11-18 academy, their sixth form was in its infancy and they had just had their first student go through the A Level mathematics course. In the federation many of the schools offered A Levels mathematics so they planned to take advantage of this expertise to grow their mathematics qualifications. Grade B progression would be important for their future growth. The plan that the head of mathematics developed had five key points: • Identify the factors that influence students’ choice of subjects at A Level by interviewing a focus group of Year 12 students from across the Harris Academies. • Use the focus group to formulate a questionnaire asking students to identify reasons for choosing to study mathematics to be distributed across the Harris Academies. • Conduct a similar interview and survey with Year 11 students. • Interview a selection of Year 11 students to identify the reasons for not choosing to study mathematics, in particular for those students who have the ability to study the subject at AS Level. • Raise awareness of the different career choices available to those who have studied the subject. As part of the promotion of the sixth form in an area where progression into the sixth form was not the norm, the school held an open evening. The head of mathematics used the opportunity to highlight “mathematics in real life” and was pleased with the response from students and parents who were surprised to see the applications of mathematics that were shown. In many cases, she found that parents showed an interest first and then brought the students to along to look at mathematics as an option. The interviews with Year 12 in the other academies produced a questionnaire which was distributed within the academy schools. The distribution of the questionnaire also gave the teacher and opportunity to ask the other centres if they had received students from the Dulwich Girls Academy. Introducing a similar procedure with the Year 11 students, of interviewing a focus group and formulating a questionnaire raised the profile of the new A Level offer. The interviews in particular were a time when the teacher could learn about the challenges that potential students saw with continuing to study AS Level mathematics. The students who were predicted to get an A*, A or B were quite confident with their choice of mathematics but the grade C students were no more than “maybe” for progressing to AS. After further interviews the main issue revolved around lack of self-confidence, summed up by the comment “If I got a grade C and went on to A Level, there’s no way I could cope with the course.” This highlighted a problem with the students’ attitude to progression and showed the need for adult support. In these circumstances the teacher’s role was vital. The survey that was conducted for the project of 165 students showed that teachers’ opinions had greater influence than parents’ and this encouraged the head of mathematics to make greater efforts to give a positive message during her lessons. Seventy per cent of those students with a predicted grade A*-B said that they wanted to do A Level mathematics but did not give a reason. The results of these interventions need to be confirmed by 2010 results. Page 44 of 44 Widening Participation in Mathematics

DOCUMENT INFO

Shared By:

Categories:

Tags:
Level mathematics, A Level, state of the nation, mathematics skills, final report, college science, Further Mathematics, Royal Society, Russell Group, sixth form colleges

Stats:

views: | 4 |

posted: | 3/10/2011 |

language: | English |

pages: | 45 |

OTHER DOCS BY hkksew3563rd

Docstoc is the premier online destination to start and grow small businesses. It hosts the best quality and widest selection of professional documents (over 20 million) and resources including expert videos, articles and productivity tools to make every small business better.

Search or Browse for any specific document or resource you need for your business. Or explore our curated resources for Starting a Business, Growing a Business or for Professional Development.

Feel free to Contact Us with any questions you might have.