The next item of business is a debate on motion 12358, in the name of Liz Smith, on education subject choices. Can I ask those members who wish to speak in the debate to press the request to speak buttons now? I call on Liz Smith to speak and move the motion. Ms Smith, eight minutes are thereabouts, please. Deputy Presiding Officer, few decisions are more important to any young person at school than those that they make about subject choice. What they decide defines their future career, and that is why the Scottish Conservatives, like many parents, teachers and young people across Scotland, have become increasingly concerned about the evidence that points to the fact that the range of choices at S4 level in many schools is now restricted. Not only does this impact most on S4 and S5 pupils who will leave school with only a NAP4 qualification or NAPFAL qualification, but also on the choice opportunities that they have within higher and advanced higher courses in S5 and S6, with the obvious implications for further entry later on. If I want to set out the evidence, I want to place the evidence in the context of what was supposed to happen in the curriculum for excellence, and I want to put proposals on the table as what has to happen to address the problem. In terms of setting out the evidence, I am going to draw upon the work of Professor Jim Scott, the evidence that was presented to the Education and Skills Committee in 2016-17 by teachers, local authorities and the education agencies, the work of Glasgow Caledonian University, Reform Scotland, the Scottish Government's own research within its annual statistical reports and various articles within the media over the last two years. All of them, without exception, are pointing to the increasing movement away from eight subjects in S4 to S6. In 2013, 28 per cent of schools had moved to six subjects in 2016, which was 47 per cent, and Professor Scott's latest research shows that the figure is now 57 per cent. Professor Scott's evidence also goes on to show that there has been a corresponding decline in S4 enrolments and S4 attainment in SQA levels three to five. He acknowledges that SQA has made 3,750 more awards per year as a result of diversifying the type of certificate course, but he points to the loss of no fewer than 143,735 annual course passes as a result of the decline in subject choice from eight to six. Deputy Presiding Officer, the real issue here is for S4 pupils who are entered for NAP4 and NAP5 courses, but who want to leave school at the end of the fourth year or the fifth year because they are going to be leaving school with fewer qualifications than would otherwise have been the case. To place all of this in context, there is a very important debate to be had about the delivery of the curriculum for excellence. There was a relatively powerful argument in principle that schools should be more free to develop their own curriculum so that it best suits the needs of their pupils. There was also the argument that learning in depth is more important than learning in breadth, and it is not fair to contrast what is happening now with the curriculum for excellence with what went before. Now, I can accept some of those arguments, but what I cannot accept and neither can young people and parents is what has happened in practice, perhaps with unintended consequences. That is the narrowing of subject choice, not just in S4, but in S5 and in S6 and how that has had a particularly marked effect on many young people attending schools in disadvantaged communities, something about which we should all be concerned for widening access. In March 2017, Glasgow Caledonian University's research concluded that many people struggle to get their preferred choice in S5 and S6 and that many people do not get the opportunity to be able to sit higher across a two-year period so that there is better scope for articulation. Let me deal with the arguments that I am sure will be put to us by the Scottish Government. The line given to us by the First Minister when she has been challenged on this issue is that more young people than ever before are achieving a higher and advanced higher passes. No one is disputing that and it is good, but that must not just become a quantitative argument. Drill down and there are many different perspectives that tell us that in qualitative terms that is not quite the picture. For example, there has been a very significant squeeze on modern languages, a key skill that most employers value very highly, and there is also some evidence that there is now a squeeze on STEM subjects, also a key skill that is highly valued by employers. The fall in subject choice from eight to six subjects inevitably makes it more difficult for young people to have the best possible combinations—a point that was noted by University of Scotland when it provided its evidence to the Education and Skills Committee last year. Secondly, we are told that we must not look at the individual years but at the senior phase as a three-year progression. In theory, I could accept that, but in practice the narrowing of subject choice in S4 is beginning to have a similar effect on S5 and S6. If there was a properly thought-out progression, we would not see the reluctance to offer young people the chance to sit higher across two academic years. We would not see the two-term dash to higher, and we would not see the very serious situation affecting advanced higher. I raise this point about the advanced higher, not just because it is seen as Scotland's most prestigious exam and envied by many educationers in other jurisdictions, and because it is in more in tune with the founding principles of curriculum for excellence than any other exam, but because it draws into question the purpose of the S6 year. How ironic is it that the Russell group of universities south of the border are stronger advocates of the advanced higher than many people in Scotland? On this side of the chamber, we believe that it is a very important question to answer, not least because more pupils want to stay on at school until they are 18 and therefore they ought to be able to access advanced higher as they want, but that is not the case just now, and most especially in the disadvantaged communities. As the widening access debate progresses, more and more people believe that the focus of that policy has to be on schools, including the early years, but not so much on the artificial targets within colleges and universities. Widening the availability of advanced higher must surely be part of that focus and ensuring that we do not end up with statistics that show that just two secondary schools in disadvantaged areas offer more than 12 advanced hires, while 27 per cent of schools can do that in a more affluent area. I know that there are some very successful developments happening in hubs arranged by Glasgow University, Dundee University and Aberdeen University, and they are all working to make more advanced hires more available, but that does not help many young people in Scotland, particularly those who are unable to travel to the hub. What must be done, Deputy Presiding Officer? Firstly, it is imperative that we address the S1 to S4 curriculum. We have ended up with no clear strategy and vision for the middle years, which means that when it comes to S4, we have to condition people down to far fewer subjects. That articulation we have lost in the early years. I finish on this point that a key part of this is about teacher numbers. We cannot hope to have effective subject choice if we have 3,400 fewer teachers in the system than we did when the SNP came to power. Nor can we hope to improve things if there is a serious shortage in core subjects like maths if there is an increasing trend for experienced teachers to leave the profession. This is a hugely significant issue. It is a very important subject for many children across Scotland. At the moment, they are not getting a fair choice, hence the reason why I moved the motion in my name. I call on John Swinney to speak to and move amendment 12358.4. Cabinet Secretary for Education and Skills I welcome this afternoon's debate and I want to try to be as helpful as I can in discussing the substantive issues that are raised by Liz Smith today. The reason for that is that this whole debate was a key focus of the national debate that informed the development of curriculum for excellence with the decisions that were taken, endorsed across the education and skills system and widely supported in this parliamentary chamber. One of the central aspects of the reform of curriculum for excellence was the extension of the broad general education to the end of S3, which was a point that I felt was not given justice by the speech that Liz Smith has just given. The extension of the broad general education to the end of S3 was a fundamental feature of the design of the new curriculum. Learners now study a wider range of subjects and, to a higher level, with a greater degree of deeper learning than under the previous curriculum. We cannot just skate past that. The benchmarks signed off by the chief inspector in 2016, endorsed also by the chief examiner of qualifications in the Scottish Qualifications Authority, provide the clarity and the evidence of the higher standards that are expected at each level of the curriculum for excellence, and particularly at the conclusion of the broad general education at the conclusion of S3. Liz Smith, I thank the cabinet secretary for giving way on that point. If that is correct, cabinet secretary, there ought to be a good progression into S4, but at the moment what is happening is that pupils are doing a considerable number of subjects in breadth in S1 to S3, and their pregnant conditions are being restricted in S4 at the very time when they want to take qualifications. That, in essence, brings me on to the other substantive point that I want to make, that the focus on the breadth of learning throughout the primary school and the first years of secondary school ensure that learners have a solid foundation on which to enter the senior phase of school. I want to highlight three particular features of the senior phase that are relevant to this debate. The first is that the periods from S4 to S6—this addresses directly the compartmentalisation point that Liz Smith is making around S4—is designed as a three-year phase of learning, where the focus is on a learner's total achievements by the end of that period rather than on an individual year-on-year attainment. The second point and the second objective of the reform is to maximise the richness of the learning throughout the senior phase, focusing on the best way to allow learners to achieve the highest possible level of attainment. That approach recognises that, although qualifications are undoubtedly important in allowing young people to pursue their aspirations, there is little value in simply accumulating qualifications at lower levels for their own state, if Mr Mundell will forgive me, I've got quite a lot of ground to cover. That might mean that learners take fewer subjects in S4 than under the previous system, where the focus was on gaining as many standard grades or O levels as possible. However, far from that being an unintended consequence, that was an entirely deliberate outcome of redesigning the senior phase. In the evidence that Terry Lanigan gave to the Education and Skills Committee in January 2017, many of those points were made about how the structuring of the curriculum had been undertaken to reflect the fact that young people were being encouraged to engage in deeper learning that enabled them to fulfil their potential as a consequence of that point. Liz Smith has been satisfied that those students in S4 are getting a fair deal when it comes to subject choice. That will be a judgment that was arrived at in individual schools based on the curriculum model that individual schools want to take forward. That is the policy position that I bring to this debate. I believe that schools should be able to undertake the curriculum model design that best meets the needs of learners in their individual schools. Recognising the strategic guidance given to the education system that the S4 to S6 experience must be viewed as a three-year experience, not compartmentalised into individual annual components, which is what the Conservatives would seek to get us through. I will give way to Ms Mundell. At a very basic level, the cabinet secretary would accept that if pupils drop a subject because they are unable to take it in S4, it makes it less likely that they will take it up again in S5 or S6. Not necessarily, because young people will have established stronger foundations in a higher and more demanding broad general education than would have been the case in the previous arrangements. The third point was the determination to focus, not solely on traditional attainment, but to recognise the range of other experiences and skills that young people need to make a success of their lives in a fast changing world. That approach has been embedded further by the successful implementation of the Developing Scotland's Young Workforce programme. I will have to make some more progress. Jenny Marr. I will give you the time back. Okay, I will be with you. Jenny Marr, sorry that I pre-empted you. I thank the cabinet secretary for giving way. He suggested that those decisions about course choice are available on a school-by-school basis, but Dundee City Council's curriculum guidelines say that pupils can study a maximum of six subjects at 4 and 5. That is for the whole local authority. Does he accept that those policies are being made on a local authority basis and not on an individual school basis, as the cabinet secretary? That gets us to the number of the reform agenda that I am interested in taking forward. I am glad that Ms Marr is a supporter of the reform agenda that I am taking forward, because I believe that those decisions should be undertaken at school level, enabling schools to put in place the curriculum that meets the needs of individual young people. The product of the approaches that we have taken has been to see a significant increase in the positive destinations that are being achieved by young people. That is the point that the First Minister made at the First Minister's question time yesterday. It has resulted in an increase in the number of higher passes exceeding 150,000 for each of the last three years, recognising the significance and the value of that qualification. It also results in nearly 60,000 skill-based awards and achievements that recognise the learning that has been undertaken by young people and identify the value of that within the Scottish Credit and Qualifications Framework for young people in the further destinations that they take forward. I also want to reflect on the fact that the models for delivery of education in Scotland are more diverse today than they were when we were talking about O grades and standard grades. We now have for the advanced higher hosting arrangements involving, for example, the Glasgow Caledonian University, the virtual school network in Highland Council, the East School in the Western Isles, which is enabling a much broader range of advanced hires to be available to a broader range of young people in their different educational settings. In this debate, there will be a lot of information and discussion about what are the right choices to be made. I believe that the fundamental choices that are made in constructing curriculum for excellence, which identified two-three-year phases in the secondary sector, enabled young people to focus on the outcomes that they achieved and on our educationists to focus on the outcomes that they achieved, are exactly the right approaches to take on other foundations for the learner journey work that the higher education minister will talk about in her conclusions to this debate, which served the young people of Scotland very well in the foreseeable future. I move amendment 9. I have to say that I am running out of spare time, but I thought that it was important to allow interventions that were direct questions, so bear that in mind as we go on. Ian Gray, please. I have not said what you are doing yet. To speak to and move amendment 1, 2, 3, 5, 8.1, just in case you have forgotten. Thank you. I had not forgotten and I do indeed rise to move the amendment in my name. That is an important issue, but it is not a new one. The narrowing of the curriculum and fallen attainment in S4 was raised by Kezia Dugdale in May 2015 at First Minister's questions, and again in June of that year. The evidence, meticulously gathered from official sources, collated and analysed by Jim Scott, was there even then. The First Minister chose not to listen. She tried to suggest that Professor Scott did not know the difference between enrolments and pupil numbers. She wrote the whole thing off as constant SNP bashing, but it was not. Three years on, the evidence for the narrowing of the curriculum in our schools has mounted. The number of schools that allow pupils to study more than six subjects in S4 has indeed fallen to 43 per cent and only 11 per cent now allow eight subjects. The numbers are stark, but so are the consequences. That narrowing of the curriculum is pushing some subjects out of schools altogether, and nothing is going to convince me that that was an intended consequence of the great education debate or curriculum for excellence. As Ms Smith said, modern languages are particularly badly affected. It is no coincidence that, last year, the number of young people gaining any language qualification was 50 per cent lower than in 2007, and Gaelic, to which we all in here committed our support only a couple of weeks ago, was exactly one of the subjects Dr Scott identified years ago as being at risk. This time, the education secretary counters with an amendment of positive statistics, which are true, but hide rather than contradict the problem. With regard to highers, yes, high-achieving pupils who are going to do five or six highers will still do five or six highers. The point is that they will be choosing those highers from a narrower S4 base. Their chances of doing three sciences or two modern languages are being undermined or even denied in some schools with a knock-on effect into university course choice. As for the statistic in the Government amendment, it is rather contrived faster increase in lower-income pupils gaining at least one qualification at level four, five or six. That is true, but it is largely driven by more of the wealthier end of that statistic, moving on to level seven qualifications. The number of exam passes by pupils in S4, as has already been pointed out, has fallen by more than 140,000 since the new exams were introduced. The number of national five entries per learner has declined by 20 per cent. The pass rate for national fives has fallen from 91.3 per cent in 2013 to 79.5 per cent now. Those who leave school with only national four and five qualifications can choose and sit fewer subjects and they are achieving fewer classes. Indeed, the very same SQA tables from which Mr Swinney's figure is derived show that, since 2013, the percentage of pupils leaving school with no qualification at all is rising, especially in lower-income details. It is not a big rise, but it is the reversal of a 50-year historical trend. Comprehensive schools, awards for all, standard grades, those took a school system that left 70 per cent with nothing and turned it into one. We could be proud of where every pupil's achievement was recognised. Those are achievements that matter, too. S4 leavers deserve the best from our schools as much as the high fliers with their higher pass rates. No-one is arguing that there is a conspiracy here, but there are unintended consequences of the new exams coupled with teacher shortages and tight budgets. The education secretary simply has to face up to it. Those consequences are impacting on those at the wrong end of the attainment gap. Parents do not understand what is going on. They do not understand why their children's choice is so constrained and they do not understand why that choice depends so heavily on which school they use. Even in my constituency, where there are as few as five high schools, some offer six, some offer seven and some offer eight subjects and S4. You must conclude with a sentence, I am sorry. Parents feel that pupils from more affluent communities have been offered more choice and more chances. Cabinet Secretary, that can only exacerbate the attainment gap. It is not enough to just accept the motion tonight. We have to hear what you are going to do to fix that problem. I am sorry. In these short debates, time is very tight. It is now tight for minutes for all speeches. I call Ross Greer, Mr Greer, please. Ensuring that Scotland's schools provide an inclusive learning environment for all young people to excel is an obvious point of consensus. Subject choice cuts right to the heart of that issue. How can we expect young people from more deprived communities in particular to succeed if they are not given the same opportunity to choose the subjects that they want or, indeed, the subjects that they need? Of course, attainment will be lower if pupils are restricted to subjects that they have less interest in. That restricted choice can have a lifelong impact, whether it is a missed opportunity to develop an interest from an early age, or knock-on effect in a career or future study choices. One of the benefits of the Scottish education system should be that our senior phase provides for a wide education, rather than shoehorning pupils towards three A levels as down south. However, with restricted subject choice, that diverse education is not being delivered. Young people are not being given the same opportunities to develop their own interests. Tackling the poverty-related attainment gap means ensuring that all pupils have a good choice of subjects at all levels—national 4 and 5, higher, advanced, higher and others. However, we are not doing that when, in Glasgow, pupils from the most deprived communities will, on average, be offered six fewer hires than those from the least deprived. That is an immediate inequality but also one with profound long-term effects. Some parts of Scotland face far greater difficulties when it comes to subject choice. Across our rural and island communities, for example, it is simply not possible for individual schools to have the same breadth of expertise within the building as in areas of larger denser population. However, that should not prevent the full breadth of subjects being offered to young people in those communities. The reality is that it does, though. Distance learning, using the internet and teleconferencing, can allow pupils to learn subjects that are not physically available within their own school. Those options are already used across Scotland, though not with consistency and with unnecessary barriers remaining. Different approaches to timetable, for example, within local authorities, can create difficulties. That is an issue where we need to grapple with the difference between granting autonomy to individual schools and headteachers and the kind of co-ordination required, particularly across rural communities. Those barriers need to be addressed. For the most part, it is teacher shortages that have had a severe impact on subject choice in particular communities and with particular subjects. We have now debated the causes of those shortages on a number of occasions, including through the inquiry process of the Education Committee. We know that issues of workload, conditions and pay have had a major impact on recruitment and retention, particularly in subject areas where those with a relevant qualification have clear alternative employment in the private sector. We know that austerity cuts are at the core of much of that. Real-term spending in education has dropped by £335 million since 2007, which is about 6.5 per cent. Many local councils sought to protect education spending after their budgets were squeezed, but that very quickly became close to impossible when the squeeze started almost a decade or over a decade ago. The Scottish Government likes to highlight the attainment challenge fund and the pupil equity fund as investments in education. Although all new money into education is welcome, as we discussed with the cabinet secretary this morning, in many cases it is simply being used to plug gaps left by core budget cuts. Given the annual nature of the funding and restrictions on how it is spent, it is obviously not resolving the issue of subject choice when restrictions are caused by staffing shortages. Core council education budgets are where funding needs to go, and we can begin to resolve some of the issues around subject choice restrictions. We can see the impact of the past decade's budget decisions on teachers. There are 3,500 fewer teachers than there were in 2007. It is not difficult to understand when their wages are 20 per cent lower in real terms than they were 10 years ago. All the fast-track schemes that we can think of will not solve that problem. A genuinely restorative pay rise is what is required there. The IIS has launched its campaign for that restorative rise, starting with 10 per cent this year. I sincerely hope that the Government takes that pay claim seriously in negotiations. It would not resolve all the issues that are affecting subject choice as Liz Smith laid out. It would go a long way on some of the major underlying issues. I think that I will rescue you there. It is time to sit down. I now call Tavish Scott. Mr Scott, please. Thank you very much, Deputy Presiding Officer. This debate that Liz Smith has brought forward today is about subject choice. I speak more as a father than as an MSP on this one, because my oldest children have been through that subject choice. I think that this is very simple. It is not the Government's fault. I think that Liz Smith and Ian Gray were quite right about this. I think that the Government should take this as a sign that we are all looking for a more considered way forward. To rest on curriculum for excellence, those of us who have saturated education committee evidence in the last two, three years in the fairness business, when he is very well aware of this, is very concerned about the implementation of that programme and how it was actually done. The unintended consequences that Ian Gray rightly highlighted, much of which came out of, shall we say, a less than perfect implementation of that, not least of which by Education Scotland. If there is one major truck that I would have with the Government on this, it always does seem and remains strange to me that we have rewarded the one body responsible for the curriculum for excellence implementation, Education Scotland, with more powers, rather than asking some fundamental questions about their role, not least of which is pointed out by OECD, among others, which Mr Swinney in fairness is keen to point out to us. I hope that the Government will take this debate in that spirit, that this is about seeking to find some solutions to this narrowing of choice. Here is why it matters, because if you are at S4 and you are given that choice that is only six, as is all too prevalent from the figures that members across the chamber have already mentioned, you simply do not have, by definition, so much choice at a higher level at S5. That matters, because, like it or lump it, I have yet to find a university that does not want my son or my daughter or any Scottish pupil to make those hires at one sitting. I entirely take John Swinney's point about the senior phase, but that is not the reality, rightly or wrongly, it is not the reality of how our higher education sector is then approaching their assessment of candidates for their universities. That is happening today. I cannot be the only parent to push the trolley down the supermarket aisle this weekend at home in Lerwick and got it in the ear from a couple of parents about a university not taking their son, because he had not got what he needed to get. The reasons for that, they considered, were also about the narrowing of choice. I should quickly add that the Anderson High School in Lerwick has offered seven. I well remember seeing the emails about that. They were told when Education Scotland was pushing the senior phase that they should only offer six, but the head teacher and her promoted team made it very clear that their school strongly believed in seven, and they were going to continue to do that. That, in my view, is the right thing to do. I believe that the central core of the subject choice argument is very important and very powerful. If the university sector changed their approach to one where they accepted the Government's arguments that the Cabinet Secretary forwarded this afternoon, that they should consider that across the senior phase, we would be discussing and debating that in a different way, but that is not the reality. That is the reason why the unintended consequence that has been described this evening needs to be addressed. I hope that the Government therefore takes Dr Jim Scott's evidence as something that needs active consideration and active work. It is interesting to note from Spice that the Government accepts that it does not have its own figures in this area. Indeed, I asked this morning what information was held. I was told that no data on school curricula models was available and therefore on subject availability. I think that Dr Scott deserves some credit for bringing this information into the public domain and giving the Government a reason for addressing the very issue that Liz Smith has brought to us this afternoon. On developing Scotland's young workforce, I would entirely agree with the Cabinet Secretary's remarks. I would simply ask him to look anew at ensuring that there is a wider accreditation of non-formal education, youth awards and courses that could help the very people whom we need to deal with in closing that educational attainment gap. Open debate, speeches of a type 4 minutes, Jamie Halcro Johnston followed by Clare Adams. First, I would like to welcome the remarks of my colleague Liz Smith. She outlined great detail in her speech and the reason for this debate is an important one. On these benches, we have sought answers from the Scottish Government over the last week on the significant change in schools, the narrowing of the subject choice. Indeed, we are told that curriculum for excellence would provide more choices and more chances for young people. We are assured that curriculum for excellence would not mean a restriction in subject choice. However, that choice has been restricted. The points that appear in our motion today were, of course, put to the First Minister on Thursday. In a response, she said, what matters is the qualification that pupils leave school with, not just the subjects that they study in S4. We cannot be alone in sharing concerns at the complacency of that answer. Ruth Davidson asked about apples, but she was told that the important thing was oranges. Subject choice, it seems, does not matter much. However, when we have leading educationalists telling us that social inequalities in entry to Scotland are mostly explained by subject choice and when we have a range of experts in the field of education telling us that the many problems that this is building up, it becomes time to take notice. One of the traditional positives of the examination structure in Scotland was the supposed breadth of learning that it provided. Specialisation in particular subjects was gradual, giving school leavers both a broader education and a greater degree of choice as they moved into higher-level qualifications. The Deputy First Minister's response has been to assert that the senior phase in secondary schools is a three-year progression, but that seems to take no notice of the impact on young people who take a different course. Again, Liz Smith mentioned the squeeze on certain subjects, highlighting particularly the concerns around modern languages and STEM subjects. Between 2014 and 2017, SQA reported the number of entrants to higher French fell by 6 per cent. For higher German, the fall is 12 per cent. With a focus on language tuition, those numbers should be extremely concerning for ministers. In terms of STEM education, where the Scottish Government has a focus, we can look to similar falls across three main sciences and a significant decline in entrants to higher maths. The qualifications that are gained at secondary level are important and valuable in themselves, but we should not turn a blind eye to the restrictiveness that places on young people who are looking towards their futures. For those who are contemplating a vocational route to enter a modern apprenticeship or otherwise move into work, restrictive subject choice obviously has an impact. Since curriculum for excellence came into play, the SQA has revealed that the number of exam passes by pupils in S4 has fallen by 150,000. Straying into the new foundation apprenticeships that are on offer through schools, I have spoken previously in this chamber about the variability of framework choice across different parts of Scotland. In my region, the Highlands and Islands, there have been as few as two frameworks offered to young people. The minister, JB Hepburn, was helpfully clear in his intention to broaden out the availability across local authorities. Universities, too, have noted that the restrictive subject choices have an impact on entry. The University of Edinburgh acknowledged that this is causing damaging exclusion for young people from less-advanced backgrounds. There is a debate to be had on how specific the choices to people—choices given to people relatively early on in their secondary education—should be. When young people are restricted to a smaller number of subjects, it continues to impact their choices later on in education. Officers, shortcomings in our education system always seem to have a disproportionate impact on the least-advantaged young people. Curriculum for excellence was introduced with great firmfare, the Scottish Government, and gained wide support on the basis of assurances and positions that were presented by ministers. Unfortunately, in the case of subject choice, it seems that those assurances have not been kept. Clare Adamson, followed by Jenny Marra. Thank you, Presiding Officer. I see the day that some of the arguments are being used in the chamber this afternoon. I served on the Education and Culture Committee in S4Term of the Parliament. Many of what has been discussed today was raised in evidence at that time. Indeed, in 2012, Ken Muir of Education Scotland, in response to questions by Liz Smith herself, said, the expectation is that youngsters will, in the main experience, a broad general education up to the end of S3 or at least will have an opportunity to receive the experiences and outcomes up to the third curriculum level. He went on to say that the new system is not about going for eight or nine qualifications in one year. It is a continuum of learning. Those are not just words. The new qualifications will and do build on experiences and outcomes of broad general education. I am sorry, I do not have time. If the Conservatives wanted a proper debate, they might have given more debate time over this afternoon to the subject. Ken Muir also said that the two plus two versus three plus three issue is a false dichotomy. Broad general education goes up to S3, and that does not mean that there is no choice before that stage. Indeed, personalisation and choice are an entitlement of curriculum for excellence. That was 2012. Again, in that year, Terry Lanigan of the Association of Directors of Education in Scotland said that one of the weaknesses in the current system is the well-known two-term dash to hires. The new system will allow the most able young people to start two-year higher courses at the beginning of S4. The other myth that has grown up is the idea that those schools that choose to print some or all pupils for eight qualifications in S4 are somehow doing better than those that adopt another model. The whole point of curriculum for excellence is to ensure that the needs of the individual young person are addressed and that each young person gets the chance to attain qualifications at whichever point is appropriate for their needs. That was the whole reason behind curriculum for excellence, making it pupil-based, making it pupil-focused and allowing pupils to advance an appropriate speed and an appropriate time for their own areas. I can also go back to 2014, when we were discussing this. Larry Flanagan of Education Institute of Scotland, talking about the implementation of curriculum for excellence, at the end of all this, if all we have done is replace the exams and we have not changed the pedagogical approach in schools or whatever year youngsters make their future choices, we will not have achieved curriculum for excellence. Curriculum for excellence is about giving teachers, giving individual schools the opportunities to design the courses and design the plans for the young people to ensure that the best outcomes for those young people. Larry Flanagan also went on to talk about the 160 hours that are required for SQA qualifications. If he has a mass head of department, he will want those 160 hours. How on earth do you try to table 160 hour courses without squeezing teaching and learning of young people if you are going to ask them to do more than that? You can maintain six or seven or even eight choices for young people, but that is not in one year. That is over the final phase of curriculum for excellence and the final phase of that implementation. If I could just finish an anecdote, there have been a few of those this afternoon. My own son did advanced higher music. He is now studying music at the University of West of Scotland. He did not do it at his school, he did it in a cluster because his school couldn't do the advanced higher but he got on the bus, went to the other school and he got to get the choices that he wanted. A lot of what has been talked about this afternoon does not take into consideration the way that schools work together. Jenny Marra, followed by Richard Lochhead. Excuse me, could we stop the private conversation across benches, please? Jenny Marra. It comes as a surprise to no one and certainly not to me that the limited choices that the motion outlines today are the case in Dundee. I understand and quoted from a policy paper to the cabinet secretary there that Dundee City Council's policy is for pupils to study a maximum of six subjects at national four and five in S4 and up to five hires and advanced hires in S5 and S6. Yes, it is equal across our city but the policy has been used to limit choice for everyone in the city in all eight secondary schools. Cabinet secretary, at higher level we only have two out of those eight secondary schools in the city that are hitting their target for the number of higher passes that they are expected to achieve and that is with deprivation factored in. We find that locally a couple of schools previously considered to have the highest achieving or performing schools in the city fall well below beneath their benchmark expected figure of higher passes. I feel so strongly that that is not good enough for the children that are going through education at the moment and I am sure that a number of parents locally agree with me. We have a duty, Presiding Officer, to look carefully at exactly what is happening. At lunchtime today, Bill Bowman and I spoke to primary six from Fintrey primary school in Dundee. In a year's time they will go to Braveview academy. Twelve per cent of pupils at Braveview achieve five or more hires and their benchmark figure with deprivation factored in by the Scottish Government is 27 per cent, so less than half of the pupils that should be achieving five hires or more are being allowed to fulfil their potential. For that lovely class of bright-eyed enthusiastic primary sixes, the restriction and subject choice is a problem, as it will hit them the hardest as Ian Gray outlined. The attainment gap for them is real and is going to hit them in the terms of the motion today in three or four years. The cuts to teachers in our schools for them is a reality. However, Presiding Officer, if you will allow me this week, we have seen the storm brew in Dundee over pupil equity funding. We learned at the start of the week that swimming lessons for primary school pupils across Dundee have been withdrawn, something that I will raise directly with the First Minister tomorrow. Targeted Scottish Government funding of £200,000 for the top-up swimming programme came to an end and has never been replaced. That came to an end in 2015. Dundee City Council said in response, and I quote, headteachers have been given the opportunity to explore how swimming lessons can be delivered through the pupil equity fund and leisure and culture's family swimming initiative. It seems that headteachers can raid the pupil equity funding pot or parents can pay for the lessons themselves. Pupil equity funding was trumpeted by John Swinney as extra cash for schools in deprived areas to spend as they know best to close that attainment gap. No, I do not have time. The SNP council is now telling headteachers to spend this money to replace services that used to be provided centrally. They are being asked to use the pupil equity funding to mitigate the cuts. However, I heard this morning in the education committee that John Swinney said that the SNP council in Dundee is wrong to do this. Can he perhaps clarify that? No, Ms Marr, are you closing? For this afternoon, because I do not know how he expects the pupil equity funding not to be spent on mitigating the cuts when he cut £12 million from Dundee City Council's budget. I think that it is probably worth saying at the outset that I firmly believe that you cannot just measure a pupil's success by the number of hires they have on their hand when they leave school, or the school's success in educating children by the number of qualifications that children have when they leave school. I think that they are very important factors, but we should not dwell on those alone in determining the success of individuals or our education system. Liz Smith closed her speech by talking about what she felt was one of the underlying causes of the lack of subject choice in some schools in Scotland, which was teacher numbers and teacher shortages. I really want to focus on that for my short speech. Clearly, that is an issue in terms of teacher numbers that affects many parts of Scotland at the moment, particularly some rural parts of Scotland. The money that I represent, of course, I have been involved in that issue for the past few years. The issue is that it is not a question of cash. The money is there, so when we keep calling about resources and more money, in the case of where we do have some of our teacher shortages, it is not about money. The money is there, and people are simply not applying for the jobs in some of our more rural areas in particular of Scotland. That puts pressures on the school's particular primary level, where the headteachers and deputy headteachers have to help out in the classroom and it takes focus away sometimes from the leadership role at the same time. In some secondary schools, of course, it can mean that there is not enough subject choice, as perhaps one would like. However, there is enough to give people a good education, and that is what matters at the end of the day. It is not just teachers that many rural areas are struggling to attract, but other professionals and other occupations as well. We need to research as a Government, as a Parliament, into why people are not applying to work in rural areas when it comes to some of those more professional jobs. Of course, it is not just Scotland. Those are also issues in England. The English education secretary was speaking to English teachers just recently in Birmingham, where he said that he recognised that recruitment retention is difficult for schools and that one of the biggest threats to that is workload. It is also an issue in England. The Education and Skills Committee, which I sit on, just recently visited Finland and Sweden to discuss their education system. What we heard from the Swedish education, as we spoke to, was that teacher recruitment is a big issue in Sweden as well. They are projecting teacher shortages in the years ahead. It is not just Murray, it is not just Scotland, it is England, it is Sweden and it is many other places in Western Europe as well. We have to research why that is the case. There are some measures that are being taken that are very important. I welcome the cabinet secretary's intervention to lead to more home-grown teachers in their local communities. In the Highlands and North of Scotland, of course, that means working with the University of Highlands and Highlands, with some good initiatives under way to help to retrain people from other careers to become teachers or to help people just to train locally as teachers. That is now beginning to make a difference, so there are things that we can do. There are also things that the UK Government can do, working with Scottish authorities, and maybe the Conservatives can look into that as well, which is dealing with our immigration situation. It is very difficult for teachers who are sometimes married to Scots, who sometimes have jobs in schools to get their visas to actually fulfil their job and work in those schools and plug those vacancies. I perhaps would suggest to the cabinet secretary that I am not sure if there is anything else that the Government can do in terms of sponsoring visas. I know that there are some issues in some local authorities. The local authorities do not sponsor visas and perhaps the Government can step in or some other authority, and that is something that we can look at as well. The final issue that I want to mention briefly is that the Conservatives can help us with this debate if we are going to take a Team Scotland approach and deal with the poverty that is impacting on the classroom in Scotland. Education committees are looking at the impact of poverty on educational attainment at the moment. Many of the witnesses, indeed all of the witnesses who have spoken about it, have cited the UK Government's welfare reform programme as damaging people's educational opportunities in our schools. It is leading to a huge burden for our teachers, our schools, our education budget, our local authorities and the Scottish Government. We would ask in closing that the Scottish Conservatives look at this in the whole so that we can give the best future to young people of Scotland. Thank you, Deputy Presiding Officer. May I say at the outset that I consider this to be a very important debate, a debate that has rightly been the subject of much discussion in the education world. Indeed, subject choice is a matter increasingly raised with me by constituents, so too is the issue of career guidance in our schools. Subject choice is crucial when it comes to the future career paths of our young people. Do not get me wrong, many schools do an excellent job in this respect, but we also know that a sizable minority of schools are not providing our young people and their parents with everything that they need to know. Professor Jim Scott's work has uncovered a worrying picture that over a third of schools are not adhering to the Scottish Government's guidelines to local authorities when it comes to the comprehensive details surrounding the column structures offered on their curriculum, and that is surely a matter that we need to address and with some urgency. However, let me deal with the specific issue of the curriculum for excellence. It was intended to build upon the traditional broad education for which Scotland was long renowned. Instead, however, as a lack of the joined-up approach between S1 and S3 and then the senior phase, it has unwittingly narrowed subject choice in S4 and with particular concerns for those pupils who are leaving school at the end of S4 or at the end of S5 with passes at only not 5. If their subject choice is restricted, they leave with fewer qualifications. The concern that might happen was flagged up in the early stages of the curriculum for excellence development, and it certainly manifested itself on a practical level six years ago when parents in Aberdeenshire complained about what was happening in some schools. A recently retired head teacher wrote to one of my colleagues last week, after First Minister's questions, to say that he knew at first hand what the slow erosion of subject choice was doing, and he particularly singled out the effect on modern languages, citing the case of how few pupils sat higher German this year. Professor Jim Scott's recent report showed that, in the past year alone, the number of schools offering just six subjects at S4 has increased from 45 to 57 per cent. Only 32 per cent allow children to sit seven subjects and just 11 per cent offer eight. The consequence of that does not stop at S4, but it is having a knock-on effect on what subjects are available at higher and advanced higher, and the severity of that problem is felt in some of the most disadvantaged communities. It is shocking that if you go to a school in one of the wealthiest parts of Scotland, you have got a 70 per cent chance of being able to choose between 12 and more advanced hires, yet there are just two schools in the poorest parts of Scotland that pupils can choose between that number. 89 per cent of schools surveyed, saying that difficulties recruiting teachers constrained subject choice. The fact that the Scottish Government's own statistics show that there has been a 13 per cent decline in secondary school teachers over the past 10 years speaks for itself. In priority STEM subjects, including maths, several councils have been unable to fill teacher posts, resulting in whole courses and subjects being dropped. However, let me conclude on the issue of careers guidance. It is absolutely essential that careers guidance is well informed and thorough, most especially when many pupils are facing fewer subjects to choose from. I would be very interested to know what assurances the cabinet secretary can give us that career guidance will in fact improve. Advice has not been provided on a universal basis, which, when compounded with more restrictive subject choice in S4, and a teacher shortage, is a major worry. That is why I support the motion in the name of Liz Smith. The last of the open debate contributions is from George Adam. Thank you, Presiding Officer. This is a very important debate and one that I am glad to take part in. At the beginning I would like to say that I agree with Richard Lochhead, my colleague, when he says that let us not measure young people or schools' success on the number of hires they have in their hands. It is about the destination, the development and where they actually end up as time goes on. However, this debate is one that we have had in various guises over the years in my time in the education committee, and that in itself is no bad thing, because it shows how serious we all are about this subject. However, I would like to take this opportunity to talk about what is happening in our communities, because all in all it is a positive story. Things are improving, but I am not for one minute saying that everything is perfect. There is always scope to be better and do better, but the facts speak for themselves. More young people than ever before are leaving school with marketable, reputable and well-respected qualifications, and that is a testament to our education system and our teachers. Importantly, more young people from our most deprived communities are gaining higher and advanced hires and moving on to positive destinations. Indeed, the number of students from Scotland's most deprived areas, gaining a university place, reached a record high of 4,150 after results day last year. That is an increase of 680 students on the last two years alone. With numbers like that clearly laid out, I find it absolutely fascinating that we continue to talk down the Scottish education system and from then to suggest that pupils achieve in spite of the system, not because of it. We all know our teachers' work exceptionally hard to make sure that every student in Scotland, irrespective of their background or postcode, can reach their full potential and gain the necessary qualifications to move on to their college, university or employment choice. In my constituency alone, the area has a huge diversity. Over 92 per cent of school leavers are going into positive destinations, and I have personally met and spoken with many of the students who are the first in their family to attend university. The young people whom I have had the pleasure of chatting to when I am out and about in the constituency have never once suggested that they have achieved what they have in spite of the education system. Quite the opposite is true. Most paisley students have nothing, but good things to say about their school experience. I admit that there are always many challenges for us all to face and we will continue to face them, but I think that everyone in here wants their children and young people to be happy in school and leave with a breath of the depth of knowledge that will give them the best possible start in life. It goes without saying that we all want our young people to have the widest possible choice of subjects and classes. It is for those reasons that the Scottish Government is encouraging schools not only to be flexible on their timetabling but to look at options to give students choices beyond their own school walls. Last session's education committee we visited a number of schools that embraced that flexibility in timetabling and explained to us what a difference it made in the school. Those were schools that were in some of the areas of deprivation and challenges that they had there. They told us that when they got that opportunity they could make that difference. There are many examples of schools being flexible and looking for outside options. We have already heard about the higher hobbit Glasgow Caledonian University and the virtual school network in the Highland Council area. Those are real examples of how the Government is encouraging local authorities to widen the curriculum and allow students to make early connections with further education institutions. It is only right that we debate this issue due to the fact that it is very important to every single one of us here. There is nothing more important than creating opportunities for our children and young people. I think that while we have this debate we have to look to the future but let us not forget that progress has and is being made. We move to the closing speeches and we are tight for time that may affect the next debate. I call Mary Fee up to four minutes, please. I begin by thanking the Conservatives for bringing this debate to the chamber today, allowing us to debate the choices available to children and young people to allow them to follow whatever path they may choose. It is also an opportunity to discuss the attainment gap as we have recognised in our amendment, which I would ask the chamber to support tonight. In the opening speeches in this debate, both Liz Smith and Iain Gray very clearly laid out the concerns over the narrowing of curricular choice and the impact that that has on attainment, particularly in relation to language and STEM. The issue around language, as highlighted by Iain Gray, is a long-standing one with a huge drop in pupils pursuing a career in language. Again, a huge concern, as highlighted again by Iain Gray, is the rise in pupils leaving school with no qualifications at all. Lack of curricular choice is also exacerbated by where you live, with many rural schools being disadvantaged. Claire Adamson spoke about curriculum for excellence being pupil-based and pupil-focused. Limiting choice does not support pupils, it disadvantages them. Since 2007, as Liz Smith said, we have lost nearly three and a half thousand teachers. We have also lost teaching assistants with literacy and numeracy rates falling and the attainment gap rising. Jenny Marra spoke of situations where PEF funding is used to mitigate cuts to core funding. The First Minister has asked to be judged on her education record, and I hope that she and the education secretary will take on board the very legitimate concerns of MSPs across the chamber and the concerns of teachers, pupils and parents. Limiting subject choice limits opportunity. Children in S4 should not have the paths that life can offer them, narrowed at such a young age. Of course, we want children to achieve the best qualifications, but it is short sighted to limit the subject choice in order to glorify exam outcomes. We welcome the recognition by the education secretary that the attainment gap needs addressed. However, we need wide-reaching solutions and investment to match those solutions in order to tackle the stubborn gap. The attainment gap in our schools will not vanish or reduce with one single fix. PEF funding is an important tool but is not available in every school, and where it is, evidence would suggest that schools need better support and better guidance in how to best use the funding to close the attainment gap. In the long term, limiting subject choice, as our amendment highlights, particularly for schools in the poorest areas, will harm any attempt to reduce the attainment gap, as well as limiting the opportunities for many to attend university after leaving school. Local authorities need security of funding to recruit more teachers on a permanent basis. Only then can we offer pupils more choices in what to study in order for each pupil to go on to pursue whatever career path they wish. All of our young people, regardless of what school they attend or where they live, should have the same choice, the same opportunity and the same support. Aspiration cannot and should not be limited by the choices that are available. Scottish education has traditionally been well respected across the UK and abroad. Given the scale of cuts and the damage done to schools and the limiting of subject choice, the First Minister and the Education Secretary are presiding over an education system that will lose respect of its teachers, pupils and parents. In closing, we in Scottish Labour want to work with the First Minister and the Education Secretary to ensure that education in Scotland remains as revered as it always was and should always be. Gillianne Somerville, up to five minutes, please. Thank you, Presiding Officer. This afternoon's debate has focused on the issue of choice, highlighting the importance of ensuring that young people have a range of options available to them and are well supported in making the decisions that are right for them. As the Deputy First Minister highlighted in his opening speech, those are essential themes of the report of the learner journey review that was published on 10 May. Tavish Scott, when he spoke, asked for a considered way forward, and I would suggest that the learner journey review does exactly that on this and many other issues. It is informed by the views of partners across the education and skills system, but perhaps more importantly in this year of young people, by the views of young people themselves. Those young people have made it clear that in order to ensure that they have the right access to choices that are right for them, we need to strike the right balance and blend of learning options in the post-15 education and skills system, a parity of a scheme across the whole system. We are equally clear that every young person has the right to effective guidance, advice and support, so that they can make sure that they are making the right decisions about their learning and career pathways. The first of the themes within the learner journey review is about the needs for better advice and guidance. I would point to the learner journey review, particularly to Alison Harris when she spoke about that, because that is an integral theme of the entire year-long process that we have been through. It talks about the connection between guidance that young people receive on subject choices, but also on their longer term career options. In progressing that priority, we will be undertaking work to map the availability of advanced higher provision across Scotland. That will help to fulfil our commitment to provide practitioners, parents, carers and learners with access to online prospectuses, setting out the learner choices available in their region building on a one-stop-shop approach. That again deals with some of the points that Ross Greer and other speakers mentioned during the debate around the challenges in some areas, particularly rural areas, in the breadth of curriculum. The learner journey review is exactly what Mr Greer asked us to do, to look at the barriers that need to be addressed to ensure that all schools and councils are being innovative and providing greater choices within their area. John Scott I thank the minister for taking an intervention. With S4 places down by 150,000 since 2016, college places down by 150,000 since 2006, teacher numbers down by 3,400, teacher salaries down by 20 per cent, would the minister agree with me that you do not need to look for complicated reasons when these simple reasons exist, that educational attainment and achievement in the broadest sense is falling across Scotland? Shirley-Anne Somerville The member won't be surprised to know that I utterly disagree with that assessment of the education system. Taking two points of that, he talked about the college places. I'm not going to apologise for the fact that we've actually developed college places that are based on recognised qualifications leading to employment. The discussions around what happens within S4 really do lack an understanding that S4 is the start of the learner's journey in the senior phase. That is what curriculum for excellence is all about. It focuses on the learner's total achievement, and it focuses on that three-year progressing through that senior phase. I'm sorry if Mr Scott doesn't understand the basis for which curriculum for excellence was brought in. The second priority that we will look in within the learner journey is to ensure that more choice is provided through work-based learning opportunities. We want to be able to provide that balance of work-based and academic skills that will be informed by employer engagement. We want to see those opportunities that the member spoke about around foundation apprenticeships, for example, to be driven as a good destination for our young people as well as the needs for the Scottish economy. Thirdly, we want to improve the alignment of courses between schools, colleges, apprenticeships and universities so that young people are able to progress through the post-15 education system as smoothly and effectively as possible. I believe that the learner's journey review, which we have undertaken within the Government, echoes many of the themes that have emerged in this afternoon's debate. Liz Smith mentioned in her opening remarks about the purpose of S6. That is dealt with very clearly within the learner's journey review. It also looks at the point about informal learning, which Tavish Scott brought up, and I happily agree with him on that. The Government is working to ensure that there is more recognition of informal learning, particularly dealing with some of the points that Ian Gray made in a previous discussion and debate around the year of young people. There is a need to provide young people with better advice, more opportunities and coherent routes to education. The attainment gap is closing, and the Government is continuing with more work to do on that, but we are proud of its work on the agenda so far. I call Oliver Mundell to close this debate for up to six minutes, please. Clearly, the minister was listening to a different debate to the one that took place, because very little in those remarks touched on the core issues that were brought forward as part of this motion. Nor did he really connect with the many points that came from different parties across the chamber talking about their own experience and the substantial evidence that was forensically laid out by my colleague Liz Smith at the start of the debate. That matters, because no task is more important for this Parliament than ensuring that our young people get the best start in life, ensuring that they are fully equipped for the challenges of the future and ready to contribute to and lead in our society. Subject choice, and I stress the importance of the word choice, lies right at the heart of making good on this promise. I may be young enough to still remember how important those decisions are in an ever-changing world, where people's career opportunities change several times across their lifetime. I think that people should continue to benefit from the same opportunities that I enjoyed and many other members across the chamber will have enjoyed too. We talk about curriculum for excellence as being about empowering the individual learner, giving them more input into their own education. It is surely quite ironic, as we have heard today, that the reality of the new curriculum for many young people in Scotland is that less choice than ever before exists at a crucial juncture. I find it astonishing to hear the cabinet secretary try and claim that that was an intentional consequence. Clearly, like Clare Adamson, he does not remember what Fiona Hyslop had to say to Parliament back in 2009 when she said in a quote, I want to see the breadth of experience in S4. There are some misplaced concerns that there will be restrictions. She goes on to say, I will not accept a situation in which there are restrictions. Now we see detailed evidence laid out over a period of time that shows that there has been restrictions, and there is no getting away from that. As we have heard from across the chamber, there is no doubt that that problem is confounded and comes about in many cases because of teacher shortages and vacancies, particularly in STEM subjects. That is just not good enough. We know that there is a problem there, yet the action to fix it is painfully slow. I agree with the cabinet secretary that many of the curriculum choices should be decided at school level. We think that that is a good idea, and we think that it enhances the system. However, how can we possibly expect that a broad range of subjects will be on offer when a number of schools do not even have the teachers to teach them? Alex Rowley. I accept that part of the reason for the restriction in the number of courses in five schools is down to alachy teachers, particularly in STEM subjects, but the party is also down to budget. Does it accept that failed austerity coming from the Westminster Government is contributing to that problem? Oliver Mundell. I do not accept the point that the member makes. The Scottish Government has got more money to spend than ever before, and its political choices are made in this Parliament that are having an effect on our young people. It is time to recognise that fact, and the SNP Government should stop hiding behind other people. To be fair, if the cabinet secretary wants to stop shouting, Richard Lochhead will give a far more considered and reasonable speech on those points, highlighting some of the issues that we face in rural areas. I would welcome more research into the causes of that, looking at my constituency. From the general reaction, it is easy to understand why, throughout this debate, the SNP Government has sought to muddy the waters and talk about a different issue. The cabinet secretary does not want to talk about choice, and I can give him a few practical examples. Just last week, I visited Langham academy in my constituency, and the one issue that pupils chose to raise with me was the fact that they were not able to take the subjects that they wanted. They were in a position not of availability but of being reduced to six subjects. They were not able to take both history and chemistry. One young person felt that he loved history. John Swinney I am grateful to Mr Mundell for giving way. I will cite an example on Langham academy. If we were to follow the view of the world that Mr Mundell views about choice being available to schools, if a school decided, like Langham academy, to have a particular level of choice available to young people, what would Mr Mundell do if he disagreed with it? Would he accept the right of the school to set that, or would he just come here and complain about something that he approves of in principle? Oliver Mundell I think that that is a complete mischaracterisation of the situation, because teachers at Langham academy support the view of pupils. They would like to see a broader range of subject choices, but they do not have enough teachers to deliver them. Secondly, they are being directed by the local authority, and they feel that, as clearly a significant number of schools do now over 50 per cent, that they are being directed and pushed towards just six subjects. That has not happened by accident. It is not a school-level choice. That is a systematic problem across the whole of Scottish education, and it is about time that the cabinet secretary took that You must close, please. Thank you, Mr Mundell. That concludes the debate on education subject choices. It is time to move on to the next item of business. We are short of time, so if you could shuffle around quickly, it would be appreciated.


Hello and welcome to the session. In this session we will discuss k-method for proportions. If a series of fractions are equal, that is say we have p upon q is equal to r upon s is equal to x upon y is equal to so on. Then each of these fractions or you can say each ratio is equal to the sum of the numerators that is p plus r plus x plus and so on divided by the sum of the denominators that is q plus s plus y plus and so on. That is this is equal to the sum of the antecedents of the given ratios upon the sum of consequence of the given ratios. So let us suppose that we are given upon q is equal to r upon s is equal to x upon y. Then we have to prove that each of the given ratios is equal to p plus r plus x upon q plus s plus y. After the proof we take let the given ratios p upon q is equal to r upon s is equal to x upon y is equal to k. Then this means that p would be equal to q into k, r would be equal to s into k and x would be equal to y into k.  Now this would be equal to in place of p we put qk so qk plus sk that is in place of r we put sk plus x which is yk. This whole upon q plus s plus y. Now taking k commons on the numerator we have k into q plus s plus y the whole and this whole upon q plus s plus y. q plus s plus y cancels in the numerator and denominator and we are left with k.   So we have proved that each ratio is equal to sum of the antecedents upon the sum of their consequence. We can extend this proof to prove this result for a series of fractions equal to each other. Let us consider one example to illustrate this result that is of k method. Suppose we are given that p is to q is equal to r is to s and we are supposed to prove that p plus q upon r plus s is equal to fourth root of p is to the power 4 plus q is to the power 4 upon fourth root of r to the power 4 plus s to the power 4. We suppose that the ratios be equal to k that is p upon q is equal to r upon s is equal to k. From here we have p is equal to q k r is equal to s k. Now we will consider the LHS which is plus q upon r plus s.  So now taking q common in the numerator q into k plus 1 d whole upon taking s common in the denominator we have s into k plus 1 d whole. Now these cancel with each other and we are left with q upon s. So we have the LHS as q upon s. In the same way let us now consider the LHS which is fourth root of p to the power 4 plus q to the power 4 upon fourth root of r to the power 4 plus s to the power 4.  So we have fourth root of q to the power 4 into k to the power 4 plus q to the power 4 upon fourth root of s to the power 4 into k to the power 4 plus s to the power 4. Now we can take fourth root of q to the power 4 common from the numerator. So we have q into fourth root of k to the power 4 plus 1 d whole upon taking fourth root of s to the power 4 common in the numerator we have s into fourth root of k to the power 4 plus 1. Now these cancel and so we have q upon s which is same as the LHS. Thus we have the LHS is equal to the LHS and hence we have proved the required result. Now we will discuss application of k method to continue proportions. Let us consider an example for this. If we have p to r s r n continued proportion then we need to prove that p to the power 4 is true. q to the power 4 is equal to p minus q whole to the power 4 is true q minus r whole to the power 4.  And we suppose let each of these ratios be equal to k. So from here we have p is equal to qk, q is equal to rk and r is equal to sk. Now in place of r here we will put sk so we get q is equal to sk square and in place of q we put sk square here so we get p equal to skq. So we have p equal to skq, q equal to sk square and r equal to sk. Now we need to prove this so first of all we will consider the LHS which is p to the power 4 is true q to the power 4 that is p to the power 4 upon q to the power 4. Now in place of p we will put skq so this is equal to s to the power 4 into k to the power 12. This upon q to the power 4 that is sk square to the power 4 which is s to the power 4 into k to the power 8. So this is equal to k to the power 4. Now in the same way we will consider the RHS which is p minus q whole to the power 4 is 2 minus r whole to the power 4. That is this is equal to p minus q whole to the power 4 upon q minus r whole to the power 4. Now in place of p we will put skq and in place of q we will put sk square. So we have skq minus sk square this whole to the power 4 upon in place of q we have sk square minus in place of r we have sk this whole to the power 4. Now taking sk square whole to the power 4 common in the numerator we have this into k minus 1 whole to the power 4. This upon taking sk whole to the power 4 common in the denominator we have this into k minus 1 this whole to the power 4. Now these cancel with each other and this is equal to s to the power 4 into k to the power 8 upon s to the power 4 into k to the power 4. Now s to the power 4 s to the power 4 cancels and here we are left with k to the power 4. So we have RHS is k to the power 4 and also the LHS is k to the power 4. That means we now have LHS is equal to RHS. Hence we have proved the given result. This is how k method is applied in case of continuous proportions. So this complete session hope you understood the concept of k method in proportions.