We Need to Talk about Numeracy!!!

The current English system of setting GCSE grades using comparable outcomes, (GCSE grade distribution is pegged to what cohorts of similar ability achieved in the past), means that roughly a third of 16-year-olds year in, year out do not achieve a Grade 4 pass in English and Mathematics. Those young people who fall below this bar pay a high price in terms of reduced prospects in progression to further and higher education and to careers.

Of this ‘forgotten third’, less than 20% (18% in 2018, 17% in 2019) of them will achieve a Grade 4 in mathematics by the end of compulsory education and we are all aware of the benefits to long term prospects if a GCSE Pass is achieved. Over the last ten years there has been different projects, programmes and policies aimed at improving outcomes and trying to give the best opportunity for achieving a GCSE Grade 4 Pass or equivalent before students leave compulsory education at age 18, yet levels of numeracy in the UK are still very low.

Firstly, let’s look at the recent history of reports and programmes and what they suggested.

Starting in 1999, with the Moser Report, it was found over a quarter of adults were not functionally numerate and the Report suggested that by 2010, 90% of all 19 year-olds should be numerate. Suggested solutions were to allow any adult without a GCSE or O-Level to access a fully funded basic numeracy course and to introduce a new curriculum and qualification that focused on practical numeracy skills. But it was only in 2006, that this new qualification (Functional Skills) was introduced. Just prior to this The Smith Report was published, (Inquiry into Post-14 education, 2014), which concluded that there was a large shortage of qualified mathematics teachers and poor quality CPD in both secondary and tertiary settings. While in 2011, the Wolf Report stated that only half of 16 year-olds gained both English and mathematics GCSE passes, while only 4% of those continuing with their studies post-16, achieved a Pass during this period. So in order to try and improve the numbers of students achieving GCSE passes the Government reformed the Condition of Funding in 2014, requiring any student entering further education without a Grade 4 or better in GCSE mathematics or English to continue their studies in the subject, until they achieved a Grade 4 pass.

The major outcome of this change was the huge increase in the numbers of students studying Level 2 mathematics that added extra pressure to an already stretched workforce, (Inquiry into Post-14 Education). In addition, there were no prescribed hours for the teaching; so many colleges opted to use vocational tutors to deliver mathematics sessions during vocational sessions to cover the lack of mathematics specialists. This resulted in a wide range of quantity and quality of teaching received by students and standards of numeracy did not improve. This was confirmed by three reviews between 2017 and 2018, (Sainsbury Review, Industrial Strategy and Smith Report). So, in 2018, the Government, launched a five-year programme called ‘Centres for Excellence in Mathematics’ (CfEM) with 21 centres around the country selected for extra funding of totalling approximately £30 million to design new and improved teaching approaches, develop quality teaching resources, build teachers’ skills and spread best practice across the country through mathematics networks.

The aim of the programme was to help increase the number of young people leaving compulsory education with the numeracy skills, to improve their employability, and engagement with further learning. The current offer can be seen here. Different centres were invited to lead on different programmes, ‘Mastery Teaching in Post-16’, ‘motivating learners’, ‘Contextualisation’ and ‘Use of technology & data’. For example, Greater Brighton Metropolitan College (GBMET), have focused on developing a mastery approach, while the Warwickshire Colleges group have been focusing on motivation and engagement. There have been some publications, but so far, there has been no definitive programmes that have been rolled out nationally.

In addition to this programme, the University of Nottingham and the Nuffield Foundation published findings from a 2-year study, ‘Mathematics in Further Education Colleges’, (MiFEC, October 2020), that focused on improving the outcomes in mathematics for post-16 students. The report came up with 20 recommendations that should be developed in order to improve outcomes.

So with all this work being carried out, how can colleges make the best student focused decisions and improve outcomes for students?

The first section of MiFEC, focused on the creation of effective pathways for students entering FE without a Grade 4+ and the decisions colleges should be thinking about to ensure that as many students as possible can leave compulsory education functional numerate (and literate).

The study found that, currently, most colleges use one of two strategies for determining the pathways for placement and progression of students, (see the table below).

StrategyDescription
Blanket GCSEAll students placed directly onto a GCSE mathematics course, regardless of prior grade.
Skills ImprovementOnly Grade 3 students placed on the GCSE course. All others study Functional Skills and progress to GCSE or FS Level 2 after passing FS Level 1, depending on the needs of the student.
Current mathematics GCSE strategies in Post-16 establishments

Since the change in the Condition of Funding, there has been a move by colleges to place students on the Functional Skills pathway but, due to the points allocation in the Government Performance Tables (see below), some colleges still prefer the GCSE pathway.

Points allocation for Level 2 Qualifications in Post-16 establishments

For many colleges the ‘stepping stone’ pathway can be difficult due to the differing demands of GCSE and Functional Skills, (such as the lack of algebra in Functional Skills). Sitting alongside this is the often referred quote that, ‘employers do not know about Functional Skills, or think it is an inferior qualification’. In 2015, a report from the ETF, (Making Maths and English work for all), found that nearly half of larger employers knew what Functional Skills were and their value, (around 90% of all employers found the qualification useful), so this is not the case.

As a result, college management teams should be working with the maths leadership to determine the best set of pathways for their student cohort, especially determining the core differences between GCSE and Functional Skills and, alongside this, work with local employers to determine their numeracy, (and literacy) demands. If local employers are aware of the differences between the qualifications, they can make better judgement of what qualifications are suitable for their employees.

A typical Functional Skills question will have far more extraneous cognitive load, (contextualisation) that will increase the effort needed to answer the question.

For a minute, let’s remind ourselves of the definition of mastery.

Mastering maths is the acquisition of a deep, long-term, secure and adaptable understanding of the subject

Thinking about a typical Functional Skills question, is this not just mastery of a mathematical skill?

Not only are unusual contexts a barrier to success, but also many students studying Functional Skills have low literacy skills, making the interpretation of questions more challenging, especially as many of these questions involve a higher reading age than equivalent GCSE questions. Obviously, those entering with a Grade 3 will still undertake the GCSE qualification, (as required by the condition of funding), but there should be the opportunity for any student to study the qualification they feel is appropriate to them and their prior attainment in both mathematics and literacy.

Recommendation 1: Colleges develop good quality advice and guidance for students, with regard to potential pathways for mathematics. This advice should include testimonials from employers, as well as precise descriptions of both GCSE and Functional Skills, (Recommendation 2 from MiFEC), to support employers in understanding the skills obtained from each qualification.

The success of this recommendation can be measured by the numbers of successful students, (using points progress measure currently used), as well as effective guidance, including to local employers, enabling both students and employers to make effective decisions about the type of qualification, (and improved numeracy), for future employment.

The CfEM projects include two distinct themes being investigated, Mastery and Contextualization, but surely, if true mastery is to be developed, then contextual problem solving is a key part of it. Currently, most maths teachers often create fabricated contexts in order to fulfill the problem solving aspect, which extend the extraneous cognitive load even further for many students.

Perhaps a solution is further integration between maths staff and vocational staff, as this would bring better contexts that have the right amount of extraneous cognitive load, enabling students to utilise their mathematical skills in problem solving that is relevant and known.

Recommendation 2: Mathematics departments and Vocational departments should be given CPD time to develop banks of contextual questions that have specific mathematical skills identified, so they can be used in mathematics classes, ‘Numeracy across the Curriculum’ for Colleges.

On the other hand, there is a requirement for all vocational courses to identify the mathematical skills within their courses. Identification of the key skills required is one thing, knowing how to teach it is another.

Recently a report into maths anxiety, (Disentangling the individual and contextual effects of math anxiety: A global perspective, 2021), showed that students’ perception of teacher confidence in mathematics is the strongest predictor of mathematical anxiety. Personal confidence in mathematics is a British cultural issue, (National Numeracy Research Review, 2020), and this is true within all levels of education in this country. One only has to walk around any educational setting to notice the anxiety from staff with regard to mathematical skill level, (how many times have you overheard a member of staff saying, ‘Maths is not my strong point’!!) and this explicit demonstration of mathematical anxiety can only be increasing anxiety of resit students. This high level of anxiety will pervade into lower student engagement and learning will not be effective. This will apply to any situation requiring mathematics skills, so it is vital that vocational tutors are confident in their own mathematical skills (beyond the level they are teaching).

In 2014, the UK government began the ‘Numeracy across the Curriculum’ programme, where schools had explicit training on developing cross-curricular links with mathematics. The focus of this programme was raising standards in numeracy by developing consistent practice and increased collaboration between departments. Again, the key missing part of the jigsaw is the explicit training of staff with their own mathematical skills; if you do not know correct vocabulary or supportive methods, then you will be anxious when asked to deliver this. A recent blog (Ten things your child’s maths teacher wants you to know), was published on CompleteMaths and was aimed at parental anxiety, but many of the points could be extended to vocational tutors as well.

Therefore, the increased collaboration should also lead to specific mathematical training for vocational tutors, who would improve their own personal mathematical confidence. This would mean students benefit from using appropriate contexts in problem solving in maths, but also receiving consistent teaching methods for mathematical skills.

Recommendation 3: ALL FE tutors should be entitled to high quality mathematics ‘refresher’ courses that will support the development of personal confidence, (MiFEC report, Recommendations, 9, 12 & 13 & RS General Mathematical Competencies  for T-Levels)

Alongside the focus on vocational tutor mathematical development, we must not forget the mathematics teachers themselves. We need to understand that the ‘C’ in CPD stands for continuous, so we should be regularly checking our own skills and our own teaching pedagogies to ensure we are supporting students learning in the most effective way. This means access to high quality training and support.

Recommendation 4: High quality training for mathematics teachers to develop mathematical pedagogies, as well as support with developing appropriate contexts for the backgrounds and vocational studies of students.

When investigating the number of hours allocated for Post-16 GCSE students, there is a lot of variation between colleges, but there is one thing they all have in common, there is not enough time to revisit the whole curriculum, (8 months, including holidays). Therefore it is vital that colleges use different methodologies for supporting all students. Currently, the CfEM centres are looking into online learning, as well as ideas such as flipped learning, (see here), but probably the most impactful method is the use of prerequisite assessments. For any effective, responsive teaching to take place, the teacher needs to know what the students’ knowledge base is, otherwise, they are ‘shooting in the dark’! Some CfEM centres are doing action research on these ideas and have written report about their findings. There were many positive findings from them, including improvement in student engagement and motivation, as they were getting regular successes, while sessions were more productive for learning.

Recommendation 5: Use of Online Learning Platforms for prerequisite assessment of learning needs and intervention sessions.

Many colleges already have high quality maths teaching, with high quality CPD, and many have a student focused qualification structure, underpinned by good understanding of the different specifications and the benefits for students. In addition, colleges are using online platforms so that students can access work remotely in their own time; this is especially useful, for many students who struggle to attend. It also means that personalised programmes of study are much easier to create, a key part of raising student engagement and attainment, but the proportion of students attaining a Level 2 pass is still low. Meanwhile across the every educational stage, numeracy across the curriculum programmes are being developed to try to make mathematics more relevant to students, yet still there are extremely high levels of student anxiety of mathematics and therefore low levels of engagement with the subject. Perhaps the biggest impact colleges could make is from improving personal mathematical confidence of vocational tutors as this could lead to a paradigm shift in attitudes for everyone involved, in turn, improving levels of numeracy for all students.

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