My proposal for 21st century mathematics education in the UK, Europe and the world; encouragement for all following a re-evaluation of our objectives
Sep 28
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This article aims to put forward my proposal for mathematics education. Of course, I recognise the constraints in implementing change and that alternative viewpoints are available. It isn't entirely coherent, frankly I lack the time and energy to turn this into a presentable proposal - it is me exercising the ability to voice my thoughts. With this in mind, please feel free to contribute towards this topic or write to me at harry.cheetham@alzheimers.org.uk.
To establish my proposal, it may be helpful to begin with the facts surrounding Level 2 (GCSE) and Level 3 (AS and A Level) mathematics education in the UK. This will be followed by my perspectives on each stage of learning.
Level 2:
All teenagers in the UK must take GCSE Mathematics at age sixteen. The GCSE is graded from 1-9 (9 being the highest grade, passing at grade 4).
The GCSE in Mathematics is tiered, with the majority of teenagers in the UK entered into the foundation tier (capped at a grade 5, equivalent to a C). Roughly 57% of UK teenagers sit the foundation papers for GCSE Mathematics.
40% of all UK teenagers fail the GCSE Mathematics course (failing to achieve a grade 4 or above). This group is required to resit the exams (until age eighteen) to achieve a pass.
In my view, the proportion of students failing GCSE Mathematics is too high. It may be wise to consider the definition of failure; is it not a systemic failure when nearly half of all UK teenagers are deemed unable to achieve a passing grade, a requirement for progression to further and/or higher education?
Declaring children to be incapable, as a failing grade on a transcript dutifully provides, has a socially regressive impact on already disadvantaged groups. A failing grade will discourage disadvantaged groups from pursuing education, a practice so important for any society wishing to see progress - just ask Tony Blair. If the already underprivileged have been let down by the economic and political system, it is logical to expect that the education received by these groups will fall short of (in my opinion) the quality education afforded to those more fortunate. I believe that the UK has the resources to improve mathematics education, it is a matter of allocation and distribution. I suppose my argument boils down to addressing societal inequality.
So it is reasonable to ask, what am I complaining about other than societal inequality?
In my idealistic vision for the UK, GCSEs would be scrapped. No other major advanced economy runs high-stakes examinations at age sixteen. I find it anachronistic and a tool to preserve social status. Assessment follows years of classroom distractions and a curriculum seemingly devoid of real-world application. This results in a further loss of engagement with the educational system and allows for an anti-intellectual environment to take hold within schools.
The imposition of grading and assessment for qualifications at age sixteen gives rise to terror and stress for teachers. This allows for the quality of mathematics education to take a nosedive.
As a mathematics teacher in an average state school, most of the students you teach have little interest in the subject. You know that few will pursue mathematics at A Level. However, your students need to pass the GCSE course - a decision that was never theirs. Any pass is beneficial to the students and the school, satisfying metrics (namely Attainment 8 and Progress 8). Consequently, teaching must be targeted to improve exam performance. As a student, you probably don't care for mathematics and as a teacher, you are exhausted and (almost always) have financial commitments. It doesn't help that mathematics builds upon foundational knowledge and delving into the nature of the subject and its fallibility is not practical. This leaves those with gaps in their learning behind with little chance of recovery. I recognise that it is not feasible to stop at each topic and explain the reasoning behind a concept. As a student, if you want to achieve above a grade 6 at GCSE, you must take the information at face value. My position is that rote learning is a consequence of self-serving educational and economic policy aimed at improving exam scores. Frankly, the UK is not unique in this regard.
Level 3:
I will not mention many statistics. A Levels are optional and entering into them is done in the context of private school candidates rising from 7% at GCSE to over 18% at A Level. This excludes the consideration of grammar school students and private candidates.
I anticipate that most readers can discern that much of the above has relevance to my situation and life experience. As somebody who has taken GCSE Mathematics (achieving a bogus grade 9 through teacher assessed grading in 2021), AQA's Level 3 Certificate in Mathematical Studies (at grade A) and OCR'S (H240) Mathematics A Level (at grade C), I can assure you that without understanding the concepts there is little hope for pushing past a grade B at A Level. I say this as somebody who will have spent nearly two years studying AQA's (7357) A Level Mathematics qualification and finds the above scenario a reality.
Had I known that my mathematical ability was so poor, I would have never chosen the subject. There is a systemic issue when a student is led to believe that they are mathematically competent without understanding the distributive property until age seventeen. I should not have achieved a grade 9 in GCSE Mathematics.
A Level Mathematics can be bizarre. Understanding is required and also is not. This is likely by design, allowing for students with understanding to bag the top grades and for enough students to pass at grade B or C, provided enough engagement with the course. Are the concepts allowing for understanding emphasised and taught; for example, is there any mention of the central limit theorem by the DfE or why polynomials are differentiable? Is the link between Pascal's triangle and the choose formula ever explained? A student may question these concepts and struggle to build upon them in context when topics are blended together under exam conditions. Once you question the process you are doing, epistemology takes over - nothing really makes sense. A student without confidence is unable to perform well in exams, especially one where understanding is tested and tacitly given by stretching learning beyond the standard A Level. This allows those from more fortunate backgrounds and particularly students taking Further Mathematics to succeed at A Level Mathematics, with the difficulty examiners place in assessed questions rising to compensate for their superior ability. Who loses from this situation?
The grade boundaries function in such a way that thirteen to fifteen marks is the difference between each grade. Often, this represents all the marks available for several parts of a high-tariff question. Put simply, if you cannot grasp a single question (based around a core topic, e.g. integration), you miss out on a grade. This is because the following parts of the question are only able to be answered with either a correct/completed answer from the previous part of the question. Consequently, those unable to understand a topic (perhaps due to a misconception or unanswered query) are punished. Resits occur a full calendar year later.
The A Level in Mathematics is not equal to other A Levels, plain and simple. Its difficulty is far beyond A Level Geography and A Level Economics for instance, my other subject choices. Mathematics requires reasoning and understanding, frustratingly neglected by the A Level. Choosing A Level Mathematics as a student with a burning desire to understand and rectify the gaps in knowledge left by the state sector through doubtful/critical thinking, de omnibus dubitandum, is an excellent way to drive yourself insane. This is my position.
PROPOSAL:
For the UK:
The country can allow for relevant and constructive discourse to take place regarding its approach to mathematics education. I am no expert. Decision-making will ultimately be by those in power. The inequality in mathematics education was exacerbated by Michael Gove's reform and the COVID-19 pandemic, on top of an already punitive system. The country has enough resources across the remnants of its empire to allow more to succeed; the issue is political and economic. Perhaps more importantly, we should start challenging the prevailing view of success. The above contains several questions, with many intended as rhetorical - but they should be answered.
For Europe and the world:
Remove grading or introduce a binary awarding system. Either you pass or fail; the student knows enough to be deemed competent in mathematics at a certain level or does not. No summary of marks - the diploma is awarded due to merit. The ability to appeal or repeat the process to attain the diploma must exist and be available to all.
Assessment to inform the decision on whether a student passes or fails should be carried out through various methods (in exam halls, in class and during sessions with professionals). Weighting can vary and reflect circumstances in society.
Eliminate the discrepancies between exam boards through discouraging the privatisation of education. Ideally there would be one body responsible for awarding the diploma in mathematics. This enforces a set standard and allows for teaching material to be shared - collaboration between all is crucial. Standardisation has many benefits.
To ensure mathematics remains accessible, explicitly state learning outcomes and clarify whether understanding of a certain topic/concept is expected. A vague mention of understanding in specification documents and official board material is unacceptable.
The diploma in mathematics could be learnt/have learning aided through an official online course that would allow the average student to understand the content well enough that they succeed in gaining the qualification/diploma in mathematics. This could support those from less fortunate backgrounds often having to direct their own learning.
The diploma for mathematics would involve international collaboration and be recognised as equivalent in all countries wishing to reap the benefits of a common qualification. Ideally, EU member states would agree on a qualification of this nature (different to the IB etc.), with implementation across the bloc, paving the way for a truly global mathematics diploma.
Encouragement of students must be present through recognising the shortcomings of mathematics, its history and philosophy. Identifying where a student cannot understand a concept will allow for educational professionals to target care towards the student and acknowledge alternative conceptions/misconceptions. The
constraint on resources is the barrier to ever seeing this approach come to light.
I admit that I do not know enough about economics and role allocation in society, however, at the very least we should direct policy towards a more rewarding system leading to a population with an improved understanding/appreciation of mathematics. This is certainly attainable.
I believe that a global mathematics diploma would support international development partly through a renewal of standardisation (in terms of conceptual understanding and teaching/learning material). I mention a re-evaluation of objectives in the title of this piece and I cannot think of a better metric of success than enabling more people to live healthier and happier lives.
This is my proposal. It is not the best, however, I stand by my values and will push for change.
H. CHEETHAM