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Mathematics, Further Mathematics and even Further Mathematics…

Posted: 3rd June 2020

Principal Cardiff Sixth Form College, Gareth Collier, talks about the relevance of mathematics in today’s society.

For those that know me well, the irony of me writing about mathematics will not be lost on them. As someone, who, at the age of 15 was written off by the mathematics teachers in my school, and told not to bother with taking an ‘O Level’ but to enter for a ‘CSE’ instead (more of that later), I understand the challenges faced by so-called ‘non-mathematicians’ to the study of this seemingly complex and unfathomable subject. However, I have come to learn that it is an essential part of everybody’s education and is often most needed by those that least enjoy it.

Whether you subscribe to the ideas of Richard Courant (German/American Mathematician) or not, when he says, “Mathematics as an expression of the human mind reflects the active will, the contemplative reason, and the desire for aesthetic perfection. Its basic elements are logic and intuition, analysis and construction, generality and individuality”, it is clear that it is more than just numbers and calculation to many.

It’s relevance to university applications for students interested in science, technology, engineering and mathematics (STEM) is cemented in the entry requirements set down by these very institutions. Becoming an engineer without an A Level in mathematics is almost impossible and without further mathematics, far less likely than with it. One of the three most commonly studied subjects for all healthcare courses including medicine is mathematics and in the now unpopular list of nine ‘facilitating subjects’, mathematics and further mathematics are listed separately, giving even greater importance to the subject. Katherine Johnson (African-American mathematician) says, “we will always have STEM with us. Some things will drop out of the public eye and go away, but there will always be science, engineering, and technology. And there will always, always be mathematics.”

However, what about the study of subjects like law and humanities? How is mathematics relevant to the study of these? According to ‘Superprof’ “mathematics is an application of matter and contributes to all of our methodical and systematic behaviours. It is mathematics, for instance, that has brought order to the communities across this planet and prevented chaos and catastrophes. Many of our inherited human qualities are nurtured and developed by mathematic theories, like our spatial awareness, our problem-solving skills, our power to reason (which involves calculated thinking) and even our creativity and communication.” So, mathematics helps us think analytically and have better reasoning abilities. Reasoning is our ability to think logically about a situation. Analytical and reasoning skills are essential because they help us solve problems and look for solutions. All vital skills for anyone wishing to construct or rebuff an argument, or someone wishing to understand logical connections between societies and issues. And a reason perhaps, why university admissions departments value so highly, mathematics as an A level for all undergraduate admissions.

The Dukes Education Colleges all invest heavily in the delivery of excellent mathematical education. Earlscliffe is justifiably proud of its historic performance with many students progressing to top universities on the back of impressive A Level achievement in mathematics and further mathematics; Rochester Independent College can number amongst its graduating students, scholars at Imperial College London and Cambridge University, studying engineering and mathematics due to the excellent tuition provided by highly qualified and expert practitioners; Fine Arts College, renowned for excellence in the fields of creative and performing arts notes and fosters the elusive but common link between mathematical achievement and musical creativity; and Cardiff Sixth Form College, founded on a successful basis of STEM education where, mathematics, further mathematics, MAT and STEP tuition is included as a core part of the curriculum.

Cardiff Sixth Form College has a total of twelve highly experienced and accomplished teachers of mathematics, with specialisms across the range of mathematical topics required for A Level study. However, in the area of STEP and MAT tuition, the presence of possibly the ‘world leading academic’ in this field for the delivery of teaching and learning to pre-university level is Mr Huw Kilner. His book on STEP mathematics is widely regarded as the most up to date and comprehensive tome on the subject currently available.

STEP mathematics is a well-established mathematics examination designed to test candidates on questions that are similar in style to undergraduate mathematics and is administered by the Cambridge University Assessment team.

Huw sees mathematics as essentially a tool for problem solving and reflective learning. His approach leans heavily on the work of John Dewey, American philosopher, psychologist, and educational reformer and the later refinements by Donald Schön a philosopher, lecturer and business consultant who became the Ford Professor of Urban Studies and Education at Massachusetts Institute of Technology.

He uses Dewey’s words in analysing Reflective Learning in Mathematics is an “active, persistent and careful consideration of”

1.           how we solved a problem,

2.           why we did what we did,

3.           how we might do it differently or do it better,

4.           what other parts of our learning it connects with,

5.           and what other parts of Mathematics it leads to.

He then goes on to say, “I believe that reflection in Mathematics is invaluable for consolidating learning as you go along and that it leads to greater depth of learning and an acceleration in learning when practiced over an extended period of time.  My belief is based on actual evidence of how students in my classes at Cardiff Sixth Form College have benefitted from this practice.”

This then applies to and benefits, not only the mathematics studied but also the students’ approach to their studies in other subjects. An essential value of mathematics teaching beyond the confines of the mathematics syllabus. A case perhaps for the development of another A Level subject of ‘Even Further Mathematics’!

And so back to the beginning. For those old enough to remember CSE’s and O Levels, I can confirm that I refused to accept the damning indictment of my teachers and entered for the O Level, got an A grade and resolved never to allow my performance to lead to the possibility of a similar statement or judgement in the future. I also resolved to champion excellent teaching wherever I could find it and in Huw Kilner and the rest of the mathematics teachers across Cardiff Sixth Form College and the wider group of Dukes Colleges, I am comfortable in singing their praises.

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