Maths teaching in schools has evolved greatly over the last two centuries.
While there will always be room for further improvement, great advances have been made in methods to bring maths into the everyday lives of all pupils.
Here's a look at the recent history of maths tuition, to understand how we go to where we are today.
Learning Maths in the 19th Century
The 19th century began with the waning of the Church’s power over education and schooling in the UK. The Education (Scotland) Act of 1872 transferred to secular bodies the work of administering education, formally bringing an end to the Church’s role as the custodian of learning.
The new bodies set about on the mission of eradicating illiteracy in towns and cities, which was due in large part to the mass migration of rural workers to meet the labour needs of the industrial revolution.
A basic understanding of maths was, even by this time, seen as a necessary prerequisite of modern life, and few schools excluded the subject from its timetables.
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Johann Heinrich Pestalozzi's 1803 publications influenced widespread reforms on maths teaching, including children starting to learn maths as soon as they entered school, a focus on physical objects and perception, and the prominence of maths as one of the most important school subjects. Contemporary reforms of the rules governing algebra made that discipline easier to learn.
It wasn’t until 1833 that the British state itself became directly involved education, nationwide. At this time, funding was first allocated to the building of schools for poor children. The Elementary Education Act of 1880 signaled the start of compulsory education for all children, between the ages of 5 and 10 years.
The leaving age was raised in 1918, by the Fisher Education, to 14, and to age 15 in 1944 by the Education Act.
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Maths Education since the 1960s
The Joint Mathematical Council was formed in 1963 to standardise and improve the teaching of mathematics in UK schools
Before calculators, most calculations were done by hand, with slide rules and log tables.
Decimal Day, on 15 February 1971, did away with the lengthy calculations necessary under the Imperial system of weights and measures, and saw a reduction in the amount of time allotted to numerical calculations in schools.
The appearance of affordable, portable electronic calculators in the 1980s was initially met with concern that students would decline in mental arithmetic skills; however, they eventually became a required accessory for every student. The appearance of scientific calculators makes complex functions, including logarithms and trigonometry, possible for every student.
Essential to an education in maths is a good grounding in the vocabulary of mathematics.
Psychology’s Role in Mathematics and Science Education
The field of psychology has played a vital role in forming and improving maths and science education the world over. A 2007 report published in the United States by a panel of scientific experts reviewed decades of research in areas including developmental psychology, cognitive science and educational research and assessment, to explain this relationship.
The report also highlights how advances in understanding basic maths and science, as well as advances in research into social issues and motivation shed light on possible new approaches to improve classroom practice.
The four main areas where psychology is thought to have significantly improved early mathematics and science education are:
Early conceptual understanding of mathematics:
Research has shown that the kind of maths input that children are exposed to during preschool plays a key role in determining early individual differences in maths competence, demonstrated at school.
Children from families of lower socioeconomic status are frequently exposed to less maths in their early years, which may in part explain the achievement gap seen at school.
Conceptual understanding of science:
The language of science is confusingly similar to everyday language: Everyday words often have completely different meanings in mathematics and science, which may be a source of difficulty for students.
Linguistic psychology may be able to highlight areas in which prior knowledge causes confusion in this way.
Social and motivational involvement in mathematics and science:
A variety of social and motivational factors, including gender and race identity stereotypes, have been shown through decades of research to be linked to academic achievement, with a knock-on effect on aspirations.
It is still true, for example, that by far the majority of students undertaking maths degrees at universities are male.
A student’s intrinsic motivation – their inner drive to complete a task – can be developed by applying teaching strategies which tap into the child’s natural curiosity about the world and how things work.
Assessment of learning in mathematics and science:
Effective testing is aligned with an effective curriculum that focuses on understanding the nature of science and maths.
Technology-enhanced instruction can be used to provide detailed information on how students are learning and what problems stand in their way of progress.
Time for Reform?
The UK was ranked 27th for maths in the most recent worldwide PISA ranking: Its lowest place since first participating in the scheme.
But are ranking positions a sensible goal for education?
If the goal of education is to prepare the next generation to take their place in the world, then how about shifting focus to relevance, instead of rankings?
According to a 2014 Guardian article, the problem with maths education lies in;
“the […] difference between maths in education and maths in the real world: everywhere, we are teaching largely the wrong maths […]. In the real world we use computers for calculating, almost universally; in education we use people for calculating, almost universally.”
At a time when maths, in the form of IT; telecommunications; artificial intelligence; automation and more are increasingly responsible for running the background processes of daily life, maths education still places an emphasis on laboriously practising skills that have long since become mechanised and delegated to computers, in the real world.
Students lack exposure to real world maths problems, in favour of simplified ‘toy’ problems. While real problems are messier and more complicated, they can be handled by using computers to deal with the calculations.
This current approach leads to students forming the impression that maths is irrelevant to their lives, when in fact the opposite is true, and increasingly so.
There is a growing divide between the maths that students are faced with in school, and real-life needs. The mathematical demands of the real world are increasingly complex, but our educational systems are taking the wrong direction in closing the gap.
We should ditch the rote learning of mental maths calculations, and get students to tackle real world examples, using the power of computing and calculus. Examining statistics, cracking cyphers or redesigning public transport systems would show students the creativity, lateral thinking and conceptual understanding needed to solve complex problems from the real world – with the power of computer calculations.
The UK has recently joined the small club of countries in which coding is part of the school educational system. Coding is the language of computers and a necessary step towards solving complex calculations and mathematics.
Estonia was the first country to push coding in schools and to implement a computer-based educational system for the teaching of maths. It’s also the top-ranked country in Europe in the PISA rankings.
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What will Tomorrow's Maths Tuition look like?
Ideally, maths instruction will become more connected to real life, and take into consideration students from all backgrounds.
Here are some of the challenges that need to be addressed in order for quality mathematics education to be available to all:
- Make demonstrations, for example in geometry, more accessible to the majority of students.
- Make exercises relevant to real-life situations, to combat the perception that mathematics is divorced from and irrelevant to everyday life.
- Allow for differences within the same class (students who struggle and those who find maths easy) while building on a common core of mathematics.
- Empower teachers to tailor their courses to their students' needs through customised exercises.
- Place an emphasis on the relevance of maths to careers following higher education.
How maths is taught is constantly evolving. Many teachers agree that this evolution is a positive phenomenon, whether through the influence of scientific subjects, artistic subjects the definition of a common core for classes to follow.
An objective for maths teaching in years to come should be a reduction in the number of students failing the subject due to the pressure of over-demanding instruction.
What will the 21st-century hold by way of changes in the way maths is taught?