The development of mathematics has always gone hand in hand with the development of civilisation itself. Mathematics surrounds us and underpins so many aspects of our daily lives, such as architecture, art, music, money and engineering. And while it is creative and beautiful, both in its own right and in its applications, it is also essential for progress in other areas of learning and experience, not least in Science and Technology, which would be virtually impossible without it. What is more, numeracy – the use of mathematics to solve problems in real-world contexts – is required in almost all areas of life.
Formal mathematics is founded on basic truths and develops through rigorous logical reasoning. It involves inventing or discovering abstract objects and establishing the relationships between them. It also teaches us the difference between conjecture, likelihood and proof.
Mathematical thinking involves applying similarly logical reasoning, this time to the investigation of relations within and between concepts, along with justifying and proving findings. Indeed, understanding mathematical concepts and being able to apply and reason with the abstract representations of concepts is central to learning mathematics. And essential to this is comprehension of, and proficiency with, the symbols and symbol systems used in mathematics.
Applying mathematics requires strategic competence in the use of abstraction and modelling, and learners also develop resilience, as well as a sense of achievement and enjoyment, as they overcome the challenges involved. Subsequently, mathematical activities teach learners not to be afraid of unfamiliar or complex problems, as they can be reduced to a succession of simpler problems and, eventually, to basic computations. And as they reflect on the approaches used, and on their own mathematics and numeracy learning, learners develop metacognitive skills which help them know which steps to take to improve performance. Thus they become ambitious, capable learners, ready to learn throughout their lives.
Mathematics also contributes to developing enterprising, creative contributors, ready to play a full part in life and work. It encourages learners to be creative because it requires them to play, experiment, take risks and be flexible in tackling mathematical problems. Because mathematics is essentially abstract, it teaches learners to operate with objects that do not physically exist, using and developing their creativity to imagine and discover new realities. It also supports numerical modelling and forecasting to encourage entrepreneurial thinking.
Mathematics promotes ethical, informed citizens of Wales and the world by providing learners with tools to analyse data critically, enabling them to develop informed views on social, political, economic and environmental issues. It encourages clarity of thinking, allowing learners to understand and make reasoned decisions.
In mathematics and numeracy, learners encounter contexts involving health and personal finance, and develop the skills needed to manage their own finances, make informed decisions and become critical consumers. They learn to interpret information and data to assess risk, and they use their numeracy skills across the curriculum to make effective choices, becoming healthy, confident individuals, ready to lead fulfilling lives as valued members of society.