Christopher Upton is the Academic Director of Greene’s Tutorial College. He is a graduate of University College, Oxford and received his M.Sc. in Economics at Reading University. Christopher has worked with the World Bank and the IMF and continues to tutor students in Mathematics at Greene’s.
Numeracy is a vital skill in today’s world – calculating the cost of VAT, deciding how many tiles to buy for the kitchen floor, working out how much copper piping to buy for a new central heating system, submitting expenses at work, budgeting for the month; all are problems that we encounter in our everyday lives. The study of Mathematics helps you become agile, comfortable and confident when dealing with numbers.
Mathematics and the use of numbers are the language of business and much of science. Studying Mathematics also helps you with logical reasoning as well as exercising and developing your brain to handle more complex analytical problems.
For perhaps more than any other subject proficiency in Mathematics requires regular and persistent practice. Grasping mathematical concepts comes through practice – and lots of it! As you practice, your performance improves and your understanding grows. This is as true for basic arithmetic – remember those times tables – as it is for fluency with algebraic functions.
You start by applying the rules around a mathematical concept in a mechanical fashion; after a while – and some practice – you can follow the rules proficiently; and then – after some more practice – you can follow them automatically and fluently. With these foundations you can achieve mastery and understanding. Mathematics workshops provide an environment where you can practice with help when needed and – most importantly – to make the progression to mastery.
Dealing with numbers and algebraic logic is an abstract and a sophisticated activity for the human brain – similar to learning a language extremely well with all its cultural nuances, idiom and word. Learning a language, one’s mother tongue, takes many years and takes place imperceptibly as we talk, read and write as part of our daily lives. To learn Mathematics can take the same amount of time and effort but requires us to set aside the time to do so.
Of course, mastery of skills without understanding is shallow and skills can be quickly lost as soon as regular practice stops. Understanding mathematical concepts is important to long-term retention of numeracy and other mathematical skills. The questions are: What is the relationship between the mechanical application of rule based procedures and conceptual understanding? Can daily practice of mathematical skills, often completed without full conceptual understanding, help with conceptual understanding? Is a full understanding of mathematical concepts required to the successful use of mathematical tools and methods?
Regular practice of applying mathematical rules and methods creates foundations for procedural mastery of many mathematical operations and develops mathematical skills. Procedural mastery develops the ability to use various mathematical tools and methods to solve problems in daily life, business and science. Mastery of mathematical procedures also develops confidence and comfort with numerical problems and can then lead to the understanding of mathematical concepts. Hence: “Practice makes perfect”.
Celebrate World Math Day by competing with students around the world at www.worldmathsday.com.
Dr Keith Devlin, Executive Director of the Center for the Study of Language and Information at Stanford University – various publications
Dr Ryuta Kawashima, “Train Your Brain: 60 Days to a Better Brain”