Introduction – What is Algebra?

Introduction – What is Algebra?

I remember clearly at the age of 11, my first day in secondary school, going home to ask my dad “What is this x² all about, dad?” and getting the reply “Son you are on your own!” At that point I can also remember thinking the next 5 years is going to be really hard work, and that was my perception as someone who enjoyed mathematics. Nevertheless, the teacher by the end of that first year had the class confidently reproducing the proof of the quadratic formula for solving a quadratic equation.

So, why do so many people have such a loathing, fear or lack of understanding of algebra? Is it the way it is taught? Is it introduced far to early before the learner is emotionally, conceptually ready or is it public and family perceptions of their learning experiences, or simply the perceived lack of relevance that algebra has to everyday life? Probably a combination of all these factors and many, many more.

So, what is algebra? Is algebra just letters that stand for numbers or Is it a new language? It is interesting when talking with a group of secondary school mathematics trainee teachers that they often have real difficulties explaining to other mathematicians in as simple as way as possible what algebra is. This is really important as the next generation of mathematics teachers should have the facility to clearly communicate their subject and knowledge.

Algebra is nothing more that generalised arithmetic, that is, an extension of numbers, patterns and the operations that can be performed on numbers.