Chatting with some of my maths teacher colleagues over the weekend, the topic of how we remember being taught algebra came up.

Now before you click away or start snoring, it’s not what you think!

We began talking about the common responses we hear when we tell people that we’re maths teachers. And the most common by far is “I never understood algebra at school. I just don’t get what it’s for!” In case you’re wondering what the second most common response is, it’s “You must be smart!” We sure do appreciate that one 🙂

We then got to talking about how the link between arithmetic and algebra is perhaps not made as explicit as it could be and that it’s very unfortunate that people’s memories of mathematics class is that it was quite abstract and quite unnecessary. In fact, I wouldn’t be surprised if that memory alone is the one that looms largest in your mind and casts a shadow over your experiences now as a parent.

Inevitably your own children will wonder what the point of algebra is, and in case they don’t get a satisfactory answer from their teachers, it will be up to you to help them see algebra as the next necessary link in the chain as well as all the situations in “real life” where algebra plays a role.

To help prepare you for just this sort of scenario, let me take you through a few points on the power of algebra.

x is just a number

One of my colleagues, whose husband is not a maths teacher, has said to her on numerous occasions, “I never understood what x was all about.” Her response when telling us this story: “He can’t be serious! What doesn’t he understand that it’s just a number!” But that’s just it, most people have never seen the connection between algebra and arithmetic and therefore really never have seen that the letters (pronumerals) are in fact just standing in place for numbers.

Why do we need algebra when we already have numbers?. Think of numbers like a simple calculator, they’re great for a particular task at hand, calculating or representing a quantity. But what about when you need the power of a computer? Algebra is that power. It allows you to take problems and calculations beyond a singular case and extend it to many situations and scenarios, exploring the many solutions that will help solve the problem.

Algebra is all about patterns

To understand the systems and patterns that exist in our world and our universe we need algebra. Whether it is the naturally occurring patterns in the growth of a plant or the trend and cycles in the stock market, we need a strong set of structures and tools to analyse what we notice, and this is where the power of algebra comes in.

Studies show that humans are wired for tracking patterns and causal relationships, we have developed these skills in our evolution. Algebra is an extension of this evolutionary ability and those with a good grasp of algebraic thinking can analyse modern and complex patterns.

We use models to understand the world

We can all appreciate that the world and universe we live in is a complex place with many intermingling factors and forces at play. So how do scientists and researches even begin to understand it? They make and study simple models of our world and use them to learn about the way the various structures work. When I say they make models, sure sometimes they’re physical models, but more often they are mathematical models.

I’m sure you all fondly remember studying a diagram of an arched parabolic bridge that was modelled by a quadratic equation. While technically most bridges are catenary curves and not parabolic, either way their shape can be modelled using algebraic functions. What about understanding waves? Whether we’re talking ocean waves or waves of currents, we understand them by using algebraic modelling and trigonometric functions.

Describing algebra in this way might be very helpful next time one of your teenagers is complaining about having to solve yet another quadratic equation!

Algebra is a time machine

This idea might really catch on with the fans of science fiction in your household.

We use algebra and algebraic thinking to make predictions about the future and to analyse the scenarios of the past. The weather forecast each week and the predictions for the trend of the financial markets both rely on mathematical modelling and the important use of algebra.

Think about our understanding of the growth of technology. It’s funny to see video clips from the seventies predicting that people “in the future”, that is, around the year 2010, would have personal computers larger than washing machines in their homes. It’s funny because we see how wrong those predictions were. When we analyse why they were wrong we can see that the models used were more linear in nature, showing a slow and steady rate of the increase in technology. Looking back now we can see that in fact technology has been increasing exponentially, with an ever increasing rate of change, and this is important when predicting the sorts of technology we might employ in the future.

You need a strong foundation

One thing I found useful to explain to my teenage students when they were learning (and complaining about) algebra is that it is a foundational skill much like the foundational arithmetic skills they learned in primary school. The only difference this time is that their perspective has changed.

As I explain it to them, when they were younger they held more implicit trust in the adults around them and trusted that what they were being taught was useful and necessary. Thus although they may have found long multiplication difficult to learn, they were more accepting of their teacher’s explanation that this was an important foundational skill and tool.

Now that they are young adults, questioning relevance and motives is natural, normal and a necessary element of their development. So “because it’s part of the syllabus” is no longer a satisfactory answer. I tell them that algebra is the next level of foundational tools that they need to learn to be equipped for more advanced applications and studies in mathematics. I tell them that they are at the right stage in their cognitive development to deal with abstract skills and thinking and although they can’t see where this is leading yet, it will all come together for them in the next few years. It is similar to how they saw arithmetic; they drilled through the skills without necessarily seeing how powerful a tool it was until later in their development and studies.

This explanation makes a lot of sense to kids and they always appreciate someone engaging with their concerns rather than the usual reply of “because you have to!”

It’s the true international language

Although with the internet we are moving towards English becoming the international language, in reality the language of mathematics has always been and always will be the true international language.

Understanding algebra means you are able to communicate in the international language at an intermediate level, rather than just at a basic level. Those who are numerate and can communicate mathematically have a highly valued skill set in any society.

It’s the fuel for the most powerful mathematics

Some of the most powerful branches of mathematics require intensive algebraic skills and understanding. Calculus, a driving component in the understanding of physics, is built almost entirely on algebra, and without it, access to knowledge becomes limited. As I’ve always explained to students, the real difference between intermediate and advanced levels of mathematics is the degree of algebraic skills required. Just recently, when giving advice to some students I tutor on preparing for their examinations, I advised them to ensure they practise the more algebraic demanding questions as these are often those that separate students in different bands of achievement.

If your children want access to all levels of knowledge and understanding, then conquering algebraic skills and understanding is imperative.

I hope that these points have helped enlighten your own understanding of the role of algebra in raising mathematically confident children, and that next time the whining and complaining begins over some algebra homework you might feel better able to respond with a reasonable explanation.

Photo credit: Ludie Cochrane / Foter.com / CC BY-NC-SA