How to Factor the ‘Real World’ into the Mathematics Teaching Equation

A mathematics teacher I once worked with shared a story about running into a former student.

This particular student had been that kid, for want of a better way to put it. You know the type: disengaged, occasionally disruptive, and ready to answer back to any suggestion of work with the timeless classic, “I’ll never use this stuff anyway.”

But here he was some ten years later. And the first thing he told his former teacher?

I finally get why all that stuff was important.

Why?

He hadn’t gone on to become an engineer, nuclear physicist, or principal architect of the hadron collider. Matter of fact, he never ended up finishing high school. He studied a trade instead.

Yet he was using mathematics every single day of his working life. Geometry, angles, and sophisticated measurements were his bread and butter.

He was a crane operator.

As gratifying as this story is for a mathematics teacher, it also lays bare one of the hardest parts of teaching the subject. No one could have told this student at thirteen years old that Euclidean geometry would become a pivotal part of his career. As far as he was concerned, ‘mathematics’ was just a series of inky blots on paper, completely divorced from the real world.

For many of our students, the light-bulb moment in which they realize that there is, in fact, mathematics in the real world comes after school. It comes with all the necessary components of adult life that require basic numerical fluency; taxes, personal finance, buying or selling things, putting IKEA furniture together with increasing impatience – the list goes on.

But what if we could make that light-bulb moment happen in our classrooms?

Can we teach mathematics for the real world right from the very beginning?

It’s not always easy, but it can be done. And with it comes greater engagement and a renewed commitment to learning.

Let’s take a look at some strategies you can use to bring mathematics off the page and into the real world.

Before you decide to change the entirety of mathematics education in the space of a single lesson, get your students to do some of the work.

It’s easy for students to default to the ‘We Will Never Use This in the Real World’ mindset when they’re having trouble with mathematics, or when they’re simply not up to learning on a particular day. They shouldn’t get off that easily though.

Have they ever actually looked for mathematics in the real world?

Have you ever asked them to find mathematics in the real world?

Chances are the answer to both questions is no.

Often, our first response to accusations of irrelevance is to rally our defenses and start getting a bit too passionate. (‘It’s relevant, I SWEAR. YOU’LL THANK ME ONE DAY!’).

But the discovery of mathematics in the real world is so much more powerful if it comes from the students themselves. So don’t feel as if you automatically have to justify the existence of the mathematics as a subject. Put it back on your students instead.

Try challenging them to find three things they have done at home that involve mathematics of any kind, and then to share these with the rest of the class as a weekly activity. Students will come to realize that the real world connectivity of mathematics is truly limitless.

Of course, you have a part to play in this too. You might also try to…

You might succeed in getting students to realize that they are already doing mathematics outside of the classroom, but the next step is to prove to them that there are other effective ways of using mathematics for your own benefit in everyday life.

The simplest example is a timetable. Between music lessons, sport, homework, play dates, family commitments and so on, kids these days manage out-of-school lives so complex that they basically need a full-time PA (unfortunately that’s just another part of a 21st century Mum’s job description).

Have students timetable their before and after school activities, and you get them actively using division for a real life purpose. Naturally, this also teaches them a thing or two about time management.

The list of potential applications only continues to grow as students get older. For example, a personal budget or basic financial plan is an invaluable asset as more and more of our students come to us with bank accounts, part-time jobs, and mobile phone plans.

Putting together something that students can actually use highlights that math isn’t just ‘out there’, only occasionally surfacing when we need to count up some loose change. Instead, mathematics is something students can actively engage with in order to live better lives.

Homework is the perfect opportunity to teach mathematics for the real world. After all, students are literally using mathematical reasoning outside of school hours and in a non-classroom environment. At last, they’re in the ‘real world’.

Yet we often persist in setting homework that is really just a continuation of classroom activity. Finish off the worksheet, complete the review questions in the textbook, move onto the next chapter… you get the idea.

Why not take advantage of the home environment by getting students to engage with the mathematical concepts that make a home function? Here are a few ideas:

• Budget for the week’s grocery shopping. The fact that most supermarkets have a full online catalogue makes this so much easier because it can be fully planned out with as much time as necessary. And it can’t be all candy either. A few parent-specified items on the list will force them to accommodate mandatory costs.
• Cook to a recipe. The perfect opportunity to practice measurement with a real, edible incentive. This one has the added bonus of winning over parents too!
• Simply counting items around the house is a super easy strategy in the younger years that gets them to see the numerical properties of the physical environment. As they get older, you could set more complex activities – such as a fantasy bedroom renovation to scale.

Take advantage of the home environment wherever possible. The added benefit is that these activities get parents and families involved, so that mathematics becomes a collaborative real world activity, as opposed to a solitary one.

It’s not hard to understand why students perceive mathematics to be in a world of its own. It uses an entirely different language to other subjects and requires its own methods of problem solving and reasoning.

If we link mathematics to other subjects in the curriculum, we show our students that mathematics doesn’t stand alone. It’s part of an integrated system of knowledge that helps us to understand the world.

I once observed a mathematics teacher and an English teacher team-teach a lesson on picture books. Student minds were blown when they saw them in the same classroom, but their respective teaching points came together in a way that no one would have predicted (including myself).

The mathematics teacher first got the students to analyze the composition of the pictures in the book. Students overlaid the images with a grid and used this to discuss the way certain objects were given primacy over others, and how one’s eye would be drawn to specific features for emphasis.

The English teacher then used this to springboard into a discussion of students’ emotive and critical responses to the pictures, which then informed an interpretation of the accompanying text.

It was nothing short of genius. Students’ interpretations of the text were so much richer with the input of both subjects, and they left the class having seen that math wasn’t just a series of cold, hard rules governing an abstract world.

Mathematics had actually made them think and feel. Is there anything more ‘real world’ than that?

Use your colleagues outside the mathematics department. Yes, cross-curricular collaboration takes time and coordination that are often in short supply, but the rewards are worth it.

Last but not least, it’s worth taking a step away from the textbook and into real life during your actual content-centered teaching.

Instead of explaining a concept in the abstract, you can link it back to any number of the countless real world phenomena that revolve around mathematics in one way or another. Word problems and research activities can do the trick, but you might up the game by using a physical, tangible real life resource in (or out of) the classroom.

Let’s say you’re teaching patterns. Chances are that somewhere in the school there is a pattern in the built environment. It might be a tessellated floor, the pavers outside, or even just a brick wall. Instead of working off a photocopied, you can use this as an authentic resource. You could have students:

• Continue the pattern, either on paper or maybe using hands-on material.
• Describe it to a partner who has not seen it, who can then try to replicate it according to their instructions.
• Use chalk or an erasable marker to identify other familiar shapes within the pattern.

You might be thinking that the same activity could just be replicated on a worksheet in order to remove the logistical hassles, but this wouldn’t give you the opportunity to delve into the real world applications of the mathematical theory.

So in the above example, you need not stop once students are able to identify and explain a pattern. The next question you could ask (if they don’t ask you first) is:

Why might a builder choose this pattern?

And then off the back of this discussion:

So, why do you think it is important for us to know about patterns?

The ability to think independently and with curiosity is one of the in-demand mathematics soft skills is increasingly being expected to develop in students. Using this approach well and truly works to this effect. It reveals that, more often than not, you don’t actually need to spell out the real world relevance of mathematics for students. You just have to lead them to it.