We’ve all heard it before. Fractions, long division, scatter plots, y=mx+b, finding angles of parallelograms, HCF & LCM… “But when am I going to *use* this?”

We all know that one of the most powerful ways we can internalize a learning topic is when we attach a real meaning to it, when it’s something that we care about, in any form.

As we’ve explored, meaning can come in all kinds of forms. Meaning can be an abstract form of usefulness, a robust three-dimensional understanding, along with sufficient practice, of when that concept comes in handy. Meaning can also be a sense of connection with another concept that we’ve really nailed down. You may not really need to know that regrouping in subtraction is also known as borrowing, but if your teacher explains it like burrowing into a neighbour’s house to “steal a cup of sugar,” you might never forget it.

With all that said, there is another wonderful layer of meaning that we can spread right onto our hot mathematic toast, and we should try to do so regularly.

#### Usefulness and Application

We’ve discussed how word problems can be a powerful tool in showcasing a concept’s many dimensions. Word problems are also a great way for teachers to connect what the class is learning to real-world applications to help students understand the usefulness in everyday life.

Now, word problems sometimes get a bad rap for this. How often am I *really* going to need to calculate how high Jimmy’s kite is going to go based on the wind speed and how fast Jimmy runs? However, if we’re clever about it, we can make great use of verbal application.

One of the best ways a teacher can introduce real-world application right from the get-go is to use intuitive analogies when the concept is first being explained. One of my personal favourites is referencing money (dollars and cents) when decimals are being taught. Students often have a good intuition of what twenty-five cents is relative to a dollar. It’s a much smaller leap from there to showing that this is 0.25 in decimal form, and then introducing what it means to have a third decimal place, such as 0.253.

In fact, my lessons on converting decimals to fractions to percents, or dividing decimals, are often chock-full of references to money and test scores. When explaining the importance of simplifying fractions, I often explain to students that “it’s much easier to understand that one-third of your grade wears glasses than to try to grasp that 145/435 students in your grade are bespectacled”.

These are not always formal word problems, but real-life analogies that help to anchor in not only an intuitive understanding of a concept, but a graspable usefulness associated with it. Wherever possible, teachers can help their students to *see* where the math they’re learning fits into their everyday lives. Higher-level teachers can make use of research projects and investigative questions that need to use math as a means to an insight, a conclusion, or another end.

#### Careers and Future

Students are often told, “You’ll need this in the next grade.” “You’ll need this in high school.” “You’ll need this to get into university.” They go through their education with a vague notion of “someday this will be useful,” or seeing the math they’re learning as nothing but a means to get to the next level of math to learn. It’s often difficult for teachers to communicate how math can set them up on a path towards the actual work they want to be doing or the actual futures they want to create for themselves.

We can show our students how the arithmetic they’re learning is extremely useful for basic functioning, how strong mathematical intuition can help them with creative projects, work in the trades, or project management. Working with functions and graphs underlies any sort of career in a predictive or modelling field, such as actuarial science, public health, or economics. Pattern recognition is crucial for understanding how algorithms work, which has applications in computer programming, video game design, special effects, and artificial intelligence.

Along with research projects, case studies can be a great way to engage with math on a practical level. This could be retrospective analysis, investigating how organizations in the past have come up with creative math-based solutions to problems, or they can be prospective, where students are faced with a complex scenario and come up with their own solutions. As a side benefit, case projects often give students the chance to develop interpersonal professional skills. Math is often seen as a solo subject, but group projects of this nature can highlight the collaborative potential.

#### Meaning in Math

While this is all a little bit high-level, the goal is, wherever possible, to provide an intrinsic motivation for students to learn and maintain their math skills by attaching value to them. What we value, we invest in, and what we invest in, we internalize. What we internalize, we truly use and appreciate.

We don’t want to create memorizers; we want to create thinkers, creators, and analyzers. In doing so, we’ll help our students create their futures, and they will in turn help us to create our future on this planet as a whole.

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