How to Kill Number Sense in One Easy Move: Teach the Algorithm!

Have you ever heard or said these things in a maths class?

“6 take away 7, can’t do…so go next door and borrow a ten…”??

“8 add 3 is 11, so carry the one…”??

“…put in the magic zero…”??

“Divide, multiply, subtract, bring down…”

I know I’ve used all of them during my time as a primary educator. These are phrases we say when following a process we don’t truly understand. The algorithms for the four basic operations were developed when people themselves acted as the "computers." They offered a universal way to reach an answer in times when calculators and smartphones weren’t an option. But times have changed—and so has what we value in learners.

A growing body of research tells us that these beloved algorithms, ingrained in traditional mathematics curricula and held dear by many parents, are actually holding our students back. As Dr. Jo Boaler says, “the algorithm kills number sense.”?

Why This Matters

Those who excel in mathematics share a critical trait: a well-developed number sense. Number sense is an intuitive grasp of numbers and their relationships. It’s what allows someone to approximate quickly, recognise patterns, and use mental maths flexibly. Research shows that students with strong number sense are confident, adaptable problem-solvers. They don’t see numbers as fixed symbols to manipulate by rote but as tools that can bend, shift, and adjust according to need.

Children taught strictly through algorithms often begin to believe there is only one correct way to solve a problem. Personally, I remember how startled I was as a child when my brother showed me "another way" to solve a problem. “I’m not allowed to do that,” I thought, “I have to use the method my teacher taught me!” This rigid approach became a barrier, reinforcing a world of meaningless procedures where I struggled.

For example, let’s look at this equation:

32 + 65 = ?? + 30

As a child (and probably as an adult), I’d have solved it in two steps: 32 + 65 = 97, then 97 - 30 = 67. But my brother would have seen it differently. “32 is two more than 30, so I took 2 from 32 to make 67.” That’s number sense.

Why We Cling to Algorithms

Many teachers and parents hold tight to the algorithm, perhaps out of tradition, but there’s a sense of security in right-or-wrong answers. They serve as quick measures of progress, giving students (and teachers) clear-cut feedback. However, relying on algorithms also limits a child’s ability to explore maths in meaningful ways. If we were to ask parents what kind of thinker they’d want to hire at their place of work, would they choose someone who follows procedure exactly or someone who sees patterns and adapts flexibly?

So, I leave you with this question: In a world where creative problem-solving is essential, what place does the algorithm hold today? And how can we begin shifting the love for algorithms towards a love for numbers?