Mental Computation – It’s Not About Rote Learning
Rob Vingerhoets
June 2025
Let’s set the record straight: mental computation is not about automatic response or being able recall multiplication facts faster than your peers. It’s far more than that. Mental computation is about number sense—knowing how numbers work and applying efficient (not necessarily fast) strategies to solve problems mentally.
Rote learning times tables, in isolation, is of little real value. As educators, our goal should not be to produce students who can regurgitate a narrow band of maths facts, but rather develop mathematical thinkers—students who can apply known strategies such as place value, doubling and halving, the distributive property, the commutative property, compatibility, and compensation.
Consider this: if a student knows that six sevens are 42, but has no mental picture of what 42 means—they don’t visualise it as an array, as six weeks, as double 21, or half of 84—then the fact is just that: a fact with no substance. It’s meaningless unless it’s connected to deeper understanding.
Compare two students:
One quickly recalls that 6 × 7 = 42 because they memorised it.
Another thinks, “Break the 7 into 5 and 2. Six 5s is 30. Six 2s is 12. Add them—30 + 12 = 42.”
The first student wins on speed. But the second student wins on mathematical understanding. They’ve used the distributive property, doubling, place value, and logical reasoning. As a teacher, I’ll take understanding over speed any day.
Unfortunately, in many classrooms, speed is still rewarded. Fast students stay standing in maths games; slower students sit out. Fast recall gets praise, while thoughtful processing is seen as slow or weak. That mindset is all wrong. It’s not about how fast you get the answer—it’s about how well you got there.
I often return to this quote from Jo Boaler’s Mathematical Mindsets (2016):
“Math facts by themselves are a small part of mathematics, and they are best learned through the use of numbers in different ways and situations. Unfortunately, many classrooms focus on math facts in isolation, giving students the impression that math facts are the essence of mathematics, and, even worse, that mastering the fast recall of math facts is what it means to be a mathematics student. Both of these ideas are wrong, and it is critical that we remove them from classrooms, as they play a key role in creating math-anxious and disaffected students.”
The Takeaway for Teachers:
Prioritise number sense and strategy over speed.
Teach students to visualise numbers and build meaning.
Celebrate efficient thinking, even when it takes time.
Avoid overemphasis on rote recall and speed-based competition.
We don’t need fast fact robots—we need deep thinkers who understand how numbers work and can apply that understanding flexibly and confidently.
