One problem causes a ton of issues when students learn numbers

September 12, 2022

It’s hard to comprehend just how mind-bending the place value system must have been to Europeans when Fibonacci imported it from India and the Middle East in the early 13th Century. Imagine trying to multiply Roman numerals together and you get a sense of just how ungainly the previous system must have felt.

The beginning of Fibonacci’s Liber Abaci would have astonished its readers with the audacity of its opening claim.

“The nine Indian figures are: 9 8 7 6 5 4 3 2 1.
With these nine figures and with sign 0 which the Arabs call zephir any number whatsoever is written, as is demonstrated below.”

Any number can be written from a set of 10 symbols, using the place value system. Roman numerals require inventing new symbols every time you move up to a new order of magnitude. And suddenly, a finite set of symbols is sufficient to write any number.

It is, when you think about it, staggering. And it’s also staggering that we consider this idea so fundamental that we ask elementary school children to understand it.

Still, if 10 symbols and the idea of place value are sufficient to write any whole number, naming these numbers requires a bit more. In addition to then 10 numerals (0 – 9), we also need names for the places themselves. That doesn’t take too much extra work. The names we need are:

  • Ten
  • Hundred
  • Thousand
  • Million

Because we can concatenate ten and thousand to get ten thousand, or hundred and million to get hundred million, these extra four terms should allow us to name every number less than a billion. Add on “billion” and “trillion” and you’ve got 16 names to describe pretty much any whole number you’ll be talking about in your lifetime.

That should be all we need. But it’s not.

Why not? Because we have included a host of irregular number names into the process. Instead of needing 14 number names for every number before a billion, we need 28 number names to reach a hundred.

This might sound theoretical, but the profusion of irregular number names has consequences for students. Talk to a Kindergarten teacher about it; they spend months of math time helping kids learn the numbers from eleven to twenty.

We’ve erected a wall of memorization between counting to a hundred. And it’s a wall that a lot of Kindergartners spend a lot of time and energy struggling to get over.

What if we said, “one ten one, one ten two, one ten three, …” instead of “eleven, twelve, thirteen…” It feels preposterous, because we’re so used to the current irregular names. But removing the irregularities and matching the names to the symbols would mean kids would learn their numbers much faster, with less pain, and with far more coherence.

How do you effect this kind of change, though? I don’t know. Number names are stored deep in us, and we couldn’t even switch to the metric system in the US. I have a thought that we could use “T” instead of ten, and count by tens saying “one T, two T, three T, four T, five T, six T, seven T, eight T, nine T.” That would leave some of the names unchanged, which might soften the jarring quality of changing the words at all (six T instead of sixty).

In the end, I don’t really know how such a change could be effected. If we could snap our collective fingers and remove irregular number names, we’d have an early math learning curve that was improved in every way, and far more success, higher test scores, better confidence, and on and on from our young kids.

But right now, I don’t see a way forward.

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Gordon McDonough
1 year ago

While we are fixing this, can we also do it for all the languages foreign to English speakers? It can be a real barrier.

Last edited 1 year ago by Gordon McDonough