## The mathematics of learning Chinese

I like maths. Maths helps us solve numbers problems.

In some ways, learning Chinese is a numbers problem and therefore it’s reasonable that many people turn to maths to try and help them solve the problem of learning Chinese.

You need to be careful though to make sure that you are doing the right kind of maths.

For example, it’s not uncommon for a mathematically inclined person to approach learning Chinese by breaking down the numbers and figuring out how many characters they need to learn per day in order to be able to learn Chinese in the fastest amount of time.

The Chinese government defines basic literacy for white collar workers and urban residents as knowing at least 2,000 characters (source).

Let’s ignore for the moment the fact that ‘number of characters known’ is a poor indicator of literacy for Chinese learners (even though it’s a useful one for native speakers), and instead focus on something which is all too common - a newcomer to Chinese seeing a statistic like the one quoted above and thinking:

“If I learn 5 characters a day, then in one month I’ll know 150 characters, but if I learn 50 characters a day, then in one month I’ll know 1,500, and in two months I’ll know 3,000 which is more than enough to be able to read. Therefore if I can study hard for 2 months I’ll be literate by the end. Problem solved.”

The problem with this approach is that Chinese is not made up of characters.

I mean, it is at the base level in the same way that English is made up of letters of the alphabet, but the language is made up of words and you need far more than 2,000 words in order to achieve literacy. You’re probably looking at around 5,000-6,000 words for basic literacy (simple comics, content aimed at younger children, HSK level 6 and around 10,000 words before getting to a point where newspapers and novels become approachable without heavy reliance on a dictionary.

Undeterred, an interepid newcomer takes the same approach as before and thinks “HSK 6 requires a vocabulary of 5,000-6,000 words, I’ll learn 50 words a day, study hard for 4-5 months and achieve basic literacy by the end. Problem solved.” More ambitious learners might even decide to up the rate to 100 words a day in order to achieve maximum results in the shortest amount of time possible.

They have broken down the maths to the following equation:

Total words learnt = words per day * days spent learning

and decided that the optimal way to increase ‘total words learnt’ is to increase the ‘words per day’ variable.

This approach is flawed however because 50 (or 100) words a day is an unsustainable rate.

Learning 50-100 new words a day is definitely doable (including time to revise words learnt from previous days), as long as you are able to devote several hours per day to full-time study. It’s not sustainable however and although you might be able to keep it up for a short time, if you do it for too long you’ll burn out, stop doing any learning for a few months and forget most of what you ‘learnt’ anyway.

Note the quotes around ‘learnt’ though, because the next flaw with the ‘learn as much as possible in as short an amount of time as possible’ approach is that if you are learning 50 words a day you probably aren’t learning each word well, at least not in terms of long-term retention and ability to use the word.

Learning 50 words a day is not a problem. Remembering all those words and being able to use them well one year later is.

To learn a word well for the purposes of literacy, you need repeated exposure and usage over time, and SRS tools aren’t going to be nearly as effective as you think at helping you with that because the skills required for reading are different from the skills developed by reviewing flashcards.

Assuming that you are going to be spending at least 2-3 years studying Chinese, and that you’re still going to have an interest in the language in 5 years time, you are better off considering strategies that use time as the multiplier rather than words per day.

I know there are people who think “I’m in a rush. I don’t want it to take 2 years before gaining literacy, I want to do it in months”, but you’re not going to be able to do that. Even if you learn a massive number of words and characters, you’ll run in to the problem where you understand all the characters in a sentence but you don’t have any idea what the sentence means.

You are going to be much better off in the long term if you are realistic about the challenge you face and set appropriate goals and strategies.

If you’re working with the same equation mentioned above, and if you want to maximise the ‘learnt’ component of ‘total words learnt’, then the part you should be focused on is not ‘words per day’, but ‘days spent learning’.

If you take the long view, and accept it’s going to take at least 2-3 years (and probably longer) to obtain basic literacy, you might as well set yourself a nice easy pace for ‘words per day’ that will guarantee you get where you want to go so long as you keep at it.

Slow and steady wins the race.

How many words per day is a good amount to learn? The answer will be highly dependent on each person and the time they are able to put in, but I have found that 5-10 words per day to be a good, sustainable amount. Sustainable being the key word.

Learning 5-10 words a day is easy, trivial almost. It’s such an easy target to achieve that you’d not expect it to be the recommended amount on a site called ‘Chinese the Hard Way’, and yet that’s the amount that I recommend.

Where does the hard part come in? The hard part comes in doing it every day.

5-10 words. Every day. Without fail.

If you can do that, then before you know it you’ll be reading Chinese.

Here’s a table that breaks down the maths.

Years 5 Words per day 10 Words per day
1 1,825 3,650
2 3,650 7,300
3 5,475 10,950
4 7,300 14,600
5 9,125 18,250

For example, if you learn 5 words a day, then in 1 month you’ll know 150 words, in 6 months you’ll know 900 words, and in 1 year you’ll know 1,825 words. After two years that number will be 3,650, and in three years you’ll be at 5,475 words.

Those 5,475 words will contain somewhere in the region of 2,000-3,000 characters, and if you’ve been learning useful words you’ll be on the right path to reaching basic literacy. All from 5 words a day. You might scoff at 5 words a day, but no-one will scoff at knowing 2,000-3,000 characters.

The numbers look even better if you learn 10 words a day, and if you can keep up that pace, then 2-3 years from starting you should be able to read simpler newspapers and books without too much difficulty, and in 5 years you’d have a sizeable vocabulary.

Beyond 10 words a day and you’ll start to hit the laws of diminishing returns in terms of effectiveness because everyone has a finite amount of time per day they can spend studying Chinese and this means that 1) learning too many new words per day decreases the amount of time you can spend on each word, and 2) spending too much time on vocabulary acquisition decreases the amount of time you can spend practising other skills.

Don’t be in such a rush to learn Chinese that you lose sight of your long-term goals, and don’t focus on the wrong part of the Chinese learning equation.

Chinese is a numbers problem, but more importantly it’s a problem of time.