Let's Talk | Language

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By David Robson26th May 2023

Language can influence how quickly kids learn to count – but does it make a difference in the long run?

I

Is 2/3 bigger than 3/5?

How quickly and confidently you can answer this question may depend on your age, education – and possibly, on your native language.*

According to a growing body of research, the words that different languages use for numbers can affect how easily we learn to count and understand basic concepts such as fractions.

For children taking their first steps into the world of mathematics, this can mean that some are presented with additional challenges based on the language they speak, while others are offered a head start.

They may for example find it more or less difficult to answer seemingly simple questions like "Which number is bigger – 17 or 70?" or "How many quarters in a half?".

While the effect is subtle, exploring it can help us understand the deeper factors that shape our maths ability – and perhaps, allow the many children and adults who struggle with maths to see their problem in a new light.

A schoolgirl in Germany does her maths homework (Credit: Getty Images)

**Is counting easier in Chinese?**

Let's first consider the difficulties that a child may face with counting. In English, there is no systematic rule for the naming of numbers. After ten, we have "eleven" and "twelve" and then the teens: "thirteen", "fourteen", "fifteen" and so on. If you didn't know the word for "eleven", you would be unable to just guess it – you might come up with something like "one-teen".

Even more confusingly, some English words invert the numbers they refer to: the word "fourteen" puts the four first, even though it appears last in the number 14 (we'll look at the impact of such inversions later).

For multiples of 10, English speakers switch to a different pattern: "twenty", "thirty", "forty" and so on. It can take children a while to learn all these words, and understand that "thirteen" is different from "thirty", for example. In the meantime, they may unconsciously try to make the pattern more regular, by slotting words like "five-teen" or "twenty-ten" into their counting sequence.

Other languages have even more intricacies. In French, for example, numbers are named somewhat consistently up to 60, after which the system changes to a so-called vigesimal structure, meaning, it is based on multiples of 20. The French word for 71 is *soixante-et-onze *(sixty-and-eleven), for example, and 99 is *quatre-vingt-dix-neuf* (four-twenty-nineteen).

Even native French-speaking children seem to wrestle with this system: in one study, they performed worse in transcoding numbers over 60 compared with English-speaking children. Transcoding means correctly converting words into numbers and vice versa, for example, reading out 71 as seventy-one, or indeed, *soixante-et-onze*.

A primary school child in Cardiff, Wales, writes down maths excercises (Credit: Getty Images)

## Chinese children were about a year ahead of American children in their capacity to count to higher numbers

In Chinese, the number words lack these irregularities. Once you know the words for one through 10, you can easily infer all the others.

For example, the word for one is *yi*, two is *er*, and ten is *shi*. Eleven is *shi yi* (ten-one), twelve is *shi er* (ten-two) etc. Twenty is *er shi* (two-ten), twenty-one is *er shi yi* (two-ten-one). This consistent characteristic is known as linguistic transparency by psychologists, and it was long thought to aid children's first steps to basic numeracy. (BBC Future has reported on a similar effect in writing.)

In the mid-1990s, Kevin Miller at the University of Illinois at Urbana-Champagne and colleagues put the idea to the test by comparing the numerical abilities of four- and five-year-olds in the US and mainland China. They found that the children from both countries were equally able to count up to 12, but the Chinese children were about a year ahead of the Americans in their capacity to count to higher numbers.

Further studies suggested that Chinese children find it easier to grasp the basic logic of our "base-10" counting system. Put simply, this is the fact that we use multiples of tens and units to represent numbers and that the order of the digits tells us which is which. In Chinese, this is more obvious: *er shi*, "two-ten" is easily understood as 2 x 10 = 20. The English word "twenty" doesn't spell this out so clearly.

To investigate whether this makes a difference to children's understanding, six-year-olds of various nationalities were given one set of blocks to represent tens and another set to represent units. Their task was to use the blocks to illustrate different quantities. Children in China and other East Asian countries with greater linguistic transparency were more likely to represent larger numbers using a combination of both sets of blocks, while those who spoke English, Swedish or French were more likely to count out the larger numbers in individual units.

How to count to 1,000 on your hands

As intriguing as these studies are, they couldn't rule out the potential influence of the different education systems in the different countries – it's possible that maths is just taught more effectively in some countries than others. However, a clever test of Welsh speakers in the UK managed to rule out this confounding factor.

Like their Chinese equivalents, Welsh number words have greater linguistic transparency. The Welsh words for one, two and 10 are "*un*", "*dau*" and "*deg*". Eleven in Welsh is "*un deg un*" (one ten one), twelve is "*un deg dau*" (one ten two), and twenty-two is "*dau ddeg dau*" (two tens two). Crucially, children in Welsh-speaking schools follow the same curriculum as those in the English-speaking schools.

When Ann Dowker, a lecturer in psychology at the University of Oxford, learnt about Welsh's linguistic transparency, she saw it provided the perfect opportunity to study the effects of the language's counting system on children's mathematical ability, without educational differences potentially muddying the results.

Dowker's findings were nuanced. She found, for instance, that six-year-olds who spoke Welsh at home and school made fewer errors when reading aloud pairs of two-digit numbers. They were also better able to point out which was the bigger of the two, compared to those who spoke English. "There was a significant advantage," she says.

However, these benefits didn't seem to translate to advantages in other measures of general mathematical ability. For this reason, Dowker concludes that the effects of language on numerical ability are subtle and specific rather than large and "pervasive". She certainly doesn't believe that linguistic transparence, alone, could explain why East Asian countries tend to be placed higher in educational league tables.

Cross-country comparisons within Europe support this position. Consider German, which shares many of the irregularities seen in English, including the inversion of certain numbers. Forty-five, for example is *fünfundvierzig* in German (five-and-forty). Some studies suggest that inversion confuses German children as they learn to write numbers as digits. (Hearing *fünfundvierzig *they might write 54, for example.) But that doesn't seem to hold them back for long. "Germany does rather well in international comparisons," says Dowker.

Visitors take pictures of an art installation named 100 colours by French architect Emmanuelle Moureaux (Credit: Getty Images)

**Fractious fractions **

Even if the influence of language does not extend to the whole of mathematics, emerging evidence suggests it might extend to a handful of skills beyond counting. So far, there is some evidence that language may affect how quickly children learn to use fractions. "When thinking about fractions, we have to look at the big part first and then see how much of that is in the numerator," explains Jimin Park at the University of Minnesota, whose PhD thesis concerns the linguistic representation of fractions.

In Korean, this relationship is explicitly spelled out. The term for 1/3 is *sam bun ui il*, which translates as "of three parts, one", and 3/7 is *chil bun-ul sam*, which translates as "of seven parts, three" – where the English terms "one third" or "three sevenths" do not make this so immediately obvious. And this seems to give young Korean children a slight advantage in matching named fractions to diagrams illustrating the quantity, before they have even been taught formal lessons in the idea. "When they have to verbally understand fractions, the Korean children definitely benefit," says Park. Intriguingly, when English children are taught to describe fractions with the Korean style of phrasing, it does seem to improve their intuitive understanding of the quantities.

Neither Park nor Dowker would suggest widespread revisions of how we name numbers, but the simple awareness of these linguistic quirks and obstacles may help teachers to give children the right support.

If nothing else, this research can help to remind us adults of the first steps of our intellectual journey, and take pride in having mastered something as unexpectedly complex as counting. Perhaps it will encourage those of us who feel we are simply bad at maths, to give it another try.

*Answer: 2/3 is bigger than 3/5

*David Robson is a science writer and author of**The Expectation Effect: How Your Mindset Can Transform Your Life**, published by Canongate (UK) and Henry Holt (USA) in early 2022. He is**@d_a_robson**on Twitter.*

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## FAQs

### What's the best language for learning maths? ›

**Chinese, Japanese, Korean and Turkish** use simpler number words and express math concepts more clearly than English, making it easier for small children to learn counting and arithmetic, research shows.

**Which math language is fastest? ›**

C# typically gets decent math speeds, on small data sets. C or C++ for larger ones. Perl is almost never faster. **Haskell or Mathlab** or something along those lines may give significant gains, but will take a lot of translation.

**Is there a language for math? ›**

The language of mathematics or mathematical language is an extension of the natural language (for example English) that is used in mathematics and in science for expressing results (scientific laws, theorems, proofs, logical deductions, etc) with concision, precision and unambiguity.

**Can you learn math like a language? ›**

Because mathematics is the same all over the world, **math can act as a universal language**. A phrase or formula has the same meaning, regardless of another language that accompanies it. In this way, math helps people learn and communicate, even if other communication barriers exist.

**Is it easier to learn a language or math? ›**

Language is hard. In fact, **it's infinitely harder and more complicated than math**. And yet, nearly every small child can learn and master language. Why is math so overwhelming for so many students?

**What language is best for learning math? ›**

- Python. Python is the most popular programming language in the world, and many of the biggest tech companies rely on it for data analytics, machine learning, artificial intelligence, web development, game development, business applications, and more. ...
- R. ...
- MATLAB. ...
- Wolfram Mathematica. ...
- Fortran. ...
- SAS. ...
- Julia. ...
- Maple.

**What is powerful math language? ›**

Mathematical language being powerful is **its ability to express complex thoughts with relative ease so that most people can understand them**. Mathematical symbols are used to refer to certain quantities, concepts, and ideas, among other things.

**Why does Chinese language make math easier? ›**

This stereotype might just be true, since researchers found that Chinese is a more efficient language for learning math than English. In Chinese, numbers are much simpler. **Every number from 0 to 10 only has one syllable, making them easier to say and remember than numbers like the the multi-syllabic “zero,” or “seven.”**

**What are the 3 types of mathematical language? ›**

It is: • **precise (able to make very fine distinctions); • concise (able to say things briefly); • powerful (able to express complex thoughts with relative ease)**.

**Are the French good at math? ›**

The result was analytic geometry. In the centuries since, **France has developed a powerful math tradition and a fearsome teaching apparatus that has made its mathematicians, pound for pound, the best in the world**. Of the 52 winners of the Fields Medal, often called the Nobel Prize of math, 11 have been French.

### What is harder math or language? ›

**Language is hard**. In fact, it's infinitely harder and more complicated than math. And yet, nearly every small child can learn and master language.

**Can you be fluent in math? ›**

**Fluency in math is the ability to flexibly apply strategies in an efficient and accurate way**. On the other hand, automaticity in math, is being able to provide an automatic response. When a student is fluent, they are automatic. When a student is automatic, they are not necessarily fluent.

**Does duolingo teach math? ›**

**With Duolingo Math, we are offering a free way to learn math and build foundational, essential skills that everyone can use throughout life**. Making math accessible and fun is the natural next step in our quest to bring high-quality education to everyone on the planet!

**At what age is it easiest to learn math? ›**

Numerous studies show that learning mathematics is best during **the first 4 years of a child's life**. This means that during this peak period, learning mathematics is much easier and quicker for young children.

**What age is best to learn math? ›**

Learning to read, write and do math is always a milestone in kids that parents treasure. Children will learn to read between the ages of four and six and write and do math **between six and 10 years old**.

**What age is the hardest to learn a language? ›**

They concluded that the ability to learn a new language, at least grammatically, is strongest **until the age of 18** after which there is a precipitous decline. To become completely fluent, however, learning should start before the age of 10.

**Why language is very important in mathematics? ›**

**Language is fundamental to teaching and learning mathematics**. Often, students must apply literacy skills to read and interpret worded problems. However, literacy errors related to problem solving can occur before students attempt to apply their mathematical knowledge.

**What is the hardest math type? ›**

What is the hardest branch of Maths? Algebra is the hardest branch of Maths. **Abstract algebra** particularly is the most difficult portion as it includes complex and infinite spaces.

**What's the hardest math? ›**

Today's mathematicians would probably agree that the **Riemann Hypothesis** is the most significant open problem in all of math. It's one of the seven Millennium Prize Problems, with $1 million reward for its solution.

**What is the world's hardest math type? ›**

**Advanced Calculus** is the hardest math subject, according to college professors. One of the main reasons students struggle to understand the concepts in Advanced Calculus is because they do not have a good mathematical foundation.

### Why are Japanese so good at math? ›

Unlike traditional methods in the U.S. that stress memorization, Japanese math **emphasizes problem solving**. Its sansu arithmetic aligns with the Common Core standards, providing a strong incentive for teachers to adopt the pedagogy.

**Why Asians are so good at math? ›**

A better explanation has to do with education policy and federal immigration laws. Countries that invest in teacher education and high-quality curriculum do better on international tests. In the US, the 1965 Immigration and Nationality Act gave preference to STEM professionals from Asia.

**Are Koreans good at math? ›**

**South Korea has some of the highest math scores in the world**. On the 2012 PISA math test, the mean score for a South Korean student was 70 points higher than for an American student.

**What are the four basic mathematical language? ›**

The fundamental arithmetic operations are typically thought to be **addition, subtraction, multiplication, and division**.

**What does T stand for in math? ›**

T, Tera- as in **one trillion**.

**How many mathematical languages are there? ›**

There are approximately 6,500 languages spoken worldwide, but there is **only one language of math**. Although some cultures use different symbols to represent numbers, the mathematical “ideas” those symbols stand for are universally known.

**What country does best in math? ›**

**Here are the 10 countries with the most top-ranked math scientists:**

- United States - 977.
- France - 148.
- United Kingdom - 145.
- Germany - 144.
- China - 116.
- Canada - 105.
- Italy - 81.
- Australia - 61.

**How good is the average American at math? ›**

In the United States, adults weighed in at an average numeracy rate of **253 out of 500**.

**Which country maths is toughest? ›**

Which country has the hardest math? The United Kingdom, The United States of America, etc are the countries having one of the best education systems. But when it comes to having the hardest math, **China and South Korea** top the list.

**What is the hardest math taught in school? ›**

What is the Hardest Math Class in High School? In most cases, you'll find that **AP Calculus BC or IB Math HL** is the most difficult math course your school offers. Note that AP Calculus BC covers the material in AP Calculus AB but also continues the curriculum, addressing more challenging and advanced concepts.

### Why is it so hard for me to learn math? ›

**Because math involves using plenty of multi-step processes to solve problems, being able to master it takes a lot more practice than other subjects**. Having to repeat a process over and over again can quickly bore some children and this may make them become impatient with math.

**Are people naturally good at Maths? ›**

Research from Johns Hopkins University suggests that **some people are naturally good at math, whereas others may never be**. For those who can count very well, there is something vaguely infuriating about doing business with (or even living with) people who can't count past three.

**How can I train my brain for math? ›**

**Brain Boosting Exercises For Mathematical Intelligence**

- Playing math games.
- Solving math puzzles.
- Several pawn and memory matching card games.

**Is math 100% accurate? ›**

The conclusion is that while mathematics (resp. logic) undoubtedly is more exact than any other science, **it is not 100% exact**. We cannot be 100% sure that a mathematical theorem holds; we just have good reasons to believe it. As any other science, mathematics is based on belief that its results are correct.

**Does being bilingual make you better at math? ›**

Learning two languages at an early age develops language skills in general. But **bilingual kids also do better in other cognitive subjects – like mathematics.**

**What grade level is Duolingo Math? ›**

According to the company, Duolingo Math teaches **elementary-level** mathematics that help younger kids have a stronger foundation. The app provides lessons in multiplication, division, fractions, area and perimeter, geometry, measurements, and decimals.

**How far does Duolingo teach you? ›**

At Duolingo, we're developing our courses to get you to **a level called B2**, at which you can get a job in the language you're studying. Reaching that kind of proficiency requires dedication, varied practice opportunities, and a lot of time.

**Does Duolingo count as studying? ›**

We have a team of PhDs dedicated to this. According to an independent study conducted by the City University of New York and the University of South Carolina, **an average of 34 hours of Duolingo are equivalent to a full university semester of language education**. You can see a full report of the study here.

**At what age does math anxiety begin? ›**

The study found that 36% of younger (**15-24 year-olds**) people feel anxious about maths, compared to 10% of older people (65+), and some studies suggest that maths anxiety can begin very early when young children are learning basic number skills.

**At what age did Albert Einstein learn math? ›**

"It is, in fact, nothing short of a miracle," he wrote, "that the modern methods of instruction have not yet entirely strangled the holy curiosity of inquiry." **Einstein taught himself geometry at the age of 12**, wrote his first "science paper" at age 16 and received his Ph.

### Is 35 too old to learn math? ›

Maybe you're 35. Maybe you're 55. or 75! The short answer is, “Yes, mathematics is not out of your reach”. **You're not too old**.

**Can I learn math at 50? ›**

**You can start learning to any subject at any age of your life, as long as you are interested toward the subject age doesn't matter**. The quote you mentioned here " Mathematics is young man's game".

**What age do mathematicians peak? ›**

More specifically, that they peak **early in their twenties** (i.e. present their most important contributions / most of their work in their early twenties) and then decline fast. As opposed to Biologists, for example, who are said to peak much later in their lives and keep contributing well into their 70s or beyond.

**What age can a child count to 100? ›**

**Older 5-year-olds** may be able to count to 100 and read numbers up to 20. A 5-year-old's knowledge of relative quantities is also advancing. If you ask whether six is more or less than three, your child will probably know the answer. Keep math fun.

**What is the #1 hardest language to learn? ›**

Across multiple sources, **Mandarin Chinese** is the number one language listed as the most challenging to learn. The Defense Language Institute Foreign Language Center puts Mandarin in Category IV, which is the list of the most difficult languages to learn for English speakers.

**Is 40 too old to learn a new language? ›**

Are you ever too old to learn a new language? Well, the good news is that experts say you are never too old. Studies show that **anyone at any age can learn a new language**. In fact, it is even easier to start speaking in a foreign language now with all the advanced technology available on the market.

**What age is too late to learn a language? ›**

It does not matter how old you are, **it is never too late to start learning a foreign language**. Many language learners are put off by their advancing years; they believe age is a barrier to learning an entirely new language.

**What's the hardest math in the world? ›**

Today's mathematicians would probably agree that the **Riemann Hypothesis** is the most significant open problem in all of math. It's one of the seven Millennium Prize Problems, with $1 million reward for its solution.

**What math class is the easiest to take? ›**

**What is the Easiest Math Class in College?**

- Statistics: Statistics is a branch of mathematics dealing with the collection, analysis, and interpretation of numerical data. ...
- Finite Math: Finite math refers to a variety of math courses that do not involve calculus.

**Which is faster C or C++? ›**

C++ language is an object-oriented programming language, and it supports some important features like Polymorphism, Abstract Data Types, Encapsulation, etc. Since it supports object-orientation, **speed is faster compared to the C language**.

### What are the 7 hardest math problems? ›

Clay “to increase and disseminate mathematical knowledge.” The seven problems, which were announced in 2000, are the **Riemann hypothesis, P versus NP problem, Birch and Swinnerton-Dyer conjecture, Hodge conjecture, Navier-Stokes equation, Yang-Mills theory, and Poincaré conjecture**.

**What is the hardest math problem in the world with an answer? ›**

**x ^{3}+y^{3}+z^{3}=k**, with k being all the numbers from one to 100, is a Diophantine equation that's sometimes known as "summing of three cubes."

**What is harder than calculus? ›**

In general, statistics is more vast and covers more topics than calculus. Hence, it is also perceived to be more challenging. Basic or entry-level statistics is much easier as compared to basic level calculus. **Advance level statistics** is much much harder than advanced level calculus.

**Which is harder calculus or algebra? ›**

**Calculus is the hardest mathematics subject** and only a small percentage of students reach Calculus in high school or anywhere else. Linear algebra is a part of abstract algebra in vector space. However, it is more concrete with matrices, hence less abstract and easier to understand.

**What's the answer to x3 y3 z3 K? ›**

In mathematics, entirely by coincidence, there exists a polynomial equation for which the answer, **42**, had similarly eluded mathematicians for decades. The equation x^{3}+y^{3}+z^{3}=k is known as the sum of cubes problem.

**What math do most freshman take? ›**

Eighth grade: | Eighth grade Math |
---|---|

Freshman Year: | Algebra 1-2 |

10^{th} Year: | Geometry or Honors Geometry |

11^{th} Year: | Algebra 3-4 or Honors Algebra 3-4 |

12^{th} Year: | Pre-Calculus or Honors Pre-Calculus |

**Which math class is the most useful? ›**

**Calculus** provides the framework that makes a wide variety of modeling systems possible. Calculus has applications across a wide variety of technical and scientific fields. Calculus is used by: all types of engineers.

**How hard is calculus? ›**

Calculus is **widely regarded as a very hard math class**, and with good reason. The concepts take you far beyond the comfortable realms of algebra and geometry that you've explored in previous courses. Calculus asks you to think in ways that are more abstract, requiring more imagination.

**How fast is Python compared to C? ›**

Now, let's take a look at the same algorithm in C++. After compiling, if you run the code, it takes about 2.42 seconds to generate all 67 million 13-mers. It means Python takes **25 times more time to run the same algorithm compared to C++**.

**Is C really faster than Python? ›**

**Python is Slower than C since it is an Interpreted Language**.

The difference is that rather than being immediately performed by the CPU, the Python code will be interpreted. In terms of performance, this makes all the difference in the world.

### Is C language faster than Python? ›

**C is a faster language compared to Python as it is compiled**. Python programs are usually slower than C programs as they are interpreted. In C, the type of the various variables must be declared when they are created, and only values of those particular types must be assigned to them.