Maths is
difficult to learn and hard to teach. But one BIG problem, which few parents
fully understand, is language – the use of English.

*Jack, do you know what volume means?*

*Yes.*

*Explain it to me.*

*Ok, it’s the button on the remote control that makes your TV go louder.*

**English is irregular**

English is
a magpie language, highly irregular and puts more load on working memory and
that leads to more errors. Beyond working memory it is important to know that
irregular terms have to be stored separately in memory, regular forms don’t
have to be. This extra work, and extra steps, places an extra load on working
memory, which has a limited capacity in terms of ‘registers’ and manipulation
within these registers.

**1. Number words**

Chinese
(Japanese & Korean are similar) has just nine number names from which
larger numbers are generated, compared to English, which has more than two
dozen unique number words.

**2. Words shorter**

Chinese speakers can easily memorise this sequence of
numbers 7,3,5,6,9,8,4, compared to only 50% of English speakers. Why? Our
working memory has to cope with words that are longer. Their number words are
short, sharp sounds, like si and qi, not long-winded words.

**3. 11 & 12**

They say
‘ten-one, ten-two’, rather than the unique eleven and twelve. ‘Eleven’ and
‘twelve’ come from ‘ain-lif’ and ‘twa-lif’, meaning one-left and two-left
(after counting up to ten) in Old German.

**4. 13 & 15**

English
number names are more irregular than you’d think. For example, we say fourteen,
sixteen, seventeen, eighteen, and nineteen. Wouldn’t it be easier if we also
had oneteen, twoteen, threeteen, and fiveteen?

**5. 20, 30, 40, 50**

In counting
by tens, we have a similar discontinuity. There are sixty, seventy, eighty and
ninety but there are the irregular twenty, thirty, forty and fifty.

**6. Teen reversal**

With two
figure numbers, if we keep counting up, the numbers above twenty will have the
tens first (e.g., fifty-six), whereas for the numbers below twenty we put the
ones first (e.g. thirteen).

**7. Place value**

So, rather
than ‘twenty eight’, they say ‘two-ten-eight’. This hurdle for English speakers
is ‘place-reversal’ as the English language reverses mathematical place:
six-teen rather than ten-six, which causes problems when dealing with double-digit
calculations. Partition, or breaking numbers down into parts then adding,
subtracting, multiplying etc. is much easier if ‘making a ten’ is easy
linguistically.

**8. Hundreds & thousands**

Take the
number one hundred and four. The child may know one hundred is 100 and that
four is 4, then say that one hundred and four is 1004. Similarly with one
thousand and eleven and so on. This is not a problem in some other languages.

**9. Addition & subtraction**

In adding
eighteen plus seventeen in your head you have to reverse both numbers first
then add them. If you ask children to add seven hundred & forty eight and
forty two, in English, they will need to convert those words to numbers (748 +
42) and then do the addition. In Japanese, this would sound like, “seven-hundreds;
four-tens; eight plus four-tens; two.” There are far fewer things to interpret,
hold in working memory then manipulate as ‘place’ is reflected in the structure
of the language.

**10. Numbers are not just numbers**

I have a
two baths of water at 25 degrees centigrade. What is the temperature if I pour
a bath of water into the other? Some children will say 50 degrees. Why do kids double when they're meant to square? Because that little number hovering up tere is a '2'. Confusing or what?

**11. Division & multiplication**

Multiplication
means things get ‘bigger’ and division means things get ‘smaller’ – right? No.
if I multiply ten by a fraction the numer gets smaller and if I divide ten by a
half the number gets bigger. It’s easy to teach surface maths, that teach real
maths. This is just one of many examples where you have to ‘see’ the problem.

**12. Fractions**

Take the fraction four ninths in English, the same number in
Chinese is ‘one part out of nine, take four’. The language literally unpacks
the fraction, this makes the fraction not only easier to understand but also
makes the addition, subtraction and other manipulations of fractions easier.

**13. Shapes**

The Finnish
language has a lot of words which are easy to understand, if you're a native,
even if you don't know the word originally. An example ss the shape ‘Hexagon’
in Finnish is ’kuusikulmio’, which means ‘a shape with six corners’. This
allows the child to imagine and recall the shape with greater ease. In English,
we’re lumbered with obscure Greek and Latinate prefixes.

**14. Alphabet**

Maths may
seem like an exact language but its ‘conventional’ use of alphabetical letters
can be confusing:

a,b,c tend
to be constants (fixed values)

A,B,C
points on geometrical figures

i,j,k,l,m,n
tend to be integers for counting

x,y,z
unknown variables

This can
cause confusion in the interpretation of problems and geometric images images.

**15. Share & straight**

These two
words seem straightforward but research shows that children often interpret
these words differently when learning maths. If I said ‘Ten sweets are shared
between Rob and Jack but Jack has four more than Rob’ responses such as ‘But
they’re sharing so they must have 5 each’ are not uncommon. Similarly, when
children hear the word ‘straight’ they may interpret this as just vertical and
horizontal and not regard a sloping line s straight. These linguistic traps are
difficult for adults to spot but easy for children to fall into.

**16. Instruction**

You can be
asked to: find, calculate, work-out, how many

Addition: Add,
make, total, plus, addition, make, sum, altogether, fewer

Subtraction:
Subtract, take-away, deduct, minus, leave, less, difference between

Multiplication:
Multiply, by, times

Division: Divide,
into

Surveys,
where children voice their difficulties have uncovered many problems around the
use of these terms for mathematical problems.

**17. Literacy hits maths**

Low levels
of literacy may lead to poor or no understanding of the often convoluted
problems that mats teachers and textbooks set in maths. Most are unlikely to ever
have been heard by the child before, many using language that is beyond their
reading age.

**18. Poor, wordy test items**

Many maths
problems, set in exams, are more tests of complex literacy than maths. This is
why over reliance on word problems may hold children back as they fail to
untangle the linguistic traps that are inherent in English and poor assessment
items. Too many obscure, word-based, test items involve unpacking tense,
comparison and change models that are beyond the actual testing of addition or
subtraction.

**19. Vicious circle**

Asian
language speakers, from an early age, get more success from their efforts, This
creates a virtuous circle, where learners get quick results and feel as though
numbers are easily manipulated. Compare that to the vicious circle of English
learners, who have to cope with the irregularity of the language problems and
cognitive overload.

**20. Culture of ability not effort**

One last, but
seriously fatal, cultural difference may be the fact that some cultures see
failure in maths as a lack of effort, not ability. We have a culture that all
too often uses the language of ‘talent and ability’ not ‘effort’.

**Conclusion**

Appearances
are deceptive in maths. For most children it seems like a subject full of
traps, deliberately set to fool you. The problems set are often badly worded,
convoluted and unrealistic and often not enough variety of problems are used. This
is exactly why teachers need professional training, as the effective teaching
of maths needs a deep understanding of what has to be learned.

## 1 comment:

Donald,

I found what you had to say to be very interesting. English is irregular, and that aspect can make the wording of problems very complex and often difficult to wade through. However, the real problem regarding math education in the U.S. doesn’t seem to manifest itself until secondary school – a time when students should have the intricacies of the English language behind math down to automaticity. If this were the case, working memory would not be misallocated dealing with the irregularities and complexity of the English language. Issues within addition, subtraction, multiplication and division are all rooted in the very fundamentals of mathematic function that should require little to no working memory for a 15-year-old student. Via the information available on OECD’s website, it is evident that Asian countries don’t truly begin to dominate the competition until the secondary school level of math education. The U.S. actually ranks respectably in the top 10 in global math scores prior to secondary school education. The Program for International Assessment (PISA) is also somewhat of a corrupt system. Students from the different provinces of China are hand selected to take the test as to guarantee high marks for their region. If the test were administered to all of China, it would be found that they have much deeper problems regarding the gap in education than the U.S. On the other hand, Shanghai (China’s best province) is blowing Massachusetts (the U.S.’s best state) out of the water in math. Scores from Shanghai are on average 100 points better than those from Massachusetts, which means the way we are going about teaching math needs reform. Also in your article is information about Finnish using better prefixes to label certain shapes, well Finland has also been experiencing free fall out of the top 10 in global math scores after coming in at 15th in 2012. I think the problem lies less in the language used to ask the question and more in the specific methods used to explain and teach the basic functions. I think the Common Core standards are actually a step in the write direction as improving math skills in the U.S., but teachers and textbooks are woefully unprepared to accept and integrate this change. I think the learning of basic math facts and functions to automaticity is more important than standardizing, “add, sum, total, etc…” into a single word. If teachers were to receive more professional – outside the classroom – training in math, accept the common core, and are provided with less wordy and more straightforward textbooks, we can expect to see the U.S. return to a respectable ranking globally in math skills.

- CLC_IV

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