Friday, February 13, 2015

The problem with Maths is ‘English’ - 'twenty' examples

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?
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’.

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:

CLC_IV said...

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.