Blog entry by Chris Pim
There is a commonly held notion that mathematics has a universal quality that ensures learners have a relatively equal opportunity to succeed, whatever their background. But is this generally true when it comes to pupils learning English as an additional language (EAL), or does it require qualification and a much more nuanced analysis?
It can’t have escaped your attention, whether as an educator or parent, that there is some angst nationally over standards in mathematics compared with other nations. Whether this is a genuine problem and that the root causes can be easily explained is for another article. However, it is true that the UK differs from many other countries in the amount of language that is deliberately interwoven into the mathematics curriculum. This is important as the expression of mathematics through a linguistically rich curriculum may present barriers for learners who are not working at age-related expectations in English. This approach might also present cultural inhibitors, whether because children lack a degree of cultural capital as result of their upbringing or because they and/or their parents were educated abroad.
Pupils educated abroad
Pupils educated abroad, especially older EAL learners who have had an uninterrupted education, will have studied a lot of mathematics; finding out about their mathematical experience and ability can be problematic when they first arrive. However, it is true that mathematics is one subject in which newer to English learners have some chance to demonstrate their prior learning because it is less dependent on language than many other subjects. Testing and baseline assessment of mathematics can be helpful but the results need to be treated with caution. Whilst it is tempting to assume that mathematical approaches are similar across the world, the reality is very different. Numbers are not just numbers when a learner has routinely used different numerical symbols to the Hindu-Arabic numerals used in Western society. Not only this, but symbols, like an equal sign or a multiplication symbol, can be denoted differently. The fabric of the curriculum differs widely as well. We often find children are way ahead in certain disciplines such as algebra or calculus yet have limited knowledge of others like shape or perimeter. The mechanics of solving problems are such that a child may be secure in a method which is entirely different to those taught in UK Schools. Indeed, children abroad are not necessarily routinely taught several different methods and may find it hard to consider alternative ways of approaching a problem, particularly if they are already secure in one way.
The mathematical problem
As I am sure you are aware, our mathematical problems tend to be very wordy and the way that questions are expressed, particularly in exams, can be difficult for some EAL learners. The English is stylised, particular to mathematics and quite unlike the way that we talk or even write on a daily basis. I would also argue that most mathematical questions are culturally bound, making implicit assumptions about what experiences pupils will or will not have had, whether UK born or not.
To illustrate this quandary, consider the following problem:
At yesterday’s match 650 people watched Arsenal play on the big screen. Half of these fans bought a programme at £2.50 each.
- How many fans paid out?
- How much money was spent on programmes altogether?
Firstly, this question like many you will see in examination papers, lacks a comprehensively clear context. There are no visual clues and the setting, related to a football match, is implied but not explicitly referenced. If you don’t know about ‘Arsenal’ you are at an immediate disadvantage. The problem revolves around buying and selling ‘programmes’ which may be beyond many pupil’s experience if they have never attended a football game. The use of the word ‘programme’ is problematic as it can all too easily be linked with the phrase ‘watching on the big screen’ and interpreted as a TV programme. Like the word ‘programme’, there are other homographs as well, such as ‘match’ and ‘fan’ which may cause confusion. The relevant numerical operation is bound up in words like ‘each’ and ‘altogether’; words like this that imply a specific numerical operation, and there are many, need to be explicitly taught to EAL learners. The question also features the phrasal verb ‘paid out’; this type of language is extremely hard for English beginners.
The implications for EAL learners are far reaching. If you are working with children at an early stage of English acquisition you will need to consider both the linguistic and cultural demands of the mathematics curriculum. Making the mathematics more comprehensible will require thought and preparation - whether through the use of imagery, first language explanation, mathematical glossaries or other forms of personalisation.