As teachers, we need to ensure our lesson opportunities meet the needs of all our learners which is increasingly challenging. The range of support we provide for our pupils is personalized to the children and needs the full cooperation of the pupil, teacher and their parents and carers this is especially important when working with EAL children. It is those initial discussions that have enabled me to understand the culture of the child, family background, school history and the level of English speaking adults within the family and therefore guided me to plan the resources and programme of study which would best support the learning needs of that child within my class.
EAL children have not got special educational needs and are often very able mathematicians but the language in mathematics is their barrier to either solving the calculation or problem. As teachers it is important to diagnose when an error is caused by language proficiency or a mathematical difficulty. We must keep our expectation high and ensure the opportunities we provide enable the children to be challenged and also enable them to access the mathematics. They do not need to do ‘simpler’ mathematics only ‘clearer’ mathematics and we need to provide opportunities that enable them to engage with the learning and convey and develop their mathematical ability.
Creating a welcoming climate
Some EAL learners often lack confidence having moved from one country to another or simply from one school to another. The first issue is to support them (as we do with any new pupils) and show them how welcoming the school environment is and allow time for familiarity with school routines and language around the school. Signs and signposts that would enable them to become confident in moving around school and the support of a friendly class buddy to guide and make friends
with is ideal.
Many pupils may have attended very formal schools and now enter into a classroom where the timetable is more varied and may need a visual timetable initially to access the routine. Pupils can find it daunting entering into a new environment where a more open classroom climate has been successfully developed allowing pupils to discuss and share ideas and where children work in pairs and groups with confidence, these issues need to be considered in ensuring new pupils integrate happily in to our classes and build confidence and are then ‘ready then for learning’.
Within our daily lessons of course the main difficulty is the limited knowledge of our language EAL children have to access the content of the mathematics lesson. Therefore, it is important to make the content of our lessons accessible and in context with the experiences that our EAL pupils have had.
Real-life number activities and problem solving using shopping items they are familiar with, alongside our other provisions, will help pupils to engage and access the mathematics. A few items I bought from a Polish supermarket recently enabled pupils with limited English to access the mathematics and engage in the problems with the whole class. It also brings in lots of opportunity to discuss the items, drawing pupils into conversations, discussing their culture and helps to celebrate their ethnicity. Picture resources can be created to allow pupils to choose items from a menu where they have a certain amount of money to spend, if the items reflect a range of EAL children’s foods as well as our traditional food then pupils will engage and access better what they have to do.
It is also worth remembering that like many of our English-speaking children the opportunity to handle real money regularly in daily life is quite limited nowadays and that these pupils are unfamiliar with our coins and values. This is an area where extra support can be invaluable from a teaching assistant or parent in reinforcing an aspect like this, which may be essential knowledge for a future lesson. Coins and their numerical value should be displayed and the appropriate words, eg a picture of the coin – the symbol £1 – and the word one pound should be available for pupils to see. Mathematical language can also be learnt through songs and rhymes in the early years and are still valuable auditory stimuli to practice basic vocabulary in Key Stage 2.
The understanding of our number system is key to unlocking potential in all mathematical areas. Our number system itself is not the easiest to learn.
The grasp of numbers to 10 is not too daunting, but when we reach those ‘teens’ numbers from 11 and move to 20 each number is a new word to learn. 11 being ‘tenty one’ and 12 being ‘tenty two’ would be much more accessible then we wouldn’t have to learn new vocabulary and when we got to 20, then twenty one would fit in quite comfortably. But, unfortunately, it is not that regular!
Unfortunately, even the decade numbers can be a minefield, with twenty a new word, thirty being a new word, forty is nearly like forty but spelt wrong then fifty is not fivety so another new word too! Luckily from 60 onwards we have more regularity and you often hear and see children quite confidently joining in from 60 to 100 when counting in tens. So enabling EAL children to understand our numerical system is vital. Once children are secure with this, we can enable pupils to access mathematical symbols and a wider range of mathematics. The structured number line showing a linear view of our number progression rather than a 100 square can support pupils in visually seeing how numbers become larger as we move from left to right on the number line. This number line can then be used in developing calculation methods and help pupils model how they have tackled a calculation or problem.
Resources to support calculation are essential. Children may need bead strings or structured number lines to support them in conveying their strategies.
The range of vocabulary we use in mathematics and the many meanings the words have can be confusing for EAL pupils words such as take away, scale, match and table etc have different meaning is different contexts so it is important to ensure pupils have a clear understanding of the use and context in the lesson, explain its meaning prior to the lesson if necessary.
The mathematical signs + x ÷ – are very visible and can be accessed and used by EAL pupils to develop strong mathematical skills, but the variety of language attached to each symbol needs further support to develop. Cards with mathematical signs and the words we read and use to convey that sign must be seen by EAL pupils and can be created to attract pupil interest. Mathematical vocabulary cards, similar to the one below, reviewed regularly and accessed in lessons can enable pupils to contribute to mathematical discussions and decode problems they are tackling.
Enabling EAL pupils to access mathematical discussions can be supported with talk prompts that are visual and easy to convey their opinions on whether an answer is correct, if they agree with the working out they see, the method or answer given etc. These recent prompts enabled pupils to decide whether all the solutions to a problem were found and gave ownership to the pupils to make decisions on the answers they had found in a group. The visual picture allowed pupils to sort the negative responses from the positive ones.
The difficulties that EAL children initially have with language can be overcome and data conveys how they achieve at an accelerated progress when there is well-planned provision to support their learning and good inclusive learning and teaching practice.
Overcoming barriers to learning in mathematics
'Within the school curriculum learning mathematics is uniquely challenging in that it is highly organised, sequential and progressive. Simpler elements must be learned successfully before moving on to others. ‘It is a subject where one learns the parts; the parts build on each other to make a whole; knowing the whole enables one to reflect with more understanding on the parts, which in turn strengthens the whole. Knowing the whole also enables an understanding of the sequences and interactions of the parts and the way they support each other so that the getting there clarifies the stages of the journey.'
(Chinn and Ashcroft, 1998: 4.)Because of the interrelating nature of the subject children who have learning difficulties in mathematics may sometimes appear to feel even more lost and disempowered than those who encounter problems in other subjects.” (Frederickson and Cline, 2009, pp. 387-388)
For pupils learning EAL particular sources of difficulty are likely to include:
• Confusions between trying to achieve mathematical understanding (‘knowing both what to do and why’) and trying to learn mathematical procedures (‘knowing rules and routines without appreciating the reasons for them’, e.g. the formula for getting the area of a rectangle - “multiply the length by the breadth”).
• Increased anxiety, relating particularly to problems of mis-communication. Barwell (2002) has shown how “real life maths problems” and “word problems” create additional challenges for pupils learning EAL.
• ‘Reading’ mathematics and understanding the language of mathematics
- The vocabulary is challenging. Some words are used only in mathematical English and are therefore unfamiliar until children have been taught them (e.g. hypotenuse, parallelogram), while some other words are used confusingly with different meanings in mathematical English and ordinary English (e.g. mean, product, odd).
• The syntax is challenging. It is not just the vocabulary of mathematics that causes difficulty. The syntax in which mathematical ideas are expressed is often more complex than children are accustomed to in other areas of the curriculum. Examples include the use of the passive voice (as in Each side of the equation is divided by 3) and conditional clauses (as in if…then) (Shuard and Rothery, 1984).
Making Maths curriculum more accessible: Strategies for children learning EAL and Some issues concerning EAL in the mathematics classroom provide further explanation of the difficulties that EAL learners may encounter with mathematics.
Burwell et al. (1998, p. 22) advocated that teachers use the following checklist when communicating about mathematics to children whether in written or spoken form. They should make sure that they:
(a) Use simple sentence structures
(b) Present no more than one fact per sentence
(c) Check that any extra information that is given is useful
(d) Split questions into sections where possible and appropriate
(e) Make sure that the first part of the question can successfully engage the whole group
A cycle of assessment, planning, action and review can help you: to set realistic but challenging targets for pupils with learning difficulties in mathematics, and develop clear ideas about how to work towards them.
(f) Every question tests the mathematical skills of the child, not their English comprehension.
(f) Every question tests the mathematical skills of the child, not their English comprehension.
It may be useful to have a list of some hypotheses to check when analysing how pupils who are struggling in mathematics approach work that is set in the subject. The checks can be made through testing, through the analysis of errors, through interviewing them about completed work and through observation while they are doing it:
• They do not read the instructions fully before tackling a problem or they do not act on what they read.
• They do not take time to work out what a problem is about before starting work on it.
• They adopt ineffective strategies when attempting a new task or when faced with a task on which they have made errors previously.
• They employ unsystematic problem solving strategies when tackling a task or frequently change their approach without allowing time for one strategy to bear fruit.
• They stick to a single strategy and do not try a different approach when it is unsuccessful.
• They do not seek help appropriately when faced with a difficulty.
• They lose concentration quickly when they find something difficult.
• They work at a very slow pace losing track of what they are doing.
• They race through their work making many careless mistakes without noticing that there are errors.
• They are frequently off task and take avoidance action such as making frequent trips to the toilet or interfering with other children.
• They do not check their work when it is finished.
• When working with others on a joint task, they adopt a passive role, contribute little to any discussion or wait for others to take the initiative and then follow.
• They could make effective use of concrete support materials such as interlocking cubes, a number track or a number line.
• They adopt a defeatist or hostile attitude when working in mathematics.
Tony ClinePupils with English as an Additional Language (EAL)
Admission Protocol - Communication and Information
EAL pupil's need: Supportive ethos, admission procedures in place, Induction period, Supportive learning environment.
Teacher's need to know: Pupil profile including - country of origin, Languages spoken, Religion, Previous educational experience, previous attainment - level of literacy and numeracy in first language.
Place pupil with able pupils for a good model of English
Provide visual resources to set a context (use lower key stage texts as a supplement)
Set objectives simply and clearly and link to context by visual materials or gesture
"Signpost" lessons by putting key terms on board and link to visual materials, throughout lessons
Video or note taking etc will need clear, simple objectives. "look at the video and note the customs about new babies."
Provide simple English sentences linked to lesson context as learning objective e.g. the earth rotates on it's own axis.
Be aware of overuse of idiomatic language e.g.: It's on it's last legs - explain meaning.
Check pupil's understanding s/he may not ask for help. Ask "What does ... mean?"
Ask librarian for help providing illustrated texts for topics arising.
Encourage use of dictionary and note making in first language. Also ask for extended written response in first language.
Give pupil spider diagrams/grids/charts/writing frames, to explain or support written work.
Mark content - knowledge, ideas etc in usual pen and mark some English errors in pencil.
Give occasional gentle oral feedback for spoken errors; ask for repetition of correct sentences.