Rationale For An Approach To Teaching Mathematics To New And Established Learners Of English

Mathematics is one of the most challenging subjects for children with English as an additional language (EAL) to take part in, due to their language barrier and the complex nature of mathematical vocabulary. These children therefore require additional support and structure within these lessons, to maximise their understanding.

One of the things that teachers must do during these lessons is to design their line of questioning so that it 'engages students in thinking and requires them to clarify understandings and justify their reasoning.' (Coggins et al. 2007, 80) This kind of questioning is essential as the mathematics lesson often requires children describe, explain, hypothesize, clarify, elaborate and share findings. With this increased emphasis placed on problem solving, Coggins et al. (2007) write that command of mathematical language plays an important role in the development of mathematical ability. To aid the children in their assimilation of this mathematical language, a key list of vocabulary for the lesson can be printed for each child, if possible with translations into their first language. 'Not all of the words a student hears during any lesson need become a part of his "active" vocabulary,' (Finocchairo, 1974) so it is important that the words they do retain are the important ones. For example, in a lesson on measuring capacity, the words 'litres' and 'millilitres' could be provided on large word cards, as it is essential the children be familiar with these words if they are to understand the lesson. By building their language skills alongside their maths knowledge, the children are gaining twice the amount of information from one lesson, thus maximising their potential. Thompson et al. (2008) write that combining mathematics and language instruction can afford EAL children opportunities to build their mathematics understanding while concurrently improving their ability to learn English.

Another way of helping the children to take an active role in these lessons is to introduce opportunities for conversation amongst peers. By utilising 'talk partners', the teacher can give EAL children the opportunity to participate within a smaller, 'safer' setting, without the scrutiny of the entire class. Further, placing these children in groups during a task can give them a 'relatively low-risk chance to take turns leading a group, writing down a group's ideas, reporting back to the class as a whole, and so on.' (Coggins et al. 2007, 13) Obviously this will be easier for those pupils who are beyond the beginning stages of language learning, but even new arrival EAL pupils can benefit from group work, even just by hearing models of spoken English.

Oral participation in general is greatly beneficial to EAL pupils, as increasing their oral language skills is one of the fastest and most effective ways of practicing and acquiring a new language. Even conversations which may not necessarily appear to be about the learning can be valuable. Josie Levine (1990) argues that to dismiss either the conversation as insignificant or the interactional methodology as trivial would be a mistake. These conversations can contain the starting points for conversational language, and any practice can only help the children, as they 'will still have to develop the habits of using their vocal organs perhaps in completely new ways.' (Finocchairo, 1974)

Teachers can give EAL pupils an even greater advantage by pairing them with 'strong language buddies', that is, children who are proficient at oral conversation and would be good models for spoken English. This means that the EAL pupils should be able to pick up a strong model of English, and have the chance to practice their oral language skills with someone who can help and support them.

Demonstrations and visual representations are vital for EAL children - when they cannot understand the language involved, they can learn by seeing, copying and then doing themselves. Returning to the lesson on capacity, the measuring experiment can first be demonstrated by the teacher, with narration alongside, so that they can learn the key words at the same time. As Finocchairo writes, the sound system is best learned through imitation of the teacher. The teacher can also involve the children in this demonstration, by asking them to take the final measurement, which will further reinforce their understanding of the task. The children can then repeat the experiment in their groups, even taking charge at some points, if they feel confident, which, in turn, will build their confidence! This kind of demonstration and pupil involvement is referred to as 'guided discovery'. (Coggins et al. 2007, 52)

An even stronger way of cementing a child's understanding of an experiment or concept is to give them physical objects, such as containers, to hold and explore. As Garrison and Mora write (1991), words are easier to remember when students can see and touch the objects while repeatedly hearing and saying the new words. This kind of kinaesthetic exploration allows the child to investigate the object in their own way, without being stuck behind confusing language. They can then transfer this knowledge into English at their own pace.

Mathematical concepts are extremely difficult to learn for many children, so an additional language barrier can make this seem impossible. When teaching children how to read a scale, therefore, a visual representation should be provided on the white board, and the process visually described, by pointing to each line and the corresponding number. This process should be repeated, and the less linguistically able children should be further supported by either a teaching assistant or an example sheet with some key words translated into their first language. It is important that the teacher be aware of their own oral delivery, and to 'adjust [their] own speech so that the pace and sentence structure makes students' comprehension more likely.' (Echevarria et al. 2004)

The concept of differentiation within EAL is often challenging. By checking their work, watching them in lessons and monitoring their progress, the teacher can assess how much support they might need. In the example lesson, the less able language learners are given translation sheets and adult support, whilst the more able children are occasionally provided with the same amount of assistance as the non-EAL children in the class, as their level of language has advanced to a proficient stage. They do, however, need additional support with the word problems, as they find these particularly challenging, as they often involve unfamiliar words and grammar as well as mathematical operations. The differentiation of EAL children will unlikely remain the same for long, as the children are constantly learning and assimilating their new language, so it is important to monitor their progress and accurately assess their needs.

In the broader context of the classroom, scaffolding is a recognised tool for helping children with EAL to make sense of their surroundings. According to Coggins et al. (2007), scaffolding can include verbal interaction, visible graphic organisers, cue lists, classroom routines, and other student-supportive strategies. Some of these have already been discussed, but others are part of the classroom environment, rather than the lesson itself, such as the classroom routines. The example lesson plan makes reference to a visual timetable on the white board, which helps the children to know where they are going next. This adds structure, and safety to their daily routine. It can often be confusing for EAL pupils when they are transitioning between lessons, so knowing that there is somewhere they can go to see where they need to be next.

One of the most important things to remember is that a child may be much more able in mathematics than they appear to be, due to their language barrier, so it is extremely important to give them the support they need to access their full range of mathematical ability. These children can often become frustrated when they are blocked from progressing due to their lack of language. This frustration can appear as disruptive behaviour, and this can then impact on the child's overall performance.

In conclusion, children with EAL require a variety of methods of support during mathematics lessons, in order to reach their learning potential. Strategies such as guided discovery, scaffolding, visual representations, translation sheets and the use of co-operative groups and strong-language-buddies create a structured and stimulating environment for these children to work in. Within this safe space, children with EAL should find it easier to assimilate this new mathematical vocabulary, as well as improving their English-language use through interaction with their peers. Whilst this may be a lot for a child to take in within the space of a single lesson, it will double the speed of their progress, and allow them to fulfil their full potential learning rather than being trapped behind the barrier of an unfamiliar language. It is also important to monitor the progress of these children, for example by providing them with self-assessment sheets for understanding, as noted in the lesson plan. This can give a quick indication to the teacher as to the level that these children are working at, and any alternations needed to the differentiation levels. Finally, it is essential that their first language is not de-valued. Traditionally, 'distinct separation and clear boundaries between two languages in the classroom and curriculum have often been advocated.' (Baker, 2000, 96) But securing a link between the familiar, and new languages is essential for these children's understanding. These children are mastering a second language, placing them ahead of their peers in that respect. This must be recognised, and the children reassured, as it is easy for them to feel 'behind' compared to their English-speaking peers.

Reference list

. Baker, Colin, The Care and Education of Young Bilinguals: An Introduction for Professionals, (USA: Multilingual Matters Ltd. 2000)

. Coggins, Debra et al., English language learners in the mathematics classroom, (London: Sage Publications, 2007)

. Echevarria, J., Vogt, M.E. & Short, D., Making Content Comprehensible for English Language Learners: The SIOP Model, (Boston: Allyn & Bacon, 2004)

. Finocchiaro, Mary, English as a second language: From theory into practice, (New York: Regents Publishing Company, 1974)

. Garrison and Mora, Adapting Mathematics, "Instruction for English-Language Learners: The Language-Concept Connection", Changing the Faces of Mathematics: Perspectives on Latinos (March 1999), pp. 35-48

. Levine, Josie, Bilingual learners and the mainstream curriculum, (Basingstoke: The Falmer Press, 1990)

. Thompson, Kersaint, Richards, Hunsader, & Rubenstein, Mathematical Literacy: Helping Students Make Meaning in the Middle Grades, (USA: Heinemann, 2008)