MA Dissertation: 'Does adding maths...'
Does adding Maths to ESOL learners’ timetables improve their acquisition of English?
Introduction
This enquiry based project sets out to find out if ESOL (English for Speakers of Other Languages) learners might benefit, in terms of their acquisition of English, from studying maths. This research has been conducted at a medium sized FE college in the East Midlands where I teach. I hope to evaluate this in two ways, firstly by analysing learners’ results, and secondly by asking experienced ESOL teachers to observe and reflect on an ESOL Maths session.
The learners involved in this project are all people who have voluntarily signed up for ESOL Maths, and may have just arrived in the UK, or been here for many years. They may have opted to come to the UK for work or family reasons, or been subjected to political or social persecution in their country of origin. The learners are all over 16 years of age so past the age for compulsory education in the UK; most are adults, 19 or over. The primary motivation for many of the learners attending ESOL Maths classes is to improve their English, and this can be for a number of reasons, including improving their job prospects or helping their school aged children.
ESOL Maths learners form part of a number of wider educationally-based communities, namely mathematics learners in the UK, ESOL learners in the UK, and, globally, those whose first language (L1) is not English who are learning maths in English. They may come from many countries and cultures which can be very different, both from the UK and each other, in terms of the content of maths lessons and assessments, mathematical symbols and language, and the value placed on mathematics learning.
In addition the landscape of mathematics learning can be seen to be changing in many countries including the UK, due to such factors as the development and accessibility of computer based technology and resources, and changes in funding.
Chapter 1: Literature review
1.1 The International Aspect
1.1a Education in English
Literature relevant to the enquiry comes from many parts of the English speaking world, which highlights the semi-international nature of both maths and English teaching. I have looked at sources from the UK (Barwell 2009) {including Wales (Jones 2009)}, Pakistan (Halai 2009), Malta (Farrugia 2009), Australia (FitzSimons 2002) (Clarkson 2009), the USA (Chval and Khisty 2009) (Kersaint, Thompson and Petkova 2013), Somalia (Staats 2009), and South Africa (Adler 2001), and whilst they are not specifically about ESOL Maths as this is a new line of enquiry, they are all studies of learners who are acquiring maths in a language which is not the learners’ first language, and, as such, they can be seen to inform thinking on the nature and substance of ESOL Maths courses, both from analysis of similarities and of differences in classrooms worldwide.
Much of the research in this field has been conducted in countries with original populations who have assimilated an additional language as a second, or even third, language, for instance in South Africa and Australia. This language has then become the language of education, economics and politics in those countries (FitzSimons 2002) (Adler 2001), although it may not be spoken by most inhabitants. In the 1996 census of South Africa “only 8.6% of the entire population gave English as their primary or main language” (Adler 2001, p19). This is not the case in England, as here the learners signing up for ESOL Maths are migrants to the UK, and are voluntarily studying maths in English, rather than having maths in English imposed upon them (Farrugia 2009) (Halai 2009), so this conflict does not exist in my classrooms, although I encourage the use of the learners’ first languages to enhance understanding (Stacey 2012), (Clarkson 2009) .
1.1b Funding considerations
It is of interest to the enquiry that texts published over ten years ago, and in other countries, read like books that could have been written in the UK today, for instance, in ‘What Counts as Mathematics?’ (FitzSimons 2002), written in Australia, we find discussed, amongst other topics, the moves in Education to cut teacher costs by using unqualified maths teachers (BIS 2012), decreasing face to face teaching time for learners, and encouraging the use of Virtual Learning Environments (VLE) and other methods of flexible delivery, so we can see that these issues are not just faced by the UK (Newmarch 2005), but follow a global pattern.
Political moves reducing funding in the FE sector is causing class sizes to rise and encouraging colleges to move towards use of a virtual learning environment, or VLE. This is to alleviate the need for face to face contact time with students, and is not just happening in the UK (FitzSimons 2002). ESOL is seeing a reduction in QCF funding which is leading to a reduction in hours, bringing ESOL in line with FS Maths and English (Hancock 2013. pers. comm.). ESOL Maths courses give learners an opportunity to increase teacher contact time at no cost to themselves, up to Level 2 qualifications (BIS 2012).
In the context of mathematics teaching this reduction in contact time could be conceived as a disaster, as misconceptions are often only eradicated with an experienced professional who can analyse errors and make corrections (Brown 2001). This is true for any learner, and “maths teaching is not about sitting in a classroom or at a computer” (FitzSimons 2002, p219); it is a much more active process when done well and effectively, and that is true for any student regardless of their first language.
FitzSimons also bemoans the lack of support for the VET (vocational education and training) and Adult sectors, compared to the emphasis on the school curriculum (FitzSimons 2002). However in my experience much of the work and developments going on in the school sector are also applicable to the adult sector, especially those in Primary education, as many of our learners have not actually progressed beyond entry level, although there is a need to ensure that if resources are used from the primary sector they are made appropriate for the age and cultural needs of the learners (Wilkins 2009). For instance a recent conference for the primary sector revealed strategies in use for EAL (English as an Additional Language- the term used for school based learners up to 16/17 years of age) learners in school Maths sessions that could be applied in an ESOL Maths classroom (SHU 2012).
Whilst these concerns are echoed in UK publications (Newmarch 2005), there seems to be a consensus that funding attached to qualifications encourages teachers to teach to the test, rather than developing mathematical understanding, which in turn devalues the qualifications involved (Brown 2001). There also seems to be a general acknowledgement that studying maths in a second language will not be as successful as studying it in a first language (Barwell 2009), (Adler 2001), (FitzSimons 2002), but the emphasis for my learners is focussed around their need for better English, rather than their maths (Weaver 2010), so the focus of this study differs from many of these investigations.
Some research has been done on the effectiveness of ESOL provision taught alongside other subjects such as sport, and this has been judged as successful (Hately-Broad 2006). I need to be aware that it may not be the teaching of maths that is a key to improving English acquisition; additional teaching of any subject that the learners are interested in could also improve language learning. However in other subjects adults will be charged for courses; Maths classes up to Level 2 are offered free to learners in the UK.
1.1c Confidence with Mathematics
There seems to be global concern surrounding the difficulties that many people have with maths which has led to debate on how and where this needs to be addressed. There has been a move to rebrand maths for adults as numeracy and to suggest that “numeracy is more than maths” (Tout 2006, p378) in an attempt to get adults put off by school experiences to reengage with it. Adults, including highly qualified ones, can lack confidence in maths “sometimes verging on maths phobia” (Macrae 2003, p104), and this can be seen in most cultures, including the UK, America, Europe and Asia (Macrae 2003). The importance of initial experiences of learning maths and the crucial role teachers and parental attitudes play in this is acknowledged in many reports and research work (Coben 2003) (Macrae 2003).
Teachers act as an interface for these learners, so need to be “enthusiastic- and that this is reflected in their facial expressions, their choice of words and their body language “ (Pound 2008, p66). Learners need to feel able to ask why, and get effective answers. Maths needs to be enjoyable and lively rather than “facts to be learnt” (Pound 2008, p101). These comments were made about early year’s education, but they are just as true for adults as children. Adults will value maths more if they can see that it has a purpose so will benefit from teachers who can tie it to “socially orientated decision making” (Pratt 2012, p21) to give a “utility based understanding” (Pratt 2012, p22).
It may be that the learners who have opted for ESOL maths at my college either do not share these negative experiences of maths or view the classes as extra English and therefore do not transpose previous experiences in the same way as other adult learners. Some research into language learning suggests that a reduction in anxiety levels is a crucial factor in improving language acquisition (Krashen1982 in (Wilkins 2009).
Current funding restrictions in the UK seem to be encouraging colleges to deliver maths to ESOL students as a way of drawing funds, and I know of one college in the West Midlands which intends to make maths lessons and qualifications compulsory for ESOL students. It seems likely that given the above points on views of maths (Coben 2003) the outcome for other colleges and learners might be very different from my own.
1.2 Learners and their profiles
1.2a Similarities and differences between ESOL and Non-ESOL mathematics learners
When teaching ESOL Maths I aim to support either maths or English teaching, or both, depending on the profile and needs of the learners (Adler 2001) (Jones 2009). Maths teaching for all learners can be informative, investigative or some combination of both.
Many of the issues which confront teachers of monolingual adults in maths classes may be present in ESOL Maths classes. For instance often teachers have to overcome an aversion to mathematics with adult learners whose first language is English (Newmarch 2005); many years of compulsory maths education combined with a feeling of being out of their depth for much of the time can leave potential learners with a fear of maths that can take some while to overcome (Macrae 2003). These needs are not generally recognised (FitzSimons 2002), and whilst society tends to be highly critical of those with poor maths skills, it is often not very helpful in helping people to improve (FitzSimons 2002).
Some ESOL learners will have low maths skills like monolingual learners in other Numeracy classes, but others may have high skills, in excess of those of the teacher in some cases, such as the engineers in one of my own classes (Newmarch 2005), thus “the range of skills among these learners may be very diverse: some may already have high levels of maths while others may have little or no formal schooling” (Newmarch 2005, p6). This is a fundamental difference from the usual maths provision, and I will need to consider if this is having an impact when considering the implications of my results.
This indicates a need for ESOL Maths teachers to be cognisant of and sensitive to the spiky profiles and educational backgrounds of their learners, many of whom may only be in the maths classes in order to improve their English (Weaver 2010), (Stacey 2013). Improving our understanding of learners’ profiles could also include developing an awareness of mathematics teaching in the learners’ countries of origin, both in terms of how maths is taught (Back 2013) (Clarke, Keitel and Shimizu 2006), and what is taught (Barwell 2002) (Clarke, Keitel and Shimizu 2006). For instance, the words used for ‘add’ in the UK include ‘and’, ‘altogether’ and ‘plus’, but other languages use different words than those used in the UK, including ‘extra’ and ‘joined’ for add (Barwell 2002). This knowledge can help teachers focus on what to teach learners to improve their chances of success on their maths courses, skills which are given a high status in many cultures (Coben 2003) including our own.
It also supports the need for some teacher training for ESOL Maths teachers, additional to the current training format, and to include information on the more uncommon of some of the UK curriculum topics, such as the work on estimation, which does not appear in all cultures (Stacey 2013).
Comparisons of how maths topics differ between countries leads me to think that we should encourage all ESOL learners to study maths in the UK, as what is taught could be needed in the UK work environment, such as the importance of pronunciation of amounts, and the devastating consequences of confusing 15 and 50 in, say, the NHS (National Health Service) (Colquhoun and Delaney 2009).This example of mispronunciation by not sounding word endings is common in languages as diverse as French and Chinese, and can impact on other learners, especially in paired or group work (Barwell 2002), or on formative assessment, in addition to implications in the work place.
The profiles of ESOL learners will also reflect their competence in English, and this competency will have a dramatic effect on their ability to assimilate the teaching (Barwell 2002). As a result we could expect the ESOL learners’ profiles to be spikier than those of native English speakers, as they “may have grown up in developing countries where there was little opportunity for education, or they may have fled from a country ravaged by war.” (Newmarch 2005, p5).
These profiles will be quite different to those of other learners disadvantaged by learning difficulties, such as those with dyslexia (Newmarch 2005), as such conditions might impact on such skills as recalling times tables facts. An ESOL learner might also struggle to recall those facts, but for very different reasons, such as decoding issues for those whose first language does not use a Romanised script (Sutherland and Spiegel 2009), however ESOL learners may also have these conditions, diagnosed or not.
Some research on dyscalculia and the functioning of the brain during mathematical activity seems to show that recognition of Arabic numerals is stored separately from word recognition in the brain, as is retrieval of arithmetic facts and manipulation of numerical quantities (Colwell 2003). As many ESOL learners will use the Arabic number system this could benefit learners in terms of an improvement in their English and may help explain improved ESOL results if these exist.
Some literature suggests that mixed level classes in ESOL do not work (Pitt 2005), but the unique profiles of learners in my ESOL Maths classes (Newmarch 2005), and the divergence between their English and maths skills means that mixed level classes are likely to be the norm, but any negative effect is likely to be offset by the levels of motivation of the learners (Newmarch 2005). I am likely to get those “learners who do not have English as a 1st language (who) want to learn how to do maths in English” (Newmarch 2005, p6) as ESOL maths is optional for our learners.
1.2b Learner motivations
Motivations can include wanting to improve job prospects, help children at home, or move on to university courses when the more academic language of maths can be useful (Newmarch 2005) (Clarkson 2009). “The power to learn depends upon the will to learn” (Spencer and Ingram 1952) shows that the importance of motivation for learners who are past the point of compulsory education has long been recognised.
It may be that the ESOL learners who sign up for ESOL Maths may be more motivated than others, they have signed up for an additional class lasting for 2.5 to 3 hours each week, over a 35 week period. This motivation could arise from necessity, perhaps a visa extension depends on it, or from interest, perhaps they have always loved maths and/or been good at it, and want to know how it differs from maths in their country of origin. Learners may have a child who needs help with homework (Newmarch 2005) (Pound 2008), or want to improve their maths for economic reasons such as employment opportunities or promotion.
The importance of the role of parents in affecting their children’s confidence with maths is exacerbated for migrant families and this factor may encourage ESOL learners to engage with the maths course (Milloy 2006). A lack of confidence is easily transmitted, (Macrae 2003) so “adults (need to be) enthusiastic- and that this is reflected in their facial expressions, their choice of words and their body language” (Pound 2008, p66). Parents who have first-hand experience of the UK education system are also less likely to need their children to act as mediators between school and home, which relieves “additional stress placed on children when their parents are not familiar with the school system” and “lightens the load for the children” (Pound 2008, p103).
Equally learners may simply wish to improve their English acquisition and see the class as a cost free option for more ESOL. These classes give learners teacher contact time, a vital factor for some in acquiring English, as many learners will live and work in an environment where little or no English is spoken, so may only get the opportunity to hear and speak English in the classroom (Stacey 2012).
The data analysis I am undertaking will not offer any explanation of why ESOL Maths students might perform better in ESOL qualifications than those who have not opted for it, but from my experience of teaching this subject for some years I would expect this to include some or all of the above reasons, bearing in mind that every learner is an individual and will have a unique set of circumstances and motivations.
1.3 Language in the Mathematics classroom
1.3a Language in mathematics
It would seem that mathematics language can be different to everyday language in English; ESOL learners will be disadvantaged in their Maths achievements by a lack of knowledge of mathematical terms in English (Barwell 2002) (Newmarch 2005), such as the use of different words, symbols or figures (Barwell 2009) (Swan and Smith 2001). For instance, mathematical symbols vary between countries and what looks to a UK learner like a decimal point (which incidentally is represented as a comma in the rest of Europe (Milloy 2006)) will instruct many ESOL learners to multiply, and what looks like the symbol for ratio in the UK is the division symbol for most of Europe. Learners will need to be aware of the UK system to be effective in examinations, if not in other areas of life.
Learners might be further disadvantaged by the wordy nature of the assessment materials for the current curriculum (Brown 2001). In allowing learners to use their L1 in the maths lessons, I run a risk of misunderstandings being consolidated because I cannot speak the language of my learners. Those teachers who are themselves bi or multi-lingual have a decided advantage here (Jones 2009), and can encourage learner talk in the classroom, which is a help with learning (Farrugia 2009) (Adler 2001). Equally the opposite will apply, and learners whose talk is restricted by lack of language will learn more slowly (Barwell 2009). As teachers we need to contextualise the mathematics (Newmarch 2005) (Pratt 2012), but this has big implications for ESOL learners.
As a teacher I need to be aware that differences between languages may slow down learning, but also be aware that sometimes this could speed up learning, for instance in Welsh the word for quadrilateral translates as four sides (Jones 2009), giving Welsh learners a potential advantage in exam questions.
Finally, there is a growing realisation in multi and bilingual classes that learners “are making more use of their first language than teachers may realise” (Barwell 2009, p164). This contrasts with my own ESOL maths classes, where I actively encourage the use of the first language by using on line translation facilities on the smart board, providing opportunities for L1 discussions to take place, and encouraging the use of book and electronic dictionaries (Stacey 2012). Thus perhaps I am facilitating ESOL learners’ acquisition of English as they are more likely to translate into their L1 in a maths class than in an ESOL class.
1.3b Investigative mathematics
The move of mathematics teaching and learning away from a knowledge based approach to a more contextualised, problem solving approach is clearly visible here in the UK and is evidenced by both GCSE Maths and Functional Skills exam papers with their increasing reliance on the student’s grasp of the English language, almost at the expense of mathematical knowledge (Brown 2001). This is also happening in Australia, and may have long term implications for the teaching of maths there, possibly leading to its demise in its current form where the basic four number operations are the focus of teaching (FitzSimons 2002). This move can be seen as detrimental to ESOL learners, as it increases the complexity of the language content of exam questions. In my classes where I am teaching Functional Skills maths this is causing a back slide to lower levels of exams than the maths skills of the learner would indicate (Barwell 2009). For instance an ESOL learner with a Master’s degree in Mathematics who has recently entered the UK and is completing Entry 1 English has come out at Entry 2 to 3 FS Maths on initial and diagnostic testing. On the other hand from the adult learner’s point of view it is probably improving their English skills, which is often their motivation for attending anyway (Weaver 2010).
Another barrier to ESOL learners achieving maths qualifications is the contexts in which scenarios for exam questions are set (Barwell 2009). These may not be familiar to ESOL learners and attempts to translate may only result in further confusion (Staats 2009). This can be an issue for English speakers as well, for instance school aged GCSE students with little life experience may struggle to decode questions on making a profit from, say, running a bakery, but ESOL learners will have extra tensions arising from these increasingly common types of questions. This would support the case for offering ESOL Maths classes to ESOL students, as in this way they are almost on a par with English speaking students as they attempt to decode complex social scenarios (Brown 2001) (Barwell 2006). If this is the mathematics of the future, where calculators do the calculations and humans decode and problem solve, everyone may benefit from Maths classes (Brown 2001). If “language forms maths phenomena” (Brown 2001, p49) and “maths activity is a subset of social activity” (Brown 2001, p25) then as ESOL exams are equally as “linguistically placed in society” (Brown 2001, p19) as maths, I should expect ESOL maths students to have better ESOL results than non-maths students.
The situation in South Africa is one where teaching maths in bi/multilingual classrooms is the norm, as the country has over ten official languages, only one of which is English, but this tends to be the language chosen by secondary schools for teaching maths, so that learners are not “disadvantaged in further education and employment” (Adler 2001, p2). Interestingly, the teachers’ first languages may not be English either, and many may have a common language with the students. These teachers find themselves explaining concepts and methods in the common language, before translating back to English (Adler 2001). Sometimes I do this myself, as I tend to give information in French if I have other French speakers in the room, and use an online translation facility on the Smart board, so I can type in instructions and information and translate into many of the first, or second, languages in the classroom. This is also occurring in other countries, such as Wales (Jones 2009), Pakistan (Halai 2009) and Malta (Farrugia 2009).
1.3c Teaching considerations
Teaching in classrooms where the most or all learners are not using their first language does clearly need to be different to other maths classes, with an increased focus on clarity, and therefore language (Clarkson 2009). We need to reinforce and reiterate instructions in more than one medium by, say, writing instructions on the board as well as giving them verbally (Baker and Westrup 2000). We need to explain or translate key words and terms (Newmarch 2005), especially where those mathematical words differ from the ‘normal usage’ (Monaghan 2009, p24). We need to allow students to help each other, using their first language as necessary (Jones 2009) (Adler 2001) (Baker and Westrup 2000) (Halai 2009). We need to show that we value students own methods and cultures (Colquhoun and Delaney 2009), and draw on their experiences to add meaning (Barwell 2009).
Adler’s research into teachers views led to the following list of “contradictory assumptions:” (Adler 2001, 6-7)
“Maths is difficult for everyone, irrespective of the learner’s main language”, as there are problems of understanding to do with maths itself
Learning maths in a language that is either or neither the teacher’s or learner’s places complex demands on both
“Language is learnt through use”, so learners must use English in class (if that is what they will be examined in)
“Learners need to be able to use their main language in mathematics lessons- they can’t understand some concepts if they are only explained in English.”
This correlates with my own views and experience of teaching maths to non-English speakers. She emphasises the increased complexity of the process of guiding and supporting learning in the modern teaching environment, with its focus on facilitating learning, rather than teaching, especially in investigative tasks, and the necessity of letting leaners speak their first or common language when working out solutions, and then translating back with the answers (Farrugia 2009) (Halai 2009) (Adler 2001). I would agree with this and encourage the use of first languages between learners in my groups, but some ESOL learners might not want to do this as they are often attending Maths classes in order to improve their English. They welcome paired and group work as an opportunity to practise their English speaking skills (Stacey 2013) (Weaver 2010).
In Adler’s research this has raised a dilemma, though, as sometimes the teachers can see that the process has gone well, but the answer given is incorrect due to a mistake in translation (Adler 2001). Perhaps due to class sizes teachers are struggling to give timely and appropriate feedback to learners, and to separate out the maths and language issues which could ‘obscure maths attainment’ (Barwell 2009, p4). I have not noticed this in my own work, but I am probably dealing with smaller class sizes and have time to reward the maths achievements whilst correcting the English. However there may be times when I have assumed the method was wrong because the verbal feedback has been incorrect, and I need to remain vigilant about this possibility.
Perhaps for any learner, maths is now so linguistically placed in society, that is all we are teaching or assessing (Brown 2001). The complexity of the exam system and the volume of students involved can be seen to have led to “a down playing of mathematics which does not lend itself to categorisation or easy transference in language” (Brown 2001, p99). His view is that we are still teaching some geometry that does not easily fit into algebraic based, easy to assess maths, because this topic ‘does not lend itself to easy description’ (Brown 2001, p99), but the use of this has declined. My own thoughts and experience would support this, as in FS Maths with the exception of scale drawing (which, coincidentally, most learners find really difficult) I am largely teaching definitions, how to use a calculator, and how to solve problems by breaking them down into small steps. The GCSE course certainly has more geometry and a need for students to be able to do maths without a calculator, but it is otherwise broadly the same.
Perhaps, past the basic four number operations ‘(h)uman linguistic constructs have been responsible for forming mathematical phenomena rather than vice versa.’ (Brown 2001, p49). Cultural differences make sense in different societies, and this may be influenced by language amongst other factors. It is clear that in ESOL Maths there are some elements of maths learning going on at the same time as language acquisition, along with social and cultural learning. I could expect this to benefit learners and thus that ESOL maths students will out-perform non-maths ESOL students, but equally need to be aware of the possibility that there is a negative impact on learners if they are distracted from their main ESOL course.
Recent research on the correlation between knowledge of the basic four number operations combined with instant recall on times tables facts and an ability to problem solve indicates that there is a correlation between these factors and a feeling among learners of being good at maths (Dobbs 2013), as touched on in the previous section on learners profiles. This correlation vindicates our current approach to maths teaching, but if there had been no correlation or this is eroded by an increasing reliance on calculators, perhaps maths teaching could change and become more like ESOL Maths teaching with its emphasis on language interpretation and question de-coding (Fletcher and Barr 2009). Some researchers already believe that learners only need sufficient knowledge of the language of mathematics to be able to transcribe problems to put in a calculator (Brown 2001). These are big questions for the future of Mathematics education world-wide.
1.4 Resources used in the classroom
1.4a Abstract vs concrete resources
Resources in maths classrooms are broadly split into two types, those which enable students to practice computations and those which contextualise the mathematics. The first type can be seen as abstract and the second type as concrete; movement from one form to the other “is to reify” (Pratt 2012, p3) and this is seen as a high level function. The “application and use in context” (Pratt 2012, p7) is what gives maths its meaning or power. I use both types of resources in ESOL maths classes depending on the needs of the learners; I use existing materials, such as those available on the internet (BBC 2013), and develop my own in response to the requirements of the learners or the session. Some of these are now available on a website I have created to help other teachers in this sector (Stacey 2013).
The extra layer of activity that occurs in an ESOL Maths class as opposed to a class for English speakers is focussed on the extra language needs of the learners, but it is useful to note that when I give the ESOL biased resources to other classes they are often engaged with, enjoyed and contribute to understanding. This is especially true of the lower ability, Entry level classes, and may highlight the need for teachers to be more aware that whilst we may be apparently speaking the same language in many maths classes, in practice what we think we have shared with our learners may not be understood by them in the way we expect or intend (Monaghan 2009). Indeed, as the teachers skills are generally higher than the learners there is every chance that we are seeing patterns and correlations that are either partly visible or invisible to our students. This insight was also recognised in research carried out in bi- and multilingual classrooms in South Africa, when resources designed to help learners with a lower level of English benefitted the whole class (Adler 2001).
There is a need to be more aware of the language used in resources in ESOL Maths classrooms, both to aid learner understanding (Wilkins 2009) and to enable learners to answer mathematically framed questions (Monaghan 2009). This will mean explaining new vocabulary at start of sessions and using pictures or real objects to add meaning for learners (Wilkins 2009) (Monaghan 2009). It may also help learners if resources are contextualised using their own lives and experiences (Barwell 2009) (Wilkins 2009), as this will aid understanding, and again this type of practice can be seen to help all learners engage and make sense of materials used in Maths classes. The use of materials either supplied by learners or built round problems they were experiencing in the UK can speed up language acquisition, improve engagement with classes and foster “a sense of solidarity in (a) group” (Lucero and Thompson 2006, p421).
The use of materials from learner’s own lives could include such items as bills, wages slips, bus timetables and bank statements (Barwell 2009) (Fletcher and Barr 2009). This could encourage concentration and engagement with topics and enhance learning, although we do need to be aware that such material might marginalise and exclude some learners for whom it might not be relevant (Fletcher and Barr 2009). Learners at a more advanced stage could be encouraged to write word problems (Chval and Khisty 2009), which are then given to the whole class to solve, which might help raise everyone’s’ awareness of some of “the innate rules in word problems, (and) of some of their subtleties” (Barwell 2009, p67); both teachers and learners could benefit from this approach.
1.4b Games, quizzes and calculators
Games and quizzes are ways of relieving tension for learners in maths classes, moving them to more relaxed and less overt learning (Newmarch 2005) (Baker and Westrup 2000). This approach can be as beneficial in ESOL Maths classes as it is in classes for native English speakers, and can be an effective way to encourage speaking and listening, which can help learners to “make it (the language) their own” (Clarke, Keitel and Shimizu 2006, p133). It can also reinforce turn taking and generally develop social interaction amongst learners, although it may be necessary to simplify instructions, define key terms (Colquhoun and Delaney 2009), and remove colloquial language, as it would when using Literacy resources in an ESOL class (Fletcher and Barr 2009). There may be a place for translating instructions into the learners’ first languages (Pitt 2005), at least in the early stages of a class, to help relieve anxiety, and this would be most beneficial if left alongside the English, so learners start to see the connections.
Care needs to be taken that materials are culturally sensitive, and this will be covered in more depth in the next section, but many maths games have little or no cultural implications as they have been devised to help people practise their maths skills, such as ‘Numenko’, a numbers based game on the lines of ‘Scrabble’, or ‘Qbits’, which supports learning of multiples and factors. Dominoes games using fractions, percentages, decimals, or whole numbers, and size ordering activities can help develop the learners’ comparatives and superlatives vocabulary (Wilkins 2009). The use of games in the ESOL maths class could be helpful to parents if it gives them an insight into the school experiences of their children and an opportunity to share that experience within the family (Pound 2008). Not all parents may choose to do this, but it does broaden their options.
The use of calculators in ESOL Maths classes where the method of assessment is a maths exam, such as functional skills, is vital, as students will need to demonstrate their ability to use a calculator at Entry Level, but this is also a life skill (Chval and Khisty 2009) that can help with learners’ job prospects, as evidence suggests that people who are numerate and confident with numbers are more likely to be in work and get promoted (Newmarch 2005).
1.4c Initial, diagnostic and summative assessment
The inappropriateness of the formal materials used in the UK for assessing and examining ESOL learners who undertake a maths qualification is an issue which has also been identified in other countries (Adler 2001), but this concern is echoed by those undertaking research to evaluate those materials particularly for those with low levels of English or maths skills (Newmarch 2005). Particularly in the initial assessment process this can be very distressing for adults who had limited access to formal learning at what is considered in the UK to be school age (Colquhoun and Delaney 2009), which might lead to them disengaging with learning altogether (Newmarch 2005).
Currently we have a number of initial and diagnostic assessment tools to use but these, like the Adult Numeracy Core Curriculum (Excellence Gateway 2011), have been designed with English speaking maths students in mind, and the level of English skills required to interpret the questions will lead to learners underperforming in terms of their maths skills (Barwell 2009), as evidenced by a number of learners in my classes with degrees from their country of origin in Mathematics or Engineering, who are studying maths in English at Entry level. From this we can see that potentially what is being assessed is not maths at all, but the learners’ levels of English. However, as dictionaries are allowed in ESOL Maths exams, some learners will perform above their English level, perhaps indicating a higher than average ability to decode maths problems (Halai 2009). This approach contrasts with mainstream education in the U.S.A., where “since the early 1990s it has become more common for ELL (English Language Learner) students to be mainstreamed into mathematics classes at their level of mathematics proficiency, not their level of English proficiency” (Kersaint, Thompson and Petkova 2013, pXIV).
For functional skills provision in the UK Maths Level 1 and Level 2 exams can be computer based, as can other funded adult provision, such as the City & Guilds 3844 (City and Guilds 2013). Initial and diagnostic exams at all levels are often completed using IT (Guroo Functional Skills 2014). This can disadvantage those learners who are unfamiliar with computers but this can be seen as an opportunity to improve IT skills in ESOL maths classes, which again could benefit the learner in the long term.
Investigative mathematics forms a substantial part of the assessment process in the UK, and is very challenging for many learners; it is even more challenging for learners being asked to work in a second or third language (Adler 2001), which is perhaps why, when I surveyed my learners for a project, they said they liked worksheets best (Stacey 2013). When I look at my own practice, I can see that whilst I confidently ask my GCSE groups to, say, investigate the existence of pi, by drawing a series of circles and dividing the circumference by the diameter, using a ruler and some string, I might do that with a (mathematically) strong adult group of English speakers, but I would be very unlikely to do that with an ESOL group, especially at Entry level. In effect, the amount of investigative maths I use is on a continuum and dependant on both the mathematical and linguistic competence of the learners (Farrugia 2009).
The argument for investigations is that they promote mathematical understanding, but this cannot be so for those with a low language competence, in fact they are likely to be intimidating and reduce learners’ confidence, because they would in most cases simply be too difficult (Barwell 2009). When I look at the gaps that ESOL learners present with, they are mostly those that can be filled by information, not investigation, and when I look at the ESOL worksheets that I have produced to help learners, that is what I see: Information. As previously stated, I have found these resources to be useful to other groups, and this is supported by Adler’s view, as she also notes the benefits of mathematical language information on the whole class, not just those with low English skills (Adler 2001) (Newmarch 2005) although “if all questions are (about) clarification… deeper mathematical thinking could be constrained” (Adler 2001, p104).
1.5 Cultural differences and their impact on the classroom
1.5a Teacher/learner relationships
There are a number of ways that cultural differences can be seen to impact on multi or bilingual classes, and much of this research material is also applicable in ESOL Maths classrooms.
Different cultures have differing views on how teachers should be treated and on what adults should know, and some of my leaners are wary of saying in front of others that they need help, in case it reflects badly on my teaching, or causes them loss of face in front of their peers (Wilkins 2009). Whether I am assessing their maths or English learning will vary from learner to learner and depend on the lesson content and the learners’ previous experiences, so may be highly individual, rather than the overview we are more used to in English speakers’ classes (Colquhoun and Delaney 2009).
This raises a point in bi/multilingual classrooms of assessing learners, and for teachers to be aware that it may be more appropriate to check individuals learning by marking work or one to one discussions, rather than checking on individuals in front of the whole class (Wilkins 2009) (Colquhoun and Delaney 2009).
There is a further issue around valuing learners’ mathematical methods which may be very different to those used in the UK. Current thinking acknowledges the need to look more broadly at Maths teaching, not just at how the number operations are performed (Brown 2001), but the emphasis to get those number operations right is the primary focus of maths teaching, and when working with any learner it is necessary to look at the answers prior to any interference in the methods in my opinion. For instance a division sum in the UK will look very different to a division sum in the rest of Europe. If the answer is correct there is no need to interfere, unless the learner has a particular need to understand UK methods if, for instance, they want to help their children with maths homework (Newmarch 2005) (Milloy 2006) and understand, quite rightly, that changing a method at an early stage of learning can cause confusion, loss of confidence and sometimes rejection of maths altogether (Macrae 2003).
A knowledge of how number operations are taught elsewhere would certainly be useful to ESOL and EAL maths teachers, in the same way that work exists showing how maths is taught and learnt in the UK, mostly with children (Brown 2001), as this could show that teachers value the contributions and differences between cultures (Barwell 2009). As far as I can see from my own experience, division has the most variation of methods, and not all learners, regardless of age or experience, have seen decimal division, perhaps because we have become more dependent on calculators worldwide. Maths teaching for adults in the UK and the emphasis on functional skills decreases the need for number operation teaching, so knowledge of other methods becomes less necessary, but if leaners are going to be encouraged to go further in their studies and take Maths GCSE, which has a non-calculator paper, sound methods of calculation will still be required.
1.5b Social and cultural considerations
When teaching ESOL Maths classes awareness is needed of the social and cultural aspects of the lessons, but this is increasingly true of all maths teaching (Brown 2001) (FitzSimons 2002), which is becoming increasing language based, which is itself “governed by culturally specific norms” (Brown 2001, p8). In an ESOL classroom this can be more diverse than we might expect when teaching native English speakers, for instance, there is a difference in communities in the UK on the roles that man and women assume, where some women may not handle money or even do the shopping. We need to be aware of the assumptions that we make about our learners’ life experiences, otherwise at the very least we might miss opportunities to extend learners’ knowledge.
Other topics on the Maths curriculum may demonstrate a lack of understanding of other social and cultural views of those who are resident in the UK. For instance some faiths prohibit gambling, which can impact on the way probability is taught by teachers and viewed by learners. Cards may be unknown in some households and banned in others. Quoting the work of A.J.Bishop, FitzSimons identifies six universal points for maths calculations, namely counting, locating, measuring, designing, explaining and playing (FitzSimons 2002), confirming that teaching maths is in fact much more than teaching the four number operations, but even this list is open to debate (Barwell 2009), and not everyone will practice all of those skills in every society.
The use of gesture has been identified as a useful resource when teaching non English speakers (Colquhoun and Delaney 2009) (Baker and Westrup 2000), but this can have cultural implications, as gestures can cause unintended offence if they have a meaning not used in the UK (Swan and Smith 2001).
Although there are many points of similarity between topics taught and used in ESOL, Citizenship and ESOL Maths, such as time, prepositions and shopping (Wilkins 2009), many topics taught are less likely to be covered in ESOL, such as carpet fitting or installing a pond, so whilst I would agree that teaching Maths should improve any person’s knowledge of English (Brown 2001), perhaps this may not be measurable by analysing ESOL results, but only by looking at ESOL Maths results, due to the specific nature of the topics and the nature of the mathematical language used.
In contrast, because so much maths is now set in social and cultural scenarios, with so much language commonly used in everyday life, perhaps there should be improved ESOL results for students who have attended both subjects, and a greater understanding for those students of the culture of the UK, even if it is only that learners are making progress as teachers become more aware of the range and depth of cultural assumptions implicit and explicit in so much of the maths work undertaken (Colquhoun and Delaney 2009) (Morgan 2009).
The value placed on maths education generally is highly visible in the UK and other cultures, where maths can be used as a filter for jobs and higher education (Black 2009), putting learners under pressure to do well, when maths competence may not be vital for their chosen progression. Some ethnic groups of students may be more likely to choose maths as “Asian and Chinese families (give) a higher status to mathematics” (Coben 2003, p98). An analysis of data by ethnicity or other factors such as age or gender is outside the scope of this investigation, but further work in this area is likely to be useful.
1.6 Summary
The effectiveness of delivering maths in English to learners whose first language (L1) is not English is the subject of consideration and research in many countries but there is relatively little research focussed on adult ESOL learners studying maths in English in the UK. Government funding for Maths up to Level 2 is increasingly encouraging FE colleges and other providers to deliver Maths to ESOL learners. Free courses are also encouraging ESOL learners to opt for maths, which gives additional teacher contact time in an environment where the focus is split between English and Maths.
The profiles of learners in ESOL Maths classes are likely to be spikier than those whose L1 is English due to wider variations in language, literacy and maths skills. Learners vary from those with low literacy and/or maths skills in their L1, to those with high levels of literacy and/or maths skills in their L1, but low levels of English. Learners may also have had different experiences of mathematics teaching which could impact on their expectations, confidence and ability, but all are clearly motivated to study maths as the course is not compulsory. These motivations could include improving job prospects, helping children or considering higher education in addition to improving their maths and/or English.
Maths teaching in many countries seems to have moved towards an investigative, problem solving approach and this is reflected in the Functional Skills maths provision here in the UK. This raises issues for all learners, especially those whose first language is not English, but these learners are allowed to use dictionaries in maths exams. Research shows that use of an L1 in maths classrooms does aid mathematical understanding, although it can raise issues for teachers if they do not speak the learner’s language, as misunderstandings can occur.
Resources that focus on contextualised mathematics with their use of scenario based activities are designed to help all learners improve their understanding of the language used in mathematical contexts but may be particularly beneficial to low level English users.
Teachers of non-English speakers need to be aware of many potential issues in the ESOL Maths classroom, including cultural differences and differences in mathematical conventions, symbols and methods in order to be effect for their learners. They will also need to be aware of the social and cultural content of many of the resources used in maths, and the necessity of information and guidance especially for learners with low levels of English skills. The role of the teacher in encouraging and engaging learners is important in all classrooms, including those with motivated adult learners.
Finally it may be that any other subject, especially one of which the learners have prior knowledge, taught in English would improve ESOL learners’ acquisition of English but this enquiry is focussed around the effectiveness or otherwise of ESOL maths classes in my FE college.
Chapter 2: Project Methodology, Methods and Ethics
2.1 A quantitative study
In order to ascertain whether adding ESOL maths to ESOL learners’ timetables has an impact on their acquisition of English I intend to compare the results of ESOL learners who have studied for maths qualifications with those who have not. This will be a small scale quantitative analysis based on an ESOL intake of approximately 130 learners each year, 11% to 18% of whom enrol for ESOL Maths.
This part of the project consists of an analysis of data held within my college, in the ABE/ESOL departmental files. This data includes records of achievements split by topic, so ESOL, English or Literacy and Mathematics are held for each learner in discrete folders. I will establish the total number of ESOL learners who have attended each year, over a 5 year period, from the 0809 academic year to the 1213 intake. I will then look at how many of those students also signed up for ESOL Maths courses, and evaluate their ESOL results against the rest of the cohort.
These data sheets are an example of a primary source, “those which came into existence in the period under research” (Bell 1993, p68). They have been produced in order to keep track of learners’ progress so teachers have an idea of how successful or otherwise their teaching and courses are, and so that learners can be moved onto the next level each year; thus they are an “inadvertent source” (Bell 1993, p68). They have not been produced in order to prove or disprove any theory, so are free from any inherent bias, vital for statistical research (Bell 1993).
It should be born in mind that this is a small scale investigation based in one college which has one ESOL Maths teacher, namely myself, although some higher level learners do attend an English speakers maths class if it falls on a more convenient day for the learner. Entry level learners are not encouraged to attend English speakers Entry level classes as they are deemed to need specialist help. As such I am examining the results of the whole population of ESOL learners at this college, of whom the ESOL maths students can be seen as a “subset of the total population” (Cohen, Manion and Morrison 2000, p92).
There has been an issue around who to consider in the analysis, for instance, should ESOL learners who are attending these 'normal' maths classes be included? Also should learners be included if they have been asked by teachers to 'sit out' for a year on ESOL, and take ESOL Maths as a way of skill building for the next level? I concluded that for inclusion learners must be attending an ESOL class where the intended outcome was an ESOL exam, at whatever level, E1 to L2, and whether it was Speaking and Listening or a full qualification. I included all learners regardless of which Maths class they attended, as it was only a few higher level ESOL learners who were affected by this, and my colleague who teaches alongside me is aware of and can access ESOL Maths resources and teaching techniques.
This has resulted in a maximum of twenty four students in any one year studying ESOL Maths out of an ESOL population of approximately 130 ESOL students. This is small even for correlational research, as “a sample size of no fewer than thirty cases” (Cohen, Manion and Morrison 2000, p93) is desirable. However as the whole college population is included, it is representative in a way that it would not have been if a sample had been used (Cohen, Manion and Morrison 2000).
There is also an issue around the data, as it differs from what might appear in an OFSTED report or in other government data held on the college. The reason for these discrepancies surround the interpretation of achievement, for instance centrally held data will focus on ESOL qualifications, recorded by a system called ProAchieve. However at the college we employ a wider portfolio of qualifications based on the ESOL learner's needs and requirements, so a small number of learners may have passed an adult basic or functional skills qualification if that was deemed most effective and practical. For the purposes of this data collection I have included all or any ESOL or English qualification, on the grounds that they all evidence an improvement in English acquisition. To give an indication of the size of this, in 1213 five ESOL learners (3%) passed a non-ESOL exam.
In a previous work I asked learners what they found useful in maths classes, why they chose to do ESOL Maths, and what they liked about it. This yielded the following two qualitative observations, namely that learners value the opportunity to increase their vocabulary of English words, and that they value the time to practise their pronunciation of English words and sentences (Stacey 2012)(Stacey 2013). I have chosen to analyse the data to see if these observations can be evidenced in some way by improved ESOL results, but in order to triangulate this information I intend to ask ESOL colleagues to observe an ESOL session and report back on their findings. This mix of quantitative and qualitative “can allow for triangulation of data” (Coben 2003, p111).
The analysis will not tell us why any correlation occurs, highlighting the limitations of data analysis (Bell 1993) and a positivist approach (Stacey 2013). It may be that the amount of teacher contact time has an effect, or that adult ESOL learners who opt for ESOL maths are more highly motivated than those who do not. I need to be aware that there may not be a correlation at all, and that if it does exist it may be for reasons unrelated to ESOL Maths; that it may be that any subject taught, from sport (Hately-Broad 2006) to flower arranging, could have the same effect.
Results may also be very different for other colleges even if they are in a very similar position to my own due to the number and extent of variables involved in different situations. There is no possibility in this type of study of isolating or controlling variables, which a positivist approach would depend on, thus “the issue of generalisation is problematical” and “others can decide the extent to which findings..are generalizable into another situation” (Cohen, Manion and Morrison 2000, p109).
It may be that there is a negative correlation on the data, as perhaps ESOL students are distracted from their main ESOL course by addition of maths classes. If so I will need to be prepared to inform my college accordingly. It can be “tempting to reject evidence that does not support our case”, (Bell 1993, p72) and I need to be on my guard for this.
In the analysis of data all persons will remain anonymous at all times. If it becomes necessary to refer to any individuals this will be done by letters only, as in ‘Learner A’.
The data will be collated by myself and analysed initially as discrete data. I will then convert the data to percentages to see if a pattern emerges over the five years under review. Whilst the data can contain no bias I need to retain awareness that the interpretation should also be free from bias. Attendances at many presentations at the university on research work enabled me to evaluate a variety of research methodologies to answer the question “Are you that sort of researcher?” (Richards 2009, p16). This is a work based project and the methods of data collection chosen do reflect my own personal preferences and interests.
I have obtained permission to use the data from the college, and approval has been given by the Ethics Sub Committee (Appendix A). I intend to supply various members of staff with a summary of my findings prior to submission, as specified in the Ethics submission.
2.2 A qualitative investigation
A qualitative investigation can be useful in a study as it may illuminate and inform the data analysis by giving reasons why the correlation might exist, if it does. The data analysis alone is limited by its positivistic approach; it can tell us that a correlation exists but it cannot tell us why. It is vital to be cautious in this project however, as the data sample is small and ‘reasons’ can start to imply causation which, due to the multiplicity and complexity of factors in social scenarios, cannot be known. “Care has to be taken not to claim more for results than is warranted”, and in small scale projects “generalisation is unlikely” (Bell 1993, p126).
I intend to investigate the views of teachers on ESOL Maths, in order to attempt to triangulate the data as “a mix of qualitative and quantitative can allow for triangulation of data” (Coben 2003, p111). Triangulation “may be defined as the use of two or more methods of data collection in the study of some aspect of human behaviour”, and can improve confidence in a piece of research “when different methods of data collection yield substantially the same results” (Cohen, Manion and Morrison 2000, p112).
I will ask four ESOL colleagues to observe an ESOL Maths session and to comment on various aspects of it, with regard to the learners’ reactions and responses, two from within and two from outside the organisation. When considering the question of “How many interviews should I do?” (Richards 2009, p19) I selected four as I believe this is a manageable number which should reveal a variety of thoughts and opinions. The opportunity exists within the time-frame of the project to extend this period of data collection if desirable (Richards 2009). In Appendix B there is a revised letter of agreement and sample questions for consideration during the observed sessions. Teachers can either respond back verbally at the end of the session or write on their thoughts and answers.
Careful consideration has to be given to the way the five questions that I will ask in the interview are framed so that responses can be checked for consistency and so that I “will be better prepared to organise and interpret (my) data” (Richards 2009, p17). The three main questions that I hope to answer are:
Can these teachers see any advantages of ESOL Maths, where the language is less overtly taught than in an ESOL class?
Do the students exhibit skills that they were unaware of, or that surprise them for the level those students are at in their English?
Does it make the teachers reassess the learners’ language skills levels?
The questions are open-ended to draw full responses (Ribbins 2006), but can be seen to be connected to allow for corroboration (Richards 2009).
I have also included a Likert scale “to discover strength of feeling or attitude” (Bell 1993, p139). I will ask observers to rank the usefulness of ESOL Maths in improving English acquisition on a scale of 0 to 10, where 0 is ‘of no use’, and 10 is ‘extremely useful’.
There is potential for any observer or interviewer to have an impact on a situation and peoples’ responses, as observed in other investigations, where observers become aware that they are an acknowledged presence in the room, and that this is disturbing the normal flow in some way (Brown 2001, p34). This is known as the Hawthorne effect, and it might affect both myself as the teacher or the students in the ESOL Maths class as we can “behave differently when subjected to scrutiny” (Cohen, Manion and Morrison 2000, p116). If I can reduce this effect it will improve the validity of the information I collect (Cohen, Manion and Morrison 2000), but this is a work based project in which I clearly have a vested interest as the main ESOL Maths teacher and I will need to consider this impact when analysing my findings.
It is also impossible for observers not to bring their own interpretations and innate bias to both observations and interviews, and I will need to be aware of my own bias, “socially, ethically and practically” (Richards 2009, p15) and that of my observers (Brown 2001, p33) , as this forms part of my investigation (Bell 1993). Choosing two observers from within and two from outside the organisation may add weight to the findings if similar observations are made, as we might expect less bias from those outside, who might have fewer vested interests in the college.
Engaging two teachers from inside the organisation and two from outside may also help to maintain the anonymity of those within the organisation (Bell 1993). All four will be volunteers and will be able to withdraw up to two weeks after the interview or observation. Their identity will be protected by using letters to refer to them. The letter of agreement was revised after the comments of the representative of the Ethics Sub Committee (Appendix A), in conjunction with my supervisor.
Teachers will be asked to do an observation of approximately 30 minutes with sight of the interview sheet, so they are aware of the focus of the subsequent discussion. We will then discuss their observations in a short interview. Interviews will be done the same day to avoid misremembering (Ribbins 2006) (Cohen, Manion and Morrison 2000). The interview will be about 20 minutes in length and I will write comments down and subsequently use quotes and refer to their opinions on the usefulness or otherwise of ESOL Maths classes.
One of the negative issues with conducting this study myself is that the outcome might be affected by my involvement. For instance there could be an issue with learners and colleagues giving less than honest answers to my questions as they, either covertly or overtly, do not want to hurt my feelings, and know that this is a topic ‘close to my heart’. This is known as “the halo effect” (Cohen, Manion and Morrison 2000, p116), where the previous knowledge of the observers affects their judgements.
An example similar to this is contained in the Basic Skills Agency’s findings in their report on retention issues in ESOL (Kambouri, Tontounji and Francis 1996). This was a quantitative study of over one thousand learners attending various educational establishments in the UK. The report surveyed ESOL learners to find out, amongst other things, why they were leaving their courses; it also surveyed teachers to find out why they thought learners were leaving. There was a 16 per cent discrepancy between two sets of data, with 20 per cent of learners citing dissatisfaction with their courses as the reason for leaving, but teachers believed this to affect only 4 per cent of the learners. This may be an example of learners, for perhaps cultural or other reasons, giving one reason to their teachers, but quite another reason to a survey which is perceived as independent from the institution attended; thus their answers are being adapted for their audience.
There is a further issue around how free my colleagues might feel to decline to take part in these observations, and whether I have made it clear enough that they are under no obligation to do so. This was particularly raised as a point for consideration in the feedback on the ethical submission (Appendix A), and I have accordingly revised the letter in conjunction with my supervisor (Appendix B), to reflect a more optional approach. I am unable to get completely away from any sense of obligation, given my previous relationship with the staff, as I have been a line manager in this area. I am aware of the need to be extremely cautious about this, and have considered asking someone else to conduct the interviews, but do not feel this will yield as much insight as if I am there in person (Bell 1993). I have trialled the interview sheet with a colleague who has left the college in an attempt to evaluate the material with someone who knows the area, but who now has no commitment to the college or to me, but feel this is still a challenge (Bell 1993).
Other points for consideration are that teachers are very busy, so I will need to offer several opportunities for observations, and that sessions may differ in content and format, so I will need to take notes I order to set the scene for the final report. I have considered trying to standardise the sessions but have discounted this on the grounds of practicality. ESOL maths sessions are planned but follow the needs and demands of the learners, and any changes to the teaching style and format could impact on the learners which in turn could affect the assessments of the sessions.
Finally, I need to be aware that:
Other teachers may not see any advantages in ESOL Maths provision
Students need to be fully briefed on who is visiting classes and why, and this will need to be presented in their L1s especially for those with a low English level. This will be done via on line translation facilities using the smart board. Where a learners’ first language is not available, such as Punjabi, I will use the learners’ second language, such as Urdu.
Teachers travelling in to college from outside will need to be offered remuneration for travel costs.
2.3 Feedback on Findings
As stated in the Application for Ethics Approval, “all will have sight of the parts of the report relating to them prior to submission to ensure I have not misrepresented them in any way”. I also “need to share the findings with management prior to completion” as although I will try to ensure that the college and my colleagues remain anonymous, in practice it will be relatively easy to identify at least the college, as it is my place of work.
Time will need to be allowed in the planning for this feedback to colleagues, whilst making it clear that I am seeking to confirm that I am not misquoting respondents, rather than “seeking feedback from them on my analysis” and it could be that “taking your interpretation back to the ‘respondents’ is often a very useful, pleasant and helpful act” (Richards 2009, p24) and might yield further insights.
However, feedback to the management team is of a different nature, as I am seeking to inform them of the findings of the report before it enters the public domain. The feedback form used for the findings review meetings is in Appendix C.
It will be important to highlight the local nature of this research, the smallness of the sample sizes and the need to be cautious about inferences that might be drawn from the quantitative and qualitative research, which might imply a causative relationship between the data which, given the complexity of social situations, we cannot know. However, “small scale studies may inform, illuminate and provide a basis for policy decisions within an institution (and) as such, they can be invaluable” (Bell 1993, p126).
Chapter 3: Findings- The Report
3.1 The quantitative analysis
3.1a Introduction
I have analysed five years of data held by my college on ESOL learners, which is held on spreadsheets and records whether they have passed or failed their ESOL or other English qualifications. I have cross-referenced this with the maths/numeracy data sheets to identify those learners who attended both classes. This information has been used to compare the achievement rates for those who did study maths with those who did not.
3.1b Quantitative Findings
The analysis of the data seems to clearly show a correlation between attending a maths class and English language acquisition at my college, as the percentage of ESOL Maths learners with ESOL passes varies from 87.5% to 100%. This compares with the performance of the group without maths classes of between 62% and 84.5% (see Table 1).
Table 1 Pass rates for ESOL learners from 2008/9 to 2012/13 academic years
*Two learners were located in English speaker’s classes due to timetable issues.
‘Five learners passed a Functional Skills English Qualification as would not pass the next ESOL level
“One learner passed an FS English qualification rather than ESOL (see ‘ above)
All but 1 ESOL + ESOL Maths student who did not get an ESOL qualification did achieve a Maths qualification
^Numbers for ESOL Maths dropped due to ESOL classes on offer going up from 2 to 3 three hour classes per week
We can see that consistently, throughout these small cohorts, those who opt for maths classes outperform those who do not in their end of year ESOL assessments.
When this information is analysed for percentage variations it becomes clear that there is a consistent positive correlation between opting for ESOL Maths and passing ESOL exams, as there is a minimum of 10.5% and a maximum of 32% improvement in ESOL Maths students’ performance compared to the non-maths cohort (see Table 2). The mean (average) value on these percentages is 22%; the median or middle value is 25.5%.
Table 2 Comparison of ESOL learners’ results with and without ESOL Maths classes
It would therefore seem from the statistical analysis of five years’ data that there is a consistent improvement in English language acquisition for those who study ESOL Maths in addition to ESOL language classes.
Variation within ESOL levels was one option for further analysis, but given the sample size this is unlikely to be useful (Cohen, Manion and Morrison 2000). The same applies to other potential analyses, such as those by age, ethnicity or gender.
The percentage comparison can be seen in Chart One.
3.2 The qualitative analysis
3.2a Introduction
The sessions observed by four teachers varied in content including ‘place value’, ‘vocabulary of number operations’, ‘money’, ‘shape and space’ and ‘probability’, so a wide variety of maths topics drawn from various sections of the Numeracy Adult Core Curriculum (Excellence Gateway 2011). The learners varied in Maths and English levels from Entry 1 to Level 1, and there were many nationalities and first languages in the room. These included Polish, Latvian, Urdu/Punjabi, French/Patois and Cantonese speakers. After introducing a topic and covering key language and methods needed I tend to set learners a task to complete either individually or in pairs, whilst I sit with the lowest level learners to support them.
Tasks are often differentiated by input, methods or outcome as appropriate for the learner, for instance a low level language learner might be given a calculator to use for the maths so that they can concentrate on the language or sequencing of number operations. All learners are encouraged to bring and use bilingual dictionaries, and an online translation facility is often displayed on the smart board for translation of key words and phrases (Stacey 2012).
Three of the four teachers who were able to observe classes were ESOL teachers, but the fourth was a Maths teacher, and all observations took place in the second term, not in the first term as originally envisaged. This was due to the workload and availability of the teachers I asked. Interestingly the comments from the Maths teacher were very similar to those of the ESOL teachers, and I have felt it unnecessary to differentiate between the two which will also help to preserve the anonymity of the teachers involved.
3.2b Evidence of language teaching
All of the observers noted language teaching taking place in the observed sessions.
One teacher expressed surprise at “the amount of language that was used in Maths and therefore it was a language lesson based on maths” and also said that the session was “very interesting and definitely beneficial to the learners as they were exposed to a different type of language use.”
Another was surprised by the level of English and fluidity of the language use: “I was surprised by the good level of English used by the students, the vocabulary was very fluid and the student’s understanding of maths on the whole was of a very good standard”.
The teachers also commented on the opportunities available to learners to practise pronunciation, such as in a “place value” recap session all learners practised using the ‘th’ sound with tenths, hundredths and thousandths. One commented that “time was given to reinforcing pronunciation, spelling of numbers and vocabulary.”
One teacher started to think about the possibility of restructuring ESOL sessions to make them more topic based, which might be beneficial to learners if topics were focussed around work needs, such as customer service or health and safety. Another said that the classes might “help individuals gain better employment”, and the need for “acquisition of language for communication and integration into wider society” was also noted.
Three out of the four teachers when asked to rate the usefulness of maths sessions in improving English acquisition on a simple Likert scale, where zero was ‘of no use’ and ten was ‘extremely useful’, rated the usefulness at 10, extremely useful.
One teacher did not use the scale, and commented that “It would be more useful if the group was not of such differing levels, so language could be more easily structured”, that “some of the language used was more advanced than might be expected for some of the learners”, but did note that the learners “were engaged and attentive”.
3.2c Learners- confidence levels
Two observers commented on how relaxed learners were in the sessions, both in their interactions with other learners and with me, and that learners clearly felt more confident and more able to answer questions than had been seen in ESOL sessions “because the focus was on maths not English”.
Paired work involving verbal problem solving was taking place between learners who would not normally speak to each other during a session, one of whom had previously refused to participate in paired work during ESOL sessions. One teacher said “Student X does not speak in English, but spoke here with other students she does not normally interact with”. Another commented that the session gave “non-speakers” “a chance to participate”.
A learner with extremely low verbal language skills was clearly prepared to attempt questions and to make mistakes which had not been seen before. “Student Y really tries and has a go, not seen that in an ESOL class” and “I could see some students were very timid but these still participated in the lesson”.
The positive response to set tasks was noted by all observers and surprise was expressed at the level of maths attempted and achieved during the sessions: One commented that “maths skills…can build confidence” and “The confidence the ESOL learners gain in tackling mathematical problems will allow them to gain confidence in learning other subjects”.
It seems that in this class we do not have an issue with maths anxiety, as identified by many researchers, but that we may have an issue with English anxiety for ESOL learners. It may be of course that those learners who opt for ESOL Maths classes are those who have had a positive previous experience of maths learning.
3.2d Learners- levels of participation
Observers commented on the increased level of participation compared to ESOL classes, and how beneficial this was for learners, as paired work “fostered greater communication in English”, and that even those with confidence issues “still participated” in the paired work: “The shyest learner in the group from the lowest level language class clearly…felt able to answer the teacher because the focus was on maths not English”.
Learners “responded well and found the experience useful and relevant”, even those “with strong educational backgrounds in maths also found the experience useful”.
Observers noted that “learners clearly felt more confident and more able to answer questions” and that the learners both responded well to the tasks set and performed well in their completion. There was “good interaction with resources/activities…working individually or in pairs”.
Thus greater levels of participation were seen than would normally be expected from the knowledge the teachers have of these learners in ESOL sessions.
3.2e Learners- language performance
Observers were generally surprised to note the level of language performance shown by the learners, and felt this was improved compared to ESOL classes. One observer noticed that “the focus is on maths where some learners who may be weaker in language are able to do better” than in an English class, as they are using other skills, not just English.
Another expressed surprise at “the good level of English used by the students” and “the vocabulary was very fluid”.
Two students performed consistently better, according to one observer, than they would have done in an ESOL class in terms of speaking and listening skills.
All of the students seemed to be performing at a “good level of English” according to one observer.
Observers did not feel that any change to ESOL exam levels set was needed, but some did feel more confident that learners might achieve.
3.2f Teaching- interface and input
The importance of the student teacher interface was noted by observers especially as it relates to those with a low level of skills. The teacher who teaches Maths rather than ESOL noted the need for a patient understanding approach compared to ‘normal’ maths classes, and the differences required in delivery to help learners, such as the focus on pronunciation, which would not occur in classes for native English speakers.
One observer commented on the increased amount of language in the maths session compared to her own experience of school education, which led to there being “a lot more to it than anticipated”.
One teacher expressed concern about the use of translation devices in the maths session as “I see it as a missed opportunity for language development”.
3.3 Feedback on Findings
3.3a Introduction
The findings of the report, as detailed in the qualitative and quantitative analyses, have been presented to my team at work, some of whom were involved in the observations, and to the managers of the team. Feedback forms were supplied to enable participants to either comment verbally or in writing (Appendix C).
In both cases the limitations of the findings in terms of the correlation, owing to the smallness of the sample, and reasons why it might have occurred, including their speculative nature, were fully discussed, but participants responded very positively to the presentations and subsequent discussions.
3.3b Observers and other colleagues
These presentations generated discussions around the quantitative findings, which generally were thought to yield a higher than expected correlation. Some teachers identified learners who might benefit from ESOL Maths classes, as they are currently unlikely to pass their ESOL exams.
Several teachers identified opportunities for further study, including one around the variation in ESOL results year on year, and whether “citizenship classes had a similar impact on achievement due to the additional language input”.
The group identified the benefit of maths classes to the learners as they already have some knowledge of the maths being taught, so might be able to assimilate new language more quickly than with an unfamiliar subject.
One teacher commented on the positive improvement in the quality of the work force that maths qualifications implied, and the reduction in ESOL funding that might be affected by improved results.
Questions were asked about the ethnicity of the students, and whether further patterns existed, but this has to be the content of further investigation.
There was one request for a change of wording in a section which referred specifically to one teacher which has been done.
All confirmed that they had been quoted accurately (Richards 2009).
3.3c Management team
The managers read the reports after a short introduction and asked a number of questions.
The presentation to the management team seemed to raise the profile of ESOL Maths within the college, and the correlation seen led to a discussion on whether or not to implement compulsory ESOL Maths for ESOL learners. After deliberation it was concluded that more information is needed on the experience of other colleges who have implemented this before a decision can be taken.
Planning for class sizes and times is currently in hand for the 1415 academic year and no changes will be made at this stage, but it was agreed that promotional activity focussed around the advantages of studying ESOL Maths be presented to learners during the first half term. The ESOL Maths classes will start in October rather than September to maximise learner participation.
One manager wrote “Very interesting to see the correlation between Maths and success on ESOL courses. It will prove useful in planning next year’s courses, arriving at optimum success”.
Two minor additions for the purposes of clarification were made, and these have both been done.
Chapter 4: What have we learned?
4.1 Quantitative findings
The data analysis does seem to show that there is a correlation between adding ESOL Maths to learners’ timetables and improved ESOL results; improvements are consistently positive, varying from 10.5% to 32%, on average around 22%. This adds to our current knowledge, as there have been no specific studies on ESOL Maths that I am aware of, and supports the findings of other research, such as that done with ESOL learners on a sports programme (Hately-Broad 2006). This is a small and statistically insignificant sample however (Cohen, Manion and Morrison 2000).
In both cases it may be that the correlation arises from many factors, known and unknown (Cohen, Manion and Morrison 2000). Prior knowledge of the subject being taught and an interest in it seem likely to be two of the contributing factors, but a potentially large range of factors could be having an impact. We have no way of knowing the nature or extent of these, and need to keep this in mind when evaluating these results.
There is no evidence to suggest that it is the maths itself which leads to this correlation; in terms of the current project it is not possible to provide evidence to either support or deny such a supposition.
4.2 Qualitative findings
The three main questions for the qualitative investigation were:
Can these teachers see any advantages of ESOL Maths, where the language is less overtly taught than in an ESOL class?
Do the students exhibit skills that they were unaware of, or that surprise them for the level those students are at in their English?
Does it make the teachers reassess the learners’ language skills levels?
4.2a International aspects
Answers to the first and second questions seem to be consistently ‘yes’. We can see from the above analysis that teachers can see the advantage of ESOL Maths, where the language use is less overt than it is in ESOL sessions, and that this seemed to increase the participation, confidence and performance of learners. This does seem to support some of the experiences of other countries, such as South Africa (Adler 2001), and perhaps add to it as all the learners observed in this study had chosen to study maths.
The increased participation and improved levels of confidence noted by the observers could indicate a reduced level of anxiety in the classroom compared to ESOL classes, a factor which has previously been linked to improved language acquisition (Krashen 1982 in (Wilkins 2009)). This low level of anxiety (Macrae 2003) may have been present from the start if only maths confident learners have signed up for ESOL maths; if those who are anxious about maths had also attended, we might not see the same correlations. This knowledge would add to our understanding and highlights a gap in this report, as I do not know if maths anxious learners have attended.
4.2b Learners and their profiles
One teacher suggested offering more provision based on the language levels of the learners, so that some learners are not over-faced by the amount of vocabulary, confirming the view in the literature section that ESOL learners may present with spikier profiles and very different needs in the same classroom (Newmarch 2005) (Wilkins 2009). This observation also supports the claim discussed in the literature review that mixed level classes are less effective for learners (Pitt 2005).
Whilst caution is required due to the statistical insignificance of the sample size (Cohen, Manion and Morrison 2000) the implication here is that ESOL learners’ English acquisition might be further enhanced by placing them in ESOL maths classes specific to their language levels. This adds to the current knowledge in my college and perhaps elsewhere in the UK, and might be useful when considering maths provision for less motivated learners. It contrasts with a change of practice in the USA (Kersaint, Thompson and Petkova 2013), as we have seen in the literature section of this report.
The need to enhance language skills for work opportunities was mentioned, and three observers noted the importance of maths for employability, supporting the findings of the literature review (Newmarch 2005) (Pratt 2012).
4.2c Language in the Maths classroom
Observation of ESOL Maths classes did seem to cause teachers to refine and extend their thinking about ESOL Maths and its usefulness in developing language skills, which can be seen as evidence of increased levels of language activity in mathematics in many countries, including the UK (Brown 2001) (FitzSimons 2002), supporting the findings of the literature review.
Observers were generally surprised by this increased use of language, but did not seem to want to change their opinion of the language levels students had been entered for, so the answer to the third question posed is ‘no’. However it did seem to make them more confident that students would achieve the level set. This can be viewed as adding to our knowledge as the texts reviewed in the literature section were concerned with maths acquisition, not English acquisition (Barwell 2009) (Adler 2001) (FitzSimons 2002).
Another teacher started to develop ideas to make the ESOL classes more topic based as a way of helping language development, and this supports the findings identified in the literature review (Hately-Broad 2006), but I do feel that the observers response on the Likert scale, awarding 10s to ESOL maths classes as an aid for language improvement adds to our existing knowledge.
The observations seem to support the idea that although mathematical language should be the focus of maths classes (Barwell 2002) (Fletcher and Barr 2009) (Monaghan 2009), there is enough other language occurring for learners to benefit in terms of English acquisition (Adler 2001) (Clarkson 2009), and this adds to our existing knowledge as far as I know.
Observers noticed the importance of the teacher interface with learners, and this supports the need identified in the literature review for specialist maths teachers to enable learners to make progress with their maths (Brown 2001) (FitzSimons 2002). This report can be seen to add to our knowledge as it has evaluated maths learners’ English acquisition, but as it is statistically insignificant a more comprehensive study is needed (Cohen, Manion and Morrison 2000).
4.2d Resources used in the classroom
The use of translation devices was queried by an observer as their use might impede language development, contradicting the alternative view previously discussed that the use of the L1 can enhance understanding (Adler 2001) (Stacey 2012) (Jones 2009).
I believe that when we consider the results in the light of the literature review, they indicate a need to reassess maths teaching to add in the need for all learners to be taught about the nature and type of language within the mathematics classroom. This could be termed a ‘triad’: Conceptual understanding, procedural competence and language acquisition. This may add to our current view of maths teaching, especially to ESOL/EAL learners.
4.2e Cultural differences and their impact
The observers commented in the feedback session on the potential usefulness of an analysis by various factors including ethnicity, and this was identified in the literature as an important consideration which might have an effect on learners’ results. Unfortunately due to the smallness of the sample size (Cohen, Manion and Morrison 2000) this has proved to be outside the scope of the enquiry.
4.3 Feedback on the findings
Feedback included surprise at the extent of the correlation in the quantitative analysis, and the similarity of the comments in the observations from the qualitative review. Participants seemed to readily assimilate the evidence for the positive correlation, whilst appreciating that it could exists for many reasons, including additional learner/teacher contact time and prior maths knowledge. This supports the view discussed in the methodology section that small scale studies can be useful to institutions (Bell 1993).
Participants in the feedback sessions all seemed to be readily modifying their behaviour, in terms of increased promotion of the ESOL Maths classes, especially to certain sectors of the ESOL population, such as those the teachers or mangers felt would struggle to achieve the next level of ESOL qualification in one year. This can be construed as having added to our existing knowledge at my college (Bell 1993), and may be of interest to other FE providers.
Chapter 5: Conclusions and Recommendations
In conclusion it seems that the two separate disciplines of mathematics and ESOL meet in the ESOL Maths classroom, and research and other work applying to both are relevant here. Language acquisition is a vital part of success in mathematics for all learners, along with conceptual understanding and procedural competence. I have applied the word ‘triad’ to this three part nature of maths teaching and believe it adds to current knowledge by synthesizing views on mathematics teaching (Brown 2001) (FitzSimons 2002).
In my FE College we seem to have both quantitative and qualitative information to warrant the inclusion of Maths in ESOL learners’ timetables, as there does seem to be a correlation between attending ESOL maths classes and an improved acquisition of English. The reasons for this are far from clear as a multiplicity of factors may have an effect, but might include increased teacher contact time, learner motivations or abilities, or the impact of covert, rather than overt, language learning.
It may be that any subject learnt in addition to ESOL would benefit learners’ English, but other subjects would not draw free funding and so might be less attractive to the learners. It might also be that the learners’ prior knowledge of maths in their L1 is a significant factor in facilitating language acquisition, and that if learners were presented with a subject about which they knew nothing, and the course was in English, that the language would be an additional barrier to knowledge.
When I started to clarify the nature of this topic and to conceptualise the question I realised that the actions of some of my colleagues might already be answering the question posed, namely “Does adding Maths to ESOL learners' timetables improve their acquisition of English?” I believe that some did think that the maths classes will help with English language, as they referred learners to classes, and promoted the classes both in their ESOL sessions and at enrolment. Some teachers have also referred learners to ESOL Maths classes if that they feel have reached an ESOL level and will need more than one year to make progress to the next level, along with other subjects such as IT, to build English skills in a year away from ESOL. This report informs and supports those decisions.
I would therefore recommend that the college use the findings of this report to promote ESOL Maths classes to ESOL learners using appropriately translated marketing materials, as those with lower levels of English might particularly benefit. The college also needs to consider briefing staff in the ‘Advice and Guidance’ department to enable them to promote ESOL maths effectively to non-English speakers.
I would recommend to other colleges delivering ESOL that they consider the potential usefulness of delivering maths given sufficient and appropriate resources, especially in terms of staff and materials. Staff would benefit from information on how maths in the learners’ country of origin could differ from the UK.
Finally I recommend that maths classes for ESOL learners remain optional until more research has been done, both on the effect of other colleges policies on their ESOL learners, and on the maths anxiety levels of those who voluntarily sign up for ESOL Maths.
Chapter 6: Reflection
6.1 Literature Review
The literature raised some interesting lines of enquiry which I would like to develop further, including that for this project it would have been very useful to consider whether the ESOL learners who sign up for Maths classes fall into the ‘maths confident’ group (Macrae 2003). If they do all or mostly fall into this group then the correlation seen might not exist in colleges that make maths study compulsory, as then both maths confident and maths anxious learners will be learning maths and the outcome could be very different. Maths anxious ESOL learners might even be discouraged sufficiently to leave ESOL courses which would have a negative impact on retention.
This knowledge could also have informed me about the degree of bias in the ESOL Maths learners towards mathematics, which could have an impact on the interpretation of the correlation and the usefulness of this study to my workplace.
I feel that this indicates that the project might have benefitted from completing most of the reading before forming the questions for the qualitative enquiry, as then the questions could have been specifically tied to the issues and questions arising from the literature review. This might have improved the usefulness of the project, but was not possible due to the timing of the ethical approval submission which comes at the start of the dissertation phase.
Whilst the literature review might seem to be quite comprehensive there is undoubtedly more information in the public domain which I have not yet seen, which might support or refute the findings of this report. It might also mean that my assessment of how this project extends current knowledge is incorrect.
6.2 Methodology and methods
Whilst I have no concerns over sampling, as I have evaluated all the data we have, these learners do form part of a wider UK population of both ESOL learners and ESOL Maths learners in the UK. I have no information on the extent of these populations, and therefore “how representative the sample is” (Cohen, Manion and Morrison 2000, p92) of the whole UK populations. Further research is needed to establish this.
There is no stratification within the quantitative data that I have presented as the sample sizes are too small, and this could have been informative. “Stratified sampling involves dividing the population into homogenous groups, each group containing subjects with similar characteristics” (Cohen, Manion and Morrison 2000, p101), i.e. splits on the data by age, gender or ethnicity might have refined and improved the analysis, had sample sizes been sufficient (Coben 2003).
I feel with hindsight that I gave insufficient consideration to “the subjectivity of respondents, their opinions, attitudes and perspectives together contribute a degree of bias” (Cohen, Manion and Morrison 2000, p105). My project might have more value if I had conducted it in a college where I was unknown, or if I had been able to use observers who were unknown at least to the students, although this would not be compatible with a work based project.
6.3 The Report- quantitative and qualitative findings
During the past 12 months as a result of my studies I have been asked to give a number of presentations both to student teachers and colleagues at various venues, both for the university and NATECLA, the National Association for Teaching English and Community Languages to Adults. These presented an opportunity to find out via a questionnaire whether other colleges are also teaching ESOL students maths, and if so how that is being achieved, with success rates if known. This would have helped my project and college be better informed about the wider picture. Subsequent to the findings presentation to management that information is now being requested, especially with regard to success and retention rates from colleges who have made ESOL Maths compulsory. I hope to start collecting this at the next round of conferences this year.
I could have included some questions in the interview to find out, at least from the internal observers, if they currently talk to new or existing ESOL learners about ESOL Maths, and whether they recommend attendance, in view of the fact that they are intending to do that subsequent to this report, even intending to target specific learners who might gain the greatest benefit in their view.
I feel I was unable to make it sufficiently clear that the outcomes of the report were of interest to me whether they were positive or negative about ESOL Maths, and that some inclusion of negatively framed questions about the observations, such as ‘what was not helpful in your view?’, or ‘what did you not like about what you saw?’ (Cohen, Manion and Morrison 2000), might have elicited different insights. Also I could have included a short interview before the observations based around the same questions, which might have shown a contrast when I looked at ‘before’ and ‘after’ in the teacher’s views, as some observers did seem to change their minds about various aspects of ESOL Maths.
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