The language of mathematics is complex. The Curriculum Assessment Policy Statement for mathematics defines mathematics as ‘a language that makes use of symbols and notations to describe numerical, geometric and graphical relationships’ (DBE 2011:8). The mathematics language describes mathematical concepts, which the everyday language cannot describe. Bohlman and Pretorius (2008) note that:

Hammill (2010) views mathematics as having dense information and a complex structure. According to Bell (2003), when children learn mathematics in English, some factors that contribute to difficulties in comprehension include mathematics vocabulary, as well as specific syntactic structures and discourse patterns found in written text. Setati (2005) also notes that when learning mathematics, one is required to acquire fluency in the mathematics language. Hence it becomes challenging, especially for ELLs who have just begun learning in English, to learn mathematics in English. In the case of ELLs, the challenge of learning mathematical vocabulary is exacerbated by their lack of proficiency in the English language (Barbu 2014). In this respect teachers need to find strategies to support learners as they engage in the complex language of mathematics. Schleppegrell (2012) suggests that mathematics learning should consist of multimodal and multisemiotic activities to support scaffolding in the academic mathematical language.

Beal, Adams and Cohen (2010) as well as Brown, Cady and Lubinski (2011) note that there is a relationship between English language proficiency and mathematics achievement. Carrasquillo, Kucer and Abrams (2004) also argue that ELLs need high levels of literacy as they go to higher grades in schooling. In a study by Kieffer et al. (2009) in the USA, it was observed that mathematics required that learners be proficient in English and those who were not proficient in English experienced more difficulties in the mathematics assessments in comparison with those who were proficient in English. Confirming this, other researchers (Abedi & Lord 2004; Beal et al. 2010; Han 2011; Jordon, Kaplan & Hanich 2002) note that learners with strong reading skills in English achieved higher results in mathematics than those who had difficulties in reading English. For Henry, Nistor and Baltes (2014), locally and nationwide, learning the LoLT at the same time with mathematics content challenges ELLs’ academic learning experiences and this is especially revealed at Grade 4 where ELLs always perform lower than non-ELLs in mathematics in many other countries. Neville-Barton and Barton (2005) also revealed that students who use English as a second language, and use it as LoLT, had a 10% – 15% lower performance in mathematics because they lacked English language proficiency. According to Neville-Barton and Barton (2005), learning challenges, especially in relation to making sense of mathematical vocabulary, depend on one’s proficiency in English, and ELLs struggle most with problem-solving.

In summary, large and small scale, local and international research confirms that language proficiency is one of the important factors that determines access to mathematical sense-making and is one of the factors influencing mathematics performance, although several other factors also play a role.

Moschkovich (2016) notes that teaching mathematics to ELLs in a classroom should include the use of many different resources in the classroom. It is important that ELLs also have the opportunity to express their mathematical ideas, yet this is difficult to do in English when one is still learning basic English communication skills (see Robertson & Graven, submitted, for discussion of the challenges of Grade 4 ELLs in engaging in mathematics classroom talk). In South Africa it has been found that using more than one language in order to draw on the learners’ home language(s) as a resource for mathematical sense-making is beneficial to learners (Setati 2005; Webb & Webb 2013). Setati’s work (e.g. Setati 2005) on code-switching has been particularly noted as beneficial and more recently Webb and Webb (2013) have argued that this is particularly useful when working with problem-solving.

Barbu (2014) argues that when bilinguals switch from English to their home language during mathematical computation, the time necessary for calculations is reduced. Hence he argues that learners should be allowed to use the language they prefer when learning mathematics. Barbu (2014) further argues that when a learner delays in giving a response, it doesn’t necessarily mean that he or she doesn’t know; but the learner may be code-switching and preparing for an answer in his or her own language. Therefore, he says ‘code-switching is an efficient use of ELLs’ language skills and should be encouraged’ (Barbu 2014:140).

While mathematics assessment should be used to evaluate or measure the level of mathematical proficiency in learners and allows one to monitor the learning progress in learners, sometimes the assessment fails to measure what it intends to assess and ends up measuring language proficiency. Mathematics assessments, like all other assessments, will be judged as valid if they assess and gain results that provide information on what they intended to assess, whether a particular skill or broader competence. So, if one wants to assess whether learners can perform the skill of adding two-digit numbers, one might design items such as 22 + 34 and 48 + 67. However, when mathematics questions require a lot of reading and interpretation in order to make sense of what is being asked, it is often difficult to tell whether poor learner performance is as a result of reading difficulties, interpretation of terminology difficulties or mathematical understanding difficulties, among others. Abedi and Herman (2010) note that administering assessments that are written in English to learners who are still learning English complicates the learning experience for those learners because they are still not proficient in English. According to Halliday (2010), for an assessment to be fair, the learners’ language proficiency should be considered. In ELLs’ mathematics classrooms, sometimes the validity of assessments is compromised if learners have a limited English proficiency. This is because their comprehension of assessment questions is low and thus learners struggle to access what is being asked of them. In this case, the results of the assessment cannot tell what learners really know. Hence in South Africa, the fairness of some ANAs has been questioned because of the inaccessibility of the language used in them (Graven & Venkat 2013, 2014; Henning & Dampier 2012).

On the assessment of ELLs, Moschkovich (2012) argues:

This captures the rationale of the use of task-based interviews in the broader study to assess the extent to which language challenges influenced Grade 4 learner access to language-based mathematics assessment items in the ANA and, as a result, their performance on these items. Thus, the research objective was to investigate the difficulties experienced by the Grade 4 ELLs as they solved mathematics problems presented in English in the ANAs.

The study reported in this article was located within the South African Numeracy Chair (SANC) Project, in which the first author was a PhD student and the second author was the chair and supervisor of the research. As the focus was on Grade 4 mathematics ANAs, two teachers participated, each from different schools involved in the SANC project, in the Grahamstown District. The schools were chosen for their close proximity to the university, allowing ease of access. One teacher at Santa Anna School taught one class (Class A), and the other taught two classes at Biko Primary (Classes B and C). All ethical permissions were obtained, and the names of the schools, teachers and learners used in this article are pseudonyms.

As the study sought to explore the experiences of Grade 4 ELLs as they solved a selection of the 2013 Grade 4 mathematics ANA items, interviews were required because written responses to the items did not allow this insight. The 2013 mathematics ANA consisted of 38 items. A sample of 15 items were selected for inclusion in the interviews (see Sibanda and Graven [2015] for discussion of this selection and the analysis of the linguistic complexity index of these assessment items). The majority of learners from the three classes performed poorly in the 15 items. Nine learners were purposefully selected from each class according to their performance in the ANAs: three top, three middle and three low performers.

The task-based interview was designed so that the researchers could ask questions that could solicit detailed information on the difficulties that the learners experienced. This interview was informed by Newman’s Error Analysis (NEA) (Newman 1977), which provided a framework that assisted in giving an explanation of the struggles the learners faced in the process of solving mathematical problems. Newman highlighted that as children solve mathematical problems, they may experience reading, comprehension, transformation, process skills or encoding problems. According to White (2005), the NEA instrument makes it possible to explore the links between one’s ability to read and the ability to understand and work with numbers. During the interview, learners were probed in order to encourage them to proceed through the stages of solving the mathematical problems, in the process uncovering the challenges they experienced. The interviews were audio recorded, which allowed us to record accurately the occurrences of difficulties represented by learners when they hesitated or became silent during responses. Field notes recorded their facial expressions or gestures. Video recording was considered to be too intrusive and was therefore not used.

As part of the interviews, learners were taken through a process of reading, interpreting and solving the problems, which were written in the ANAs in English. The interview involved probing questions to follow up on the learners’ responses on the 15 identified questions. All 15 questions consisted of English language text to be read. Learners were prompted or supported with translation at ‘break down’ points, as will be evident in the transcripts below.

A limitation of the study is that it involves only three classes of learners in township schools where learners share a single home language (isiXhosa), while in Grade 4 they learn through the medium of English. There are of course many other Grade 4 classroom contexts where learners have different linguistic backgrounds. IsiXhosa-speaking learners were assessed in this study because it is the dominant language of learners in the Eastern Cape – the province of this study. It was not the intention of this study to compare the linguistic challenges of the ANAs for ELLs to native English speakers. For that, an entirely different design would be needed. Instead, this study sought to understand the challenges that three classes of isiXhosa-speaking Grade 4 learners faced when responding to a sample of items that required reading and interpretation of English in order to make sense of what was being asked mathematically.

All ethical permissions were obtained, and the names of the schools, teachers and learners used in this article are pseudonyms.

As indicated above, all ANA items are taken from the 2013 Mathematics ANA article (DBE 2013a). In Category 1, 19 out of 26 learners had great difficulty in reading the items and required extensive assistance in reading. In Box 1 - 7 are excerpts from two learners who needed reading mediation on every question. Some learners failed to independently read several words in all 15 items and as a result struggled to comprehend those items. They reveal some of the reading and comprehension difficulties encountered by such learners. The ANA item is presented, and thereafter the interview excerpt is provided. The interaction with the researcher of the two learners chosen, Bongani (see Box 1 and 2) and Benny (see Box 3), typified the types of responses of most learners in Category 1. Bongani’s (and other learners’) pauses in speech are indicated by an ellipsis (…).

ANA Item 5.1:

Mrs Mazibe buys an apple for R1,20 and sells it for R1,95. How much money does Mrs Mazibe make by selling 1 apple? (DBE 2013a)

Bongani hesitated before reading the words ‘Mazibe’, ‘buys’ and ‘apple’, and he read the second ‘for’ in the sentence as first ‘fro’ and then ‘from’. He could not read the word ‘does’ in the question and once more grappled to read this word in the next question even though the interviewer had modelled reading it in the above question. Bongani’s poor reading skills could have affected his comprehension of the question and consequently his ability to respond to the mathematical item. Box 2 shows Bongani’s difficulty in comprehending the item that he had struggled to read.

From the excerpt, it is clear that Bongani failed to understand what was required by the question. Although the interviewer explained that ‘make’ here meant he had to look for the profit, he did not understand what the term meant and therefore could not respond appropriately to the mathematical item in order to attempt to demonstrate the mathematical skill required. In this respect introducing this term as part of the mediation process was not helpful in clarifying what was being asked. Although we are not claiming that Bongani’s failure to solve the problem was solely caused by his reading and comprehension challenges, it is important to note that fluent reading is essential for comprehension (DoE 2002), which then allows learners to access the item and interpret the question, which is the first part of the mathematical problem-solving cycle– that is, understand the problem; then come up with a plan; carry out the plan; review and check (Polya 1973). Box 3 is another example of Bongani’s challenges in reading the items.

ANA Item 7 (DBE 2013a):

Write a number sentence for the number sentence below. The difference between 1 613 and 859 is seven hundred and fifty-four.

Here Bongani failed to read accurately the words ‘sentence’ and ‘below’. This was manifested clearly by his mispronunciation of the words. As with the previous excerpt Bongani could recognise almost none of the words instantly, and this caused him to read slowly. Bongani also experienced difficulties in reading certain words in other assessment items in the interview, for example ‘departures’, ‘airport’, ‘answer’, ‘destination’, ‘midday’, ‘use’, ‘wall’, ‘symbol’, ‘correct’ ‘statement’, ‘bar’, ‘graph’, ‘amongst’ and ‘baseball’. It is also interesting to note that all the words that Bongani was unable to read were contained in items that were high in linguistic complexity (see Sibanda 2016). Bongani failed to read 14 out of 15 questions fluently. Failure to read four or five words in a single problem translated to virtually no comprehension of the test item. Most of the words he failed to read were those words with sounds that did not match the letters (e.g. ‘use’) and also words consisting of silent letters (e.g. ‘answer’, ‘does’).

In Box 4 we share excerpts from Benny’s interview. Benny struggled to read and comprehend, requiring extensive mediation in both.

ANA Item 5.1 (DBE 2013a):

Mrs Mazibe buys an apple for R1,20 and sells it for R1,95. How much money does Mrs Mazibe make by selling 1 apple?

Even after these words were explained, Bongani and Benny remained silent and the interviewer thus moved onto the next item. On this item, Benny was unable to read the word ‘buys’. On his first attempt to read it, the sound /u/ was pronounced as it is pronounced in the isiXhosa way, not English. The word ‘buys’ was not read because he was asked to leave out the words he did not know. When one is reading the word ‘buys’, sounds of the letters /b/+/uy/+/s/ are made, noting that uy makes the sound ‘I’, which is taught in the Foundation Phase. Because Benny had not become proficient in matching the sounds and the letters in English he could not read this word. It was evident that his knowledge of English phonics, which is the basis for word recognition (Shanahan 2008) was limited. By learning phonics, learners get to know how sounds and letters are related (and combination of letters such as uy in buy and guy). Benny’s difficulty with word sounds, as evident in his reading, lowered his comprehension during reading. In Box 5 a further example of Benny’s struggle in reading and how this affected his opportunity to comprehend what was being asked:

ANA Item 11 (DBE 2013a): Draw the reflection of the arrow on the vertical dotted line.

Benny clearly showed weak reading and comprehension skills on Item 11. Initially, he was not able to read the word ‘reflection’ because he failed to sound the letters. The difference in orthography between isiXhosa and English plays a role here (Prinsloo 2009). This can lead to the learner getting confused and therefore misreading words. He was also unable to read the word ‘vertical’, as was evident in his inclusion of some letter sounds that were non-existent in the word. He was not able to recognise the words ‘vertical’ and ‘dotted’. He also did not seem to understand these words even when they were read to him. The interviewer introduces the term ‘symmetrical’ in an attempt to mediate as this is a term used in the curriculum and textbooks but this too is a difficult and unfamiliar term for Benny. It is only after the interviewer rephrases it in more everyday BICS language – ‘so that the two sides … look the same’ – that Bennie is able to respond (successfully) to the question. Benny thus had the skill of completing a diagram so as to be reflected along a given axis but did not have the language skills to access what the question was asking.

Jennings et al. (2006) note that once learners succeed in recognising sight words, reading becomes easy. Words like ‘reflection’ and ‘vertical’, for example, do not need to be sounded when reading them. According to the DoE (2010), such words constitute 75% of most reading passages and they are core to reading basics. When a learner looks at the word, he or she remembers the forms and recognises the words and hence this promotes reading speed (DoE 2010). To Benny, who had not managed decoding most words, these words were difficult to read and it could explain the misreading, hesitations and silences.

Fourie (2008) notes that word recognition ability is crucial if one is to master written words and read fluently. If this skill of word recognition is missing, learners cannot get any meaning from what they read. Considering Benny’s case, it took him a longer time than expected to finish reading the question because he could not readily recognise the sight words. Hence there was pressure on his short-term memory, which compromised the recollection and retention of the first words and their meaning at the end of the sentence.

Rault-Smith (2009) suggests that learners moving to Grade 4 should be beginning to read fluently and independently. However, this was not confirmed in this study because the majority of learners who participated in the task-based interviews were still ‘learning to read’ rather than ‘reading to learn’. Instead of reading independently, reading and understanding a text on their own, learners were reading with difficulty, defined as struggling to read over 10% of the words in a text (Treptow, Burns & McComas 2007). Hence, for Bongani and Benny, the text was very difficult to read as they could not read more than four words correctly in a question consisting of 11 words. This resulted in their difficulty understanding the questions.

Two of the seven learners who required no reading support required extensive mediation in comprehension while the other five learners required only moderate mediation (see Table 1). Here, we share excerpts from two learners’ interviews to show that despite fluent reading ability, in the case of unfamiliar words and items of a high linguistic complexity, learners still struggled to comprehend what was being asked of them mathematically.

Excerpts from the interviews with Anathi (see Box 6) and Buhle are discussed below in order to illustrate the difficulties they experienced comprehending the ANA items. Their responses were typical of the comprehension challenges that other fluent readers among those interviewed faced.

The extract given above shows the challenges that Anathi faced as she tried to understand what the question asked. There is evidence from this extract that she had not understood the requirement of the text even though she had claimed to have understood all the words. She did not know the meaning of ‘number sentence’ and she thought the question instructed her to ‘write what is the difference between 1613 and 859’. Hence she could not recognise that the ‘difference’ was already provided as 754 in the question.

Secondly, while Anathi indicated that she knew what the word ‘difference’ meant, she did not understand this as a mathematical concept, as, for example, the distance between two numbers on a number line. She rather viewed them as two numbers being different (not the same) from one another. She explained ‘difference’ as ‘what is different numbers, numbers are different’. Anathi took ‘difference’ to mean ‘dissimilar’, the everyday meaning.

According to Bohlman and Pretorius (2008), a learner is able to interpret mathematical concepts and information only if he or she has understood the information with coherence. Anathi could read items quite fluently and her comprehension problems seemed to be attributable more to unfamiliar mathematical terms or terms having different meanings from their everyday use. Anathi struggled to find the solution to the problem because she could not understand what was meant by ‘making a number sentence’.

Next is an excerpt from the interview with Buhle (see Box 7). We see that his lack of familiarity with mathematical terms in English results in his struggling to make sense of and solve the word problems given to him in question 11.

Buhle struggled to understand the words that seemed to be new to him because he could not instantly recognise them when he read them. The words ‘reflection’ and ‘vertical’, are mathematical vocabulary that he was unfamiliar with. When they interact day, learners seldom hear or speak such words. Examples of such words that could not be understood by Buhle are ‘departure’, ‘convert’, ‘flow diagram’, ‘destination’ and ‘amongst’. The words that the learners could not understand were also part of the questions that had high linguistic complexity, and these are difficult for Grade 4 ELLs as illuminated by the broader study.

It is apparent that for both Buhle and Anathi comprehension was hampered by unfamiliar words and mathematical terms in the items. Duke and Pearson (2002) note that if learners have knowledge of tenses, vocabulary and participants, as well as the order of what they read, the texts will be easier to read and understand. Attention is needed to reading comprehension as many South African learners have indicated very poor performance in this aspect (Pretorius & Lephalala 2011). Howie et al. (2008) also note that there is a very low reading comprehension in South African learners, as revealed by a large-scale assessment of reading comprehension of Grade 4 and 5 learners. This study also confirms the findings by the aforementioned researchers.