LANGUAGE AS A BARRIER TO LEARNING MATHEMATICS

IMA International Conference on Barriers and Enablers to Learning Maths: Enhancing Learning and Teaching for All Learners M.A. Hersh and M. Kotecha LANGUAGE AS A BARRIER TO LEARNING MATHEMATICS Mark Prendergast ; Fiona Faulkner; Clare O Hara Trinity College Dublin ; Dublin Institute of Technology Dublin, Ireland Email: mark.prendergast@tcd.ie; fiona.faulkner@dit.ie; clare.ohara@dit.ie Abstract: Language plays a significant role in the processing of mathematical text and the interpretation of mathematical questions. This is of particular relevance in Ireland where the introduction of a new second level curriculum entitled Project Maths has led to a greater emphasis on solving mathematical word problems and applications. Students are required to translate everyday word problems into mathematics, solve them and then clarify their answers in the original context. Many educators feel that students with low literacy levels and particularly international students for whom English is not a first language are struggling with the comprehension of this material and the wordy nature of some of the questions. This two year study carried out by the authors aims to investigate such concerns and determine whether the performance of international students in a Project Maths style examination is influenced by their English language ability. Keywords: Language and literacy, international students 1. Background to the study In Ireland formal education takes place in three stages. After completing eight years of primary education all students progress to the second level system. Second level education is typically of six years (1st 6th year) and during this time students complete two main State examinations, namely the Junior Certificate (JC) and the Leaving Certificate (LC). In this system the importance of mathematics, which is one of only three compulsory subjects, is recognised by students, teachers and policy makers alike (National Council for Curriculum and Assessment (NCCA), 2005a). However despite such importance, numerous concerns have been highlighted throughout the literature in recent years regarding the delivery of mathematics education in Ireland. Such concerns include class time, class and teacher allocation, difficult content, traditional assessment and an out of date curriculum (Prendergast and O Donoghue, 2014). The Irish Government has been under increased pressure to take action as a result of such concerns. There was a realisation that the syllabi and teaching methods were inadequate for providing students with the skills and knowledge which the twenty first century requires. Mathematics teaching today must emphasise the process of learning, applications of mathematics to the everyday world and problem solving (NCCA, 2005b). In order to achieve this aim and help resolve the maths problem, the Irish Government introduced a new initiative/curriculum in second level schools entitled Project Maths. 1.1 Project Maths The overall aim of Project Maths is to teach mathematics in a way which leads to real understanding (Department of Education and Skills (DES), 2010a). It involves changes to what students learn in mathematics, how they learn it and how they will be assessed. The initiative is designed to ensure an appropriate balance between understanding mathematical theory and concepts and developing practical application skills. There is a much greater emphasis placed on students understanding of

mathematical concepts, with increased use of contexts and applications that will enable students to relate mathematics to their everyday experiences. The initiative was rolled out nationally in all second level Irish schools in September 2010. Changes were implemented using a phased approach over a number of years introducing the new curriculum using five strands of mathematics (Statistics and Probability, Geometry and Trigonometry, Number, Algebra and Functions), with assessment in the examinations being adapted as each strand of mathematics was rolled out. The assessment reflects the different emphasis on problem solving and applications in the teaching and learning of mathematics and there is a greater emphasis on reading and understanding the problems. While the first two strands of the revised syllabi were first examined in 2012 at LC level in all schools, the phased implementation means that it will be 2017 before a first cohort of students who have experienced all five strands of Project Maths from 1st to 6th year will be examined. Thus it is very early to come to any conclusions regarding the successes and/or failures of the initiative. However, an interim report commissioned by the NCCA and conducted by the National Foundation for Educational Research (NFER, UK) has been published and includes findings on students attitudes and achievements. Overall the report found that there is emerging evidence of the positive impacts of Project Maths on students experiences of, and attitudes towards, mathematics (Jeffes et al., 2013). Furthermore, students are achieving more at individual strand level, and in some instances students appear to be successfully drawing together their knowledge across different mathematics topics (Jeffes et al., 2013). This suggests that students are beginning to acquire a deeper understanding of mathematics and how it can be applied (Jeffes et al., 2013). Despite such emerging evidence of the positive impacts on students experiences of learning mathematics, many challenges remain for the implementation of the revised curriculum. The majority of these challenges are concerned with the implementation process and the availability of teaching and learning resources. Further concern has also been expressed regarding the perceived literacy demands of the revised mathematics syllabus (Cosgrove et al., 2012; Jeffes et al., 2013). Such concerns highlight the importance of language and literacy in the teaching and learning of mathematics. 1.2 Language and mathematics Mathematics can be recognised as a language in its own right, a language which has its own vocabulary, grammar, symbols and punctuation (Ellerton and Clarkson, 1996). The teaching of mathematics, however, takes place within a spoken language, such as English (Zevenbergen, 2001). This spoken language is an essential element of the teaching and learning of the subject (Gorgorió & Planas, 2001). It is the vehicle for communication within a mathematics classroom and provides the tool for teacher-student interactions (Smith and Ennis, 1961). Language permits mathematics learners to ask and answer questions, to convey their understanding and to discuss their answers with others. It also plays a significant role in the processing of mathematical text and the interpretation of questions (Hoosain, 1991). The greater emphasis on solving word problems and applications in Project Maths has led many teachers to express concern. They feel that that students with low literacy levels and particularly international students for whom English is not a first language are struggling with comprehension of this material and the wordy nature of some of the questions (Cosgrove et al., 2012). the language used when phrasing a question poses a major problem for students whose literacy skills would be weak, they can therefore not answer a question they are mathematically capable of doing! This is a major issue! (Cosgrove et al., 2012:72). Many students (including those studying at Higher Level) have also expressed difficulties with interpreting word-based problems and with providing written explanations for their solutions to mathematical problems (Jeffes et al., 2013). Students also appear to lack confidence when asked to draw conclusions from a considerable amount of written information (Jeffes et al., 2013). 2. The study Approximately 1.7 million students, almost half of whom are from non-english speaking developing nations in Asia, cross borders every year to acquire a foreign education (Sawir, 2005). In Ireland, the percentage of international students has increased from 3 per cent in 2002 to 10 per cent in 2012 (Perkins et al., 2013). The Government aims to increase this further as it bids to promote the 2

internationalisation of the Irish Higher Education sector and to significantly increase the proportion of fee-paying international students as a means to diversify the income base for Higher Education Institutes (HEIs) (DES, 2010b). This need to diversify the income base of institutions was further emphasised in the Hunt Report specifically referencing income generated from the recruitment of feepaying international students (Hunt, 2011). However, the increased arrival of international students has also coincided with the introduction of Project Maths in second level schools with its strong emphasis on literacy and the English language. Of the 10 per cent of students in Ireland classified as international, about half speak languages other than Irish or English at home (Perkins et al., 2013). This research aims to investigate the effect (if any) which Project Maths has on international students mathematical performance and to view the initiative from their perspective. 3. Methodology The authors decided to use a mixed method approach by combining both qualitative and quantitative methods of research. The use of multiple methods was decided upon in order to get an in-depth understanding of the research. The study evaluates international students opinions of Project Maths and compares their scores in a traditional style mathematics examination (which refelcts mathematics education in Irish second level schools prior to the implementation of Project Maths) with their scores in a Project Maths style examination. 3.1 Participants The participants for this study comprised of 72 international students who were enrolled in a year-long International Foundation Programme in an Irish HEI. The study took place over a two year period and thus includes particapants from two student cohorts. Mathematics is one of six core subjects that all students are required to pass, along with two elective choices, in order to complete the programme. Upon successful completion of the programme, students are granted direct entry onto an undergraduate programme of their choice in the HEI. The aim of the programme is to equip them with the skills to meet the minimum entry requirements of such undergraduate programmes. All of the students who participated in the study spoke Arabic as their first language and all bar two (one Qatari and one Kuwaiti) originated from Saudi Arabia or Oman. Thus for many of these students, a major aim of the programme is to improve their English language proficiency in addition to providing them with an access route to undergratuate education in Ireland. This langauage proficiency is measured using the International English Language Testing System (IELTS). The IELTS is an internationally standardised nine band scale. Each band corresponds to a level of English competence. All four parts of the test (listening, reading, writing, speaking) and the overall band score can be reported in whole and half bands, for example 6.5, 7.0, 7.5, 8.0. In order to gain entry to the Foundation Programme students must have an IELTS score of at least level 5.0, i.e. one whole band below the entry requirements of their undergraduate destination. Students with an IELTS score of 5.0 are defined as modest English language users (www.ielts.org). They should have a partial command of the language, and although they are likely to make many mistakes, they should be able to cope with the overall meaning in most situations. Students with an IELTS of 6.0 are defined as competent English language users (www.ielts.org). They should have a generally effective command of the language despite some inaccuracies and misunderstandings. They should be able to use and understand fairly complex language, particularly in familiar situations. As can be seen in Figure 1 the majority of students who participated in this study had an IELTS score of either 5.0 or 5.5, with a small minority having an IELTS score above 5.5. 3

Figure 1 Bar Chart showing IELTS Scores of all participants involved in the study The participants were predominantly male (79%), while 70% were 18-20 years old with smaller numbers of 22-24 year-olds and two students in their thirties. All of the data was collected by the authors in 2013 (41 students) and 2014 (31 students) in the participants first semester of the programme. 3.2 Quantitative data In order to get a quantitative measure on the effect of Project Maths on international students the authors decided to compare the scores of students in Project Maths style examination with their scores in a traditional style mathematics examination. Each examination comprised of ten questions from the Junior Cycle Number strand and each question was taken from Irish second level textbooks and previous State examination papers. Students had 50 minutes to complete each examination. The questions based on the Project Maths method of assessment reflected the emphasis on understanding, problem solving and applications. The questions in the traditional style examination were technically the same questions but had numbers changed and were mathematical procedure and skill-based only with the removal of any context or language. For example: Project Maths Style Examination Question Usain Bolt, the fastest man on earth, has a stride length of 2 4 m when he is at full stride. In a 100m 5 sprint, how many strides would Usain take to cover the final 30m when he is at full stride? Traditional Style Examination Question Evaluate 46 3 2 3 Students completed the traditional style examination first and then the Project Maths style examination directly afterwards. Ten marks were awarded per question. Each student received a mark out of 100 for each assessment. At the end of the Project Maths style examination, there were also three closed-ended questions which all participants were invited to answer. The questions explored which examination the participants preferred, which examination they found more difficult and whether their English language skills had an impact on their performance in the Project Maths examination. 4

3.3 Qualitative data At the end of the Project Maths style examination there were also a number of open-ended questions which all participants were invited to answer. The questions enquired about the main differences between both examinations, the student s opinions of Project Maths and what could be done to help international students become accustomed to the changes brought about by Project Maths. The responses to these questions were transcribed, analysed and arranged into themes by the authors. 4. Results and findings 4.1 Quantitative data Normality tests and plots on the differences between the scores on the traditional style examination and the Project Maths style examination showed an approximately normal distribution with no outliers, allowing for a paired-samples t-test to be performed on the pairs of examination scores. As can be seen in Figure 2 the mean score on the traditional examination (M:53.32; SD:20.74) was found to be statistically significantly different (t(71)=9.96, p=0.000) to that on the Project Maths examination (M:34.31; SD:19.97). Figure 2: Bar Graph comparing Traditional and Project Maths Style Mean Examination Scores. Further analysis involved comparison of the mean Project Maths scores of IELTS level 5.0 students and IELTS level 5.5 students as these comprised the majority of the participants. Each of the groups followed an approximately normal distribution although the IELTS 5.0 distribution had a slight positive skew. There were no outliers. An independent-samples t-test showed a statistically significant difference (t(57)=2.97, p=0.004) between the mean scores across the two groups, with the IELTS 5.5 students achieving a mean score of 43.05 (SD: 21.63) compared to a mean score of 27.95 (SD: 2.61) for the IELTS 5.0 students (see Figure 3). By comparison, similar analysis of the traditional-style examination scores for the two groups showed no statistically significant difference (t(57)=0.942, p=0.350). 5

Figure 3: Bar Graph comparing Mean Project Maths Style Examination Scores for different IELTS Bands. The data collected from the three closed-ended questions showed that 83% of those who responded to the first question preferred the traditional style examination, while 93% of respondents found the Project Maths examination more difficult and 80% believed that their English language skills had had an impact on their performance in the Project Maths examination. 4.2 Qualitative data Qualitative data analysis was carried out on the international students responses to the questionnaire data and several strong themes emerged under each question which provides further insights into students quantitative performances in the traditional and Project Maths styled examination papers. Upon analysis of the following question: In your opinion, what were the main differences between the Project Maths and the Traditional Style questions? three major themes emerged from the responses. The most dominant distinction which students made between the two examinations, which appeared in 87.5% of student responses, was that the Project Maths examination has words and involves analysis/thought/real life context while the traditional examination was seen as being much easier, straightforward and just numbers. One student summarised this viewpoint by stating: Traditional is much easier because it gives the numbers. A smaller proportion of students (12.5%) made the distinction between the examination in a similar way while stating that the Project Maths was better despite the fact that it was considered more difficult as it it makes you think of the actual situation and it improves our English at the same time.the final theme which emerged in terms of the differences between the two examination papers was mentioned in 8.3% of student responses which stated that the traditional mathematics was familiar to them and the Project Maths was not: With Project Maths, some confusing, less confident. But traditional we have known it. Students were also asked What is your opinion of Project Maths?. Upon analysis of this data five major themes emerged. The most dominant opinion on Project Maths mentioned by 61.8% of the international students was their believe that it is difficult/hard/complicated/tricky/challenging. Of the students, 23.5%mentioned they had an issue with the Project Mathematics due to the fact that the questions are long and take more time to complete: We need to read the question many time to understand it and that may lose time. A further 35.3% mentioned it was difficult due to its nature (i.e. applying mathematics to real life contexts) and it being something students claimed not to be familiar with. One student s opinion on Project Maths touches on all three of these dominant themes: In my opinion it takes times and sometimes it s hard because it requires deep thinking. The 35.3% of 6

students who mentioned it was difficult due to the necessity of applying mathematics to real life contexts said that this was the case without mentioning issues with the English language: It s difficult because I did all of the traditional methods in high school and it s much easier but even if you understand the Project Maths sentence it s still hard to get the answer. A further 29.4% however specifically mentioned that Project Maths was difficult because of the language in it: It s hard to keep going with it because the English language is not our language, some of the language was not familiar - the questions were like complicated short stories. Sometimes I could understand the words but found it hard to explain the answer. The final theme which emerged from responses to these questions was reported by 35.3% of respondents who said that they preferred the Project Maths style as it was seen as a better way of teaching, helped in real life, encouraged deep understanding and it was useful: one student stated Project Maths is better as it shows the importance of maths in real life while another highlighted how it allows students to practice their logic and that it was a useful type of study. The final question which students were asked which resulted in the emergence of significant themes was What can be done to help international students become accustomed to the changes brought about by Project Maths?. Three themes emerged from this analysis, which are unsurprising but will be extremely useful for the development of this research project going forward. Suggestions from 43.5% of respondents to this question mentioned the facilitation of more practice for international students with this type of mathematics in the form of homework/assignments going forward: Practice the questions more to know we can deal with it. The second most dominant theme focussed on student requests for maths vocabulary to be taught specifically to help them: Teach us mathematical words, that would help, I think if there was a class to teach math language and improve our language at the same time. Maybe more projects and discussion to give us more practice in English language in Maths. Finally a significant proportion of respondents (17.4%) requested assistance in the form of some definitions on the examination paper or the provision of a dictionary: lecturers can put some brief definitions at the end of each question for difficult words. The qualitative analysis of the students questionnaire data supports the quantitative findings that students find the Project Maths examination more difficult while also providing some further insights into why this might be. Although difficulty with the English language is mentioned as one of the major reasons for the difficulty experienced by students with the Project Maths paper it should also be noted that many students suggest this difficulty would be encountered even if attempting contextualised questions like this in their own language. Such findings allow us to see the layered issues that international students are likely to have with Project Maths style teaching and learning in an Irish context. 5. Discussion and conclusion Language in mathematics has been shown to result in difficulties for all students due to unfamiliarity with contextualised mathematics problems or issues relating to miscues in word problems (e.g. 25 would be a common answer to a question such as John has now collected 18 tokens. That is 7 more than he has last week. How many did he have last week? ) (Haylock and Thangata, 2007). However such challenges appear to be amplified for international students studying mathematics where English is not their first language. Similar to the findings of the Research into the impact of Project Maths on student achievement, learning and motivation (Jeffes et al., 2013) and Teaching and Leaning in Project Maths: Insights from Teachers who Participated in PISA 2012 (Cosgrove et al., 2012) reports, this study highlights concern for non-national students for whom English is not a first language in how they manage the high literacy demands of Project Maths. The heavy emphasis on English language in the problemsolving and application questions is difficult for international students. Statistically significant differences were found between the results of student scores in a traditional style mathematics examination and their scores in a Project Maths style examination. There was also a statistically significant difference in the scores of students in the Project Maths style examination who had an IELTS score of 5.5 compared to those who had an IELTS score of 5.0. This shows that students language levels were a main factor. To support this, 80 per cent of participants felt that their English language skills had had an impact on their performance in the Project Maths examination. In effect, language had acted as a barrier to their learning of mathematics. 7

These findings highlight the importance that language has on the teaching and learning process. A student can have excellent mathematical ability but this is futile unless they can communicate effectively with their teacher and their peers and can competently understand the language in which they are being taught and examined. Students understand mathematical ideas by making connections between language, symbols, pictures and real life situations (Haylock and Cockburn, 2003). However in line with the findings of Perry and Dockett (2005), this research shows that without sufficient language to communicate the ideas being developed, to interact with peers and their teachers, mathematical development can be seriously curtailed. At present language is a barrier to learning mathematics for many international students. By acknowledging this barrier and understanding the role of language and literacy in the mathematics classroom, educators and students alike can begin to understand each other s perspectives and ensure such obstacles are overcome. References Cosgrove, J., Perkins, R., Shiel, G., Fish, R., & McGuinness, L. (2012). Teaching and Leaning in Project Maths: Insights from Teachers who Participated in PISA 2012, Dublin: Educational research Centre. Department of Education and Skills (2010a). Report of the Project Maths Implementation Support Group, Dublin: Department of Education and Skills. Department of Education and Skills (2010b). Investing in Global Relationships Irelands International Education Strategy 2010 15, Report of the High-Level Group on International Education to the Tánaiste and Minister for Education and Skills, Dublin: Department of Education and Skills. Ellerton, N.F. and Clarkson, P.C. (1996). Language factors in mathematics teaching and learning, in A.J. Bishop et al (Eds.) International handbook of mathematics education (pp. 987-1033). The Netherlands: Kluwer Academic Publishers. Gorgorió, N. and Planas, N. (2001). Teaching mathematics in multilingual classrooms, Educational Studies in Mathematics, 47(1), pp.7-33. Haylock, D. and Thangata, F. (2007). Key Concepts in Teaching Primary Mathematics, Sage Publications. Haylock,D. and Cockburn, A.D. (2003). Understanding Mathematics in the Lower Primary Years: a guide for teachers of children 3-8, Sage Publications. Hoosain, R. (1991). Psycholinguistic Implications for Linguistic Relativity: A Case Study of Chinese. Hillsdale, NJ: Lawrence Erlbaum. Hunt, C. (2011). National Strategy for Higher Education to 2030 - Report of the Strategy Group, Dublin: Department of Education and Skills. International English Language Testing Score (IELTS) [online], available: www.ielts.org [accessed January 2015]. Jeffes, J., Jones, E., Wilson, M., Lamont, E., Straw, S., Wheater, R. and Dawson, A. (2013). Research into the impact of Project Maths on student achievement, learning and motivation: final report. Slough: NFER. National Council for Curriculum and Assessment (2005a). Review of Mathematics in Post Primary Education, Department of Education and Science, Dublin: The Stationary Office. National Council for Curriculum and Assessment (2005b). International Trends in Post Primary Mathematics Education [online], available: http://www.ncca.ie/uploadedfiles/mathsreview/intpaperoct.pdf [accessed March 2015]. Perkins, R., Shiel, G., Merriman, B., Cosgrove, J. and Morgan, G. (2013). Learning for Life: The Achievements of 15 year olds on Mathematics, Reading Literacy and Science in PISA 2103, Dublin: Educational Research Centre. Perry,B. and Dockett,S. (2005). What Did You Do in Maths Today?, Australian Journal of Early Childhood, 30(3). Prendergast, M. and O Donoghue, J. (2014). Students enjoyed and talked about the classes in the corridors : pedagogical framework promoting interest in algebra, International Journal of Mathematical Education in Science and Technology (IJMEST), 45 (6): 795 812. Sawir, E. (2005). Language Difficulties of International Students in Australia: The Effects of Prior Learning Experience. International Education Journal, 6(5), 567-580. Smith, B. O and Ennis, R. H. (1961). Language and concepts. Chicago: Rand McNally & company. State Examination Commission (SEC) [online], available: www.examination.ie [accessed February 2015]. 8

Zevenbergen, R. (2001). Changing contexts in tertiary mathematics: implications for diversity and equity, in D. Holton (Ed.) The Teaching and Learning of Mathematics at University Level, An ICMI Study. Dordrecht, The Netherlands: Kluwer Academic Publishers. 9