The Relationship between the performance
of adult learners in English as a second language
and in mathematics in L1
A Research project for the degree of Master of Applied Linguistics, faculty of Arts,
university of Groningen
Acknowledgments
Showing gratitude to whoever has helped me to produce this work at this level,
and special thanks to:
Louisa Vahtrick
Prof. Cees De Bot
who have helped me the most in editing and analyzing my work to come in this
final form.
Special thanks to:
Bogerman School
The Relationship between the performance
of adult learners in English as a second language
and in mathematics in L1
Abstract
Research to date has mainly focused on the relation between bilingualism and mathematical performance through similar perspectives: much of the research was concerned with immigrant
participants in developed English-speaking countries; others were concerned with testing this relationship through young learners of English and how they performed in mathematics in L2.
This study is set in a non-English speaking community where English is taught as L2 and mathematics is taught and tested in L1. The data of the yearly grades of pre-university students
in English and mathematics throughout four years was gathered in order to investigate the relationship between students’ performance in English and mathematics. A set of correlational
analyses as well as ANOVAs tests were conducted on these data. The results of the study showed significant weak to moderate positive correlations between students’ performance in English and mathematics. These results supported Spearman’s (1904) General Intelligence (GI)
theory – that cognitive tasks do correlate with one another.
which these theories are based. That is, Spearman did manage, through psychometric
investigations, to prove statistically and empirically the actual existence of a positive correlation among participants’ performance in different cognitive tasks. On the other hand, to date there has been not one single empirical validating study that supports Gardner’s non-g intelligence
(Gottfredson, L. S. (2006). On the basis of g-intelligence theory, the individual who performs well in mathematics (as an example of a cognitive field) should be able to perform quite as well-efficient in other cognitive tasks such as acquiring a second language, English for example. This shows, in essence, that there is a relation between the ability to learn a second language and the mathematical skills of the same person. However, the nature of this relation has not been
thoroughly enough investigated with respect to adult learners of a second language. Spearman’s theory was further backed up with a number of recent studies; one of which suggests that
students who are not proficient in learning a second language, and namely English, usually underperform in subjects that depend mainly on mathematics; in other words, science subjects (Alt & Beal ,2012). Varley (2007), Professor in Cognitive Neuroscience at the University of Sheffield and author of a number of studies on the connections between linguistic abilities and mathematics, suggests that language, as an L1 or L2, represents a unique competence which contributes to many cognitive tasks. She compares mathematics as “a parasite on our language faculties” (Freiberger, 2007). Her claims were supported by Gordon’s (2004) interesting study on an Amazonian tribe who have explicit words only for ‘one’ and ‘two’, and they refer to any other numbers as ‘many’. Through his study, it turns out that the members of this tribe are unable to perform simple mathematics tasks when numbers are greater than ‘three’ (Freiberger, 2007). Further evidence for the close connection between language learning and mathematics comes from a number of neurological studies. In one of these studies Varley (2007) uses functional imaging of the brain to prove the increased activation of language areas when certain
mathematics tasks are performed. She continues that “a considerable number of people with a language disorder: aphasia, also end up with acalculia, a condition that impairs mathematical ability" (Varley, 2007). Furthermore, through a recent study, Morales (2013) found out that bilingual children hold an advantageous position compared to monolingual counterparts in several cognitive tasks including mathematics (Morales, 2013). This study included children aged between 5 – 7 years old in two groups: Bilinguals and monolinguals. Researchers found out that bilingual children consistently outperformed the other group in cognitive tasks, including mathematics, which mainly involves using working memory. Also with more complex
capacity (WMC) (Gathercole, 1993), and the capacity to perform well in mathematics. Therefore, this kind of relation between language learning and mathematics may be useful to predict learner’s possible potentials in either of these subjects based on the performance on either of them. In other words, excelling in learning a certain language can be a sign for having high potentials in learning mathematics, and vise versa. The current study is intended to investigate the nature of the relation between learning a second language and the mathematical abilities for adult learners of English.
Several everyday observations essentially support the existence of the relation between learning a language and mathematics. An example of such relation between language and mathematics is learning the multiplication tables. Most people learn these, not as abstract patterns of number, but they rather learn these mathematical patterns through language, almost in a form that looks like a poem, and it is not strange for some people to recite the poem linked to the table in order to find the answer to a mathematical problem. Furthermore, Geary et al (1996) suggest that
Children’s mathematical abilities are greatly influenced by a complex mixture of factors that have to do with language and culture. For example, Chinese children are mostly good at mathematics owing to their mother tongue: Chinese or Mandarin (Geary, 1996, Hatano, 1990). In other words, in one of his research studies comparing the mathematical skills of children coming from different backgrounds, Miller (2000) has found out that the Chinese children at the age of four do actually outperform American children in counting numbers in their own
languages (Miller 2000). There were also a number of studies that focused mainly on
investigating the mathematics skills of students in elementary education. A number of studies (e.g. Clarkson, 1983, 1984, 1991a; Clements & Lean, 1981; Jones, 1982; Souviney, 1983), could successfully report that English as a second language plays a positive role in enhancing the mathematical abilities. As an example for one of these studies, Clarkson (1983, 1984) conducted an exploratory study on Guinean 6th grade students in order to investigate the effects of
bilingualism on other cognitive tasks. Through a set of language, mathematics tests, a survey on home background and a test on cognitive development, he found out that the level of competence in the students’ mother tongue as well as in English as L2 had a significant influence on their mathematical performance. His results particularly support Cummin’s threshold hypothesis as well as backing up the notion that bilingualism should be considered as a multi-dimensional entity rather than an one-dimensional one, and particularly when making educational decisions (Clarkson, 1984).
adult’s language system that distinguishes it from children’s language system. Hahn and Haynes (2004) presented a study which shows the significant difference in the language of children compared to the language system of an adult (Hahn & Haynes, 2004). This clearly justifies the reason why I want to investigate the relation between second language learning and mathematics for adult learners rather than younger learners of the language.
For the previously mentioned reasons, I will try, in this study, to fill in the gaps of the previously mentioned studies. I will investigate the relation between mathematics and learning a second language (English in this study) from a rather different angle. This means that I will mainly deal with the perspective of bilingualism – with English as an L2, and its relation to mathematics and logical thinking abilities for students in secondary education.
I will investigate the results of these adult learners before deciding which major they will
specialize in as well as after having decided on which major. In order to put these assumptions to test, their yearly grades at school will be investigated. The educational system already provides comprehensive evaluation for both of subjects through a set of tests that evaluates the sub-skills of each subject thoroughly which will provide accurate information about their performance throughout 4 years. I will check the correlation between the scores of the students in these tests. The results of the study are expected to be very beneficial and important in both cases: Whether the relation between mathematics and learning English as L2 is proven to be significant or not. This is because in case learning English as an L2 is significantly supportive and helpful for improving mathematics abilities, it can be then an important component that should be stressed on for all learners willing to achieve high levels of mathematical abilities. On the other hand, in case the results do not show significant, then it would provide us with evidence to de-stress the importance of English as a school subject for students willing to specialize in mathematics or the connected subjects. In other words, students who want to major in physics, engineering or mathematics in general should be given the option to study English or no. Or, at least, the
BACKGROUND LITERATURE
Measuring English proficiency levels for non-native English speakers has always been a
controversial issue among EFL teachers. One reason is because learning a second language – as a skill - is easily affected by many elements both internal and external. Woodrow (2001) was able to prove that both self-efficacy and anxiety do have a considerable impact on one’s performance in a language, especially one’s L2 or L3 (Woodrow, 2001). Motivation also plays such a vital role in both language acquisition and language performance (Dörnyei, 1994). One of the attempts made to measure the English proficiency level in an accurate way is breaking down language to a set of skills that can be measured separately. In the last decades, when educational institutions and universities started having a lot of international students studying in English, they required passing some tests before being admitted to such programs taught in English in international universities, and it has become a very important prerequisite. As a result, different measuring methods evolved which are all aimed at evaluating English proficiency level through a recognized standard. International English Language Testing Service (IELTS) or Test of English as a Foreign Language (TOEFL) are two of the most famous English tests which measure general language proficiency in the four mentioned areas: reading, writing, speaking and listening. Interestingly, Grabe (1992: 50-30) states that English, or any other language, does consist of four separate skills; each of these four skills is composed of a set of sub-components. For example, the sub-skills for reading are:
1. linguistic skills;
2. the perceptual automatic recognition skill;
3. knowledge and skills of discourse structure and organization; 4. knowledge of the world;
5. synthetic and critical evaluation skills;
6. Meta-linguistic knowledge and skills. (Grabe, 1992)
It is also quite remarkable that McCarthy (1999) argues, in reaction, that these sub-skills of reading can, more or less, also be considered as sub-skills of writing, speaking and listening. That is why, as McCarthy (1999) further comments, there is an obvious growth of realization among linguists as well as EFL teachers that language skills – which have been thought treated in isolation in the past- should no longer be separated or treated in seclusion (Wray & Medwell 1991:3). Alternatively, there is another theory that deals with language holistically referring to reading and writing skills as ‘literacy’ and listening and speaking as ‘oracy’ (ibid.:3). On the other hand, the assessment of mathematics skills is completely different. The reason is that it mainly depends on rational and logical thinking. There is a set of mathematic skills that are targeted directly and indirectly. Each of these skills is evaluated through concrete and clear cut answers. The Trends in International Mathematics and Science Study (TIMSS) is an
say that the main reason to choose this test because it is considered as the most comprehensive way to measure the mathematical as well as logical thinking skills for the learner. In
mathematics, knowing only the rules is not enough, but finding the logical relations between the rule and the problem and then applying the rule by using one’s logical thinking.
These tests for assessing English and mathematics provide a standard for the degree of
proficiency for English and an indication of learner’s performance in mathematics. Based on the results of these tests, each learner is placed in the category that best describes his performance in language. There are several criteria used to categorize students and other learners of English and other languages. One of the most used criterion used in Europe is the CEFR (Common European Framework of Reference for Languages: Learning, Teaching, and Assessment). This framework is used to describe the achievements of learners of foreign languages all across Europe, so it applies to every language spoken in Europe (Europe council, 2011). The Common European Framework divides learners into three broad divisions and each division is divided into two sub-divisions: A Basic User A1 Breakthrough or beginner A2 Waystage or elementary B Independent User B1 Threshold or intermediate B2 Vantage or upper intermediate C Proficient User
C1 Effective Operational Proficiency or advanced C2 Mastery or proficiency
The CEFR further describes what the learner should be able to do in each level. Please see (appendix 1) for the full description of each level.
These different methods and tests to measure English proficiency all have evolved with the purpose of measuring only one aspect of the human linguistic abilities, which is language proficiency.
individual’s intelligence is from the G factor. The Intelligence quotient test, or as it is widely known by “IQ test” was first developed by Alfred Binet, Victor Henri and Théodore Simon (1905) and it was first called Binet-Simon test. Their basic goal was to be able to identify mental retardation among school children so that they can offer special help for children with special needs (Kaufman, 2009). To that effect, this test was more or less considered as an indication to the child’s mental age in order to make sure he/she does not suffer from any mental problems. Afterwards, it was applied on adults in order to identify if they had any mental disorders (Kaufman, 2009). A decade later, Lewis Terman (1916) managed to develop Binet-Simon test into Stanford-Binet intelligence scale which was called later by Intelligence quotient test “IQ test” (Richardson, 2003)
General intelligence (GI), general cognitive abilities and IQ are all terms that are now used interchangeably (Deary et al 2010). Thus, we can conclude that the major difference between the two theories is that Spearman believed that intelligence can be measured by means of IQ test and that there is only one type of human intelligence. Gardner, on the other hand, believed that intelligence cannot be measured through a simple IQ test because there is more than one type of human intelligence. Linguistic intelligence and logical/mathematics intelligence are two types of the intelligences suggested by Gardner, which he believes that they should not have any
significant correlation. However, a number of studies has been conducted which might provide some evidence against what Gardner stated in his theory.
As a reaction for this fundamental theory of general intelligence (GI), or the theory of general factor proposed by Charles Spearman (1927), Gardner (1983) suggested a contradicting theory in the way we look at human intelligence. His theory proposes that the human brain consists of nine different intelligences rather than one general intelligence measured in IQ tests. His theory found a ready audience, and it was adopted by many psychologists since that time. Gardner believes that the ability of the human brain cannot be narrowed down to a simple number called ‘IQ’. Remarkably, Gardner does not approve of the IQ results proposed by Spearman in his studies about g-intelligence, and even doubts its reliability on the grounds that he claims that human’s intelligence too complex to be interpreted by a simple number through an IQ test. In spite of his opinions about the IQ test, he does admit that these kinds of tests can foretell about one’s later life in terms of the cognitive achievements (Gardner, 1983). Gardner denies the idea of the very existence of correlation between any of the intelligences, and furthermore, he compares this idea (the idea of finding correlation between types of intelligences) to Gall’s idea of phrenology. Phrenology is an idea evolved in the late 19th century which is centered on finding a correlation between the physical shape of the skull and mental abilities. He believes that within the field of psychology, almost every test of abilities correlates at some point with other test of abilities. Expectedly, Gardner’s theory was widely criticized, for he did not provide a clear definition of intelligence as it is suggested by Davis (2011). To date, there is hardly any study that validates or supports Gardner’s theory about human intelligence. Sternberg (1994) reported there is no
evidence for MI theory" (Allix, 2000). Even Gardner himself (2004) reported that he would be "delighted were such evidence to accrue" (Gardner, 2004). Interestingly, Gardner continues "MI theory has few enthusiasts among psychometricians or others of a traditional psychological background" since they require "psychometric or experimental evidence that allows one to prove the existence of the several intelligences." (Waterhouse & Lynn, 2006). Moreover, Gardner denies the existence of intelligence as traditionally understood by people supporting the GI theory. Instead, he uses the word "intelligence" where others have traditionally used words like "ability" and "aptitude". White (2006) further points out that the criteria upon which Gardner depended in his theory is “very arbitrary and subjective” (White, 2006). Others further suggest that this is just an anecdotal theory or a mere opinion about what he thinks the way the human brain works.
Miller (2000) tried to investigate the possibility that the linguistic effects may have on the mathematical cognitive abilities and how these differences may vary for different levels of development for different areas and levels of mathematical cognition. More specifically, his main concern was the cross-language variation in number naming-system. For this purpose, he studied the effects that language, whether as an L1 or L2, has on the development of
1) From ‘one’ to ‘ten’ Numeral 1 2 3 4 5 6 7 8 9 10 Cardinal Chinese Written 一 二 三 四 五 六 七 八 九 十 Chinese
Spoken yi er san si wu liu qi ba jiu shi
English One Two Three Four Five Six Seven Eight Nine Ten
ordinal Chinese Chinese ordinals are all formed by adding a prefix 第 (di) to the cardinal number
English first second third fourth fifth sixth seventh eighth ninth tenth
2) From ‘ten’ to twenty’
Numeral 11 12 13 14 15 16 17 18 19 20
Cardinal
Chinese
Written 十一 十二 十三 十四 十五 十六 十七 十八 十九 二十
Chinese
Spoken shi yi shi er shi san shi si shi wu shi liu shi qi shi ba shi jiu er shi
ordinal Chinese eleven twelve thirteen fourteen fifteen sixteen seventeen eighteen nineteen twenty
English eleventh twelfth thirteenth fourteenth fifteenth sixteenth seventeenth eighteenth nineteenth twentieth
3) From ‘twenty’ to ‘ninety-nine’
Numeral Rule Example
Cardinal
Chinese
Decade unite (two, three, four, five, six, seven, eight, nine)+ten+unit 三十七
San shi qi English
Decade name (twen, thir, for, fif, six, seven, eight, nine) + ‘-ty’ + unit Thirty seven
ordinal
Chinese Chinese ordinals are all formed by adding a prefix 第 (di) to the cardinal
number 第三十七
English Cardinal decade name + ordinal unit name (if any)
Or “-th” (if no unit value) Thirty second
Miller (2000) concludes that the complexity of the English cardinal and ordinal number names contributes to delaying a certain stage of development in their logical thinking which stems from the unavailability of a certain regular rule to follow in naming both the ordinal and the cardinal numbers. American participants usually stopped after saying “twenty-twoth” because they have never heard it, so they know that it is not correct. On the other hand, Chinese-speaking children face a much simpler process that enhances their development in their logical thinking (Miller, 2000).This shows that, learning a certain language, plays a crucial role in enhancing or hindering
the development of logical thinking which is a fundamental basis needed for excelling in mathematical skills. Other aspects of this relation were also conducted in different later studies which were more concerned about one of English skills, reading in particular, and its relation to mathematics, this aspect was thoroughly studied by Plomin (2012).
According to his observations, Plomin (2012) found out that children who have reading
difficulties, also have co-existing problems with mathematics. To investigate this effect, Plomin had studied this observation in relation to word decoding and other global measures of reading on 5,162 twin pairs at age 12 years. Results of multivariate genetic analyses of phenotypic factors of mathematics, word decoding, and reading comprehension showed substantial genetic and shared environmental correlations among all of these three domains. Plomin further explains that the relation between reading comprehension and mathematics is “an intriguing one”
(Plomin, 2012). A number of studies (e.g. Durand, Hulme, Larking, & Snowling, 2005; Hart, Petrill, Thompson, & Plomin, 2009; Hecht, Torgesen, Wagner, & Rashotte, 2001) succeeded in finding a medium to strong correlation between reading comprehension skills in English as L1and mathematics. Other studies (e.g., Dirks, Spyer, van Lieshout, & de Sonneville, 2008; Landerl & Moll, 2010) have mainly focused on word decoding and compared the difficulty in reading a word with the difficulty in mathematics. This link between these two aspects was generally attributed to the ability of the working memory and its contribution to both skills (De Smedt, et al 2010; Hecht et al., 2001).
Gathercole (1993) further suggests that working memory has a considerable effect not only on reading skills but also on a wide range of language skills such as vocabulary acquisition, speech production, reading development, skilled reading, and comprehension (Gathercole & Baddeley, 1993). This manifests in essence that that memory capacity and working memory in particular, is important in both math and language. This is indeed supported by the results of Plomin’s study which showed a correlation (which was not a very strong correlation) between word decoding and mathematics skills.
Fluent bilingual people can often think in their second language—they can understand and answer a question without translating it into their first language. However, anecdotal evidence suggests that this ability breaks down when the question is an arithmetic problem. In such cases, the person solves the problem in his or her native language, translates it, and then gives the answer in the second language. This effect was investigated by Alt (2012) in order to see how Spanish students will react to mathematical problems in English and the same problems but in their mother tongue, Spanish. Her research was mainly aimed at investigating the role language plays in supporting and promoting mathematics skills as well as facilitating acquiring its rules and even making solving mathematics problems much easier.
Alt et al. (2012) was able to prove in her research that there is a significant effect of language on mathematics learning and problem-solving. Alt investigated the effect of translating the
Spanish immigrants to the United States. The research specifically investigates whether Spanish-enhanced math assessment would result in improved scores for English Learners who used Spanish as their mother tongue and English as their second language. To test this, the participants were exposed to a set of mathematical problems in English; when participants answered incorrectly to the given items, a Spanish version comes up. Alt further predicted the degree of benefit from this translation through the participants’ degree of proficiency in Spanish. The results of this research showed that mathematics problems do not only measure the
mathematics skills of the learners, but it also measures the degree of the language dominance, and therefore, it shows the supporting role that language plays in the participants’ mathematical and logical abilities. This research and others to follow will clearly shed some light on the fact that there is a relation between language abilities and the mathematics abilities.
Although all of the previously mentioned studies discussed – each from a difference perspective – a certain aspect of the relation between language proficiency and mathematics abilities, these studies did not tackle the language abilities for an adult or a senior learner in particular and its relation to logical thinking and mathematics abilities. Since language abilities change according to age (Bornstein, Hahn & Haynes, 2004), there should be a co-existing difference that may affect the relation between English and mathematics. Despite the fact that these studies (e.g. Miller 2000, Alt 2012, Thompson, & Plomin, 2009; Hecht, Torgesen, Wagner, & Rashotte, 2001) represent a clear indication to the existence of a relation between language proficiency and logical and mathematical abilities, the nature of this relation will naturally, therefore, change, for a developmental modification in one variable of the equation (which is English proficiency development) has taken place. In other words, language development from childhood into adulthood can possibly affect one’s logical abilities in performing in mathematics and other science subjects. This fact was quickly realized by Barton and Neville-Barton (2005) who conducted an interesting study tracking the relationship between English language and
mathematics learning for adult non-native speakers. They investigated two groups of non-native English speakers to find the differences between their English proficiency and mathematics skills. The first was a Chinese group who mostly chose to major in mathematics – rather than in English or any other language – because they outperform other students of their ages in
ground while considering the results. In case of the Chinese group, the levels of disadvantage were measured by comparing the participants test results in English and in Mandarin. Similarly, the group from the Pacific Islands has undergone the same procedure. This study is, therefore, aimed at measuring the effect of one’s language on solving mathematical problems in the second language and not in their mother tongue. Elements that have to with the similarities and
differences between the L1 of these two groups may have had a noise effect on the results of the study. In other words, Polynesian, which is the language spoken in the Pacific Islands, uses the roman letters, while Mandarin, which is spoken in China, has a completely different system of alphabet. These differences may be responsible for facilitating acquiring English for a group and making it difficult for the other. A similar preceding research studies as well as other anecdotal study conducted by Neville Barton and Barton (2003) did promote the same notion. Through a mathematics test designed in English by Neville Barton and Barton, a comparison between the mathematics abilities of native speakers of English (from New Zealand) and the abilities of non-native English speakers (learning English as an L2) was conducted with the purpose of
investigating whether the native English students will have an advantage in their performance in mathematics or not. The results of this study were that they found out that native English
speakers (the New Zealander participants) hold an advantage of 10 percent over the non-native English speakers in their overall performance in mathematics (Neville – Barton 2003). Although the technical mathematics discourse should be more important than general English in
performing in mathematics in general, it seems that English does play a role in promoting or demoting performance in mathematics.
These previous studies may seem in line with investigating a relation between language, which is English in particular, and performance in mathematics. In this perspective, they do indeed tackle an aspect of this relation; nevertheless, these results cannot be a clear cut evidence of the
In order to fully understand the aiding-role that language plays with respect to technical mathematics discourse, Halliday, M. (1978) p. 65) points that out the following:
“The mathematics register in English is the distinct way in which mathematical meaning is expressed in that language. Dale & Cuevas (Dale & Cuevas, 1987) describe it in terms of unique vocabulary and syntax (sentence structure), and discourse (whole text features), examples of which are given below. Vocabulary associated with the mathematical register includes:
Technical vocabulary, e.g. quadrilateral, algorithm, factorial;
Everyday vocabulary that takes on different meanings, e.g. rational, range,
product, integrate;
Complex phrases combining more than one concept, e.g. least common multiple; Several words signaling the same mathematical concept, e.g. add, sum, and,
increase, plus;
General English vocabulary; symbols (which can be both conventional and free,
depending on context) e.g. +, =, π, x, y.”
These examples mentioned by Halliday (1978) manifest the role of a language in the discourse of mathematics and how it affects it heavily. In order to do mathematics in the second language (English, for example) it is not sufficient just to learn a list of words without knowing the mathematical context of these words. On the other hand, it is not possible to learn mathematical words without having to know first their meaning and conventions. Halliday continues with providing an example that shows that a single mathematical concept is expressed and conceived in so many different ways every time the language of the discourse changes:
“Mathematical sentences have distinctive syntactical features resulting from the importance of abstract relationships. For example, comparative structures are more frequent. This presents particular problems for EAP students whose own languages express comparatives in different ways:
In English we say: A is twice as long as B
The equivalent in some other languages are (MacGregor, & Moore, 1991): Spanish:
Chinese: Korean:
The length of A is the double of B A compared to B long two-times A B two-times is”
Another important syntactical characteristic that shows the effect of the language upon mathematics is the use of prepositions, and how the change of the implication of a single preposition in different languages would change the mathematical convention altogether.
“consider the following three sentences.
One way prepositions affect meaning is to help determine the order in which numbers are combined when written with symbols, for example: 10 is divided by 5, (10 ÷ 5), and 10 is divided into 5, (5 ÷ 10).
We often shorten a division by saying “5 into 235” to mean 235 divided by 5. But in algebra this preposition indicates distributive multiplication:
“3 into (a + 2b)” means 3 multiplied by (a + 2b) = 3a + 6b.
As another example, “by” usually indicates multiplication (5 by 4 = 5 x 4), but it is also part of the phrase used to indicate addition and subtraction, for example: “increase 5 by 4” and “decrease 5 by 4”. There are some countries where “3 by 4” is the phrase for division, meaning “three quarters” (MacGregor, & Moore, 1991). These examples driven from Halliday’s extensive study about the relation between language and the discourse of mathematics necessarily undermines the results of Barton and Neville Barton’s (2003, 2005) studies in investigating the relation between language and mathematics. The reason is that every language differs in the nature of its implications in its mathematical discourse and these differences even extend to the preposition that can completely change the rule for mathematical problems. To this effect, the best way to measure the mathematical abilities and the mathematical aptitude is measuring the participants’’ performance in mathematics in their native tongue so as to avoid any confusions or mistakes whose source is not the problem in mathematics itself but in the language with which mathematics is being produced.
Finally, it is important to understand the distinction between the adult’s language system and a child’s system of language. As it has been shown, the vast majority of the literature discussing the relationship between English as a second language and mathematics has been restricted to testing younger participants. This puts forward the necessity to investigate this relationship with adult participants. It was also presented how the studies that investigated the relationship
RESEARCH QUESTIONS
The study described below has addressed the following research questions:
There is a number studies as well as other anecdotal evidences that suggest that learners of the second language who perform well in linguistic tasks, tend to outperform monolinguals in performing in mathematics and other cognitive tasks. They are also more likely to have high potentials in mathematics or any other connected subject such as physics, algebra and any science-connected subject that necessarily involve logical thinking.
(1) What is the correlation between the performance of bilingual adult learners studying English as a second language and their performance in mathematics skills (as an
indication for logical thinking) for students of secondary education in the Netherlands? In accordance with the discussion to follow afterwards, it is hypothesized that there will be a significant correlation between the performance in English as a second language and mathematics aptitude. The nature of this relation is a positive correlation; the strength of the correlation is hypothesized to be medium to strong correlation.
Spearman (1903) as well as Howard Gardner (1983) introduced two different theories that explain how the human brain works. These two theories propose two contradicting perspectives about human intelligence. One considers the brain as one unit that processes all sorts of information while the other suggests that the brain contains ten different areas, and each of which is responsible for a certain kind of intelligence.
THE STUDY Design
The design of the study is basically tracking the development of one group of participants of adult learners for their progression in English language as well as their progression in mathematical throughout four years in their secondary and upper-secondary education. The progression of English proficiency was measured through tests which the participants had to go through as part of their school study. These tests did integrate all language skills: Reading, writing, speaking, listening and conversation, and produced a final grade at the end of each year. The mathematics progression was measured through a set of tests that the students had done throughout four years of their education system. These tests for both subjects were conducted in the participants’ schools as a part of their pre-university education system which is known in the Netherlands as Voorbereidend wetenschappelijk onderwijs (VWO) system. The data was
collected, analyzed and tested for correlation between the progressions of both of these subjects.
Methodology
The key issue associated with addressing the research questions is the method used to analyze the data collected as well as the number of the participants involved in the study. Testing a large number of participants (84 participants) is crucially important for the accuracy of the results in this study in particular. Due to the complexity of classroom reality, there are tens of other variables that indirectly contribute to affecting the main variables investigated in this study. In other words, the effect the teacher has on students’ understanding and even their attitude towards a certain subject can be profoundly great. There are other elements as well whose effect even extend outside the classroom, i.e. family problems, moving to another house, etc. The best way to avoid letting such factors affect the results of the study without having to operationalize all of them, which would be very complicated, is choosing for a larger number of participants which will minimize the effects of other elements on the final results. Moreover, through this study, the main aim is to be able to quantify the data and to generalize the results from the sample to the population so that the study would have a practical application in the educational field. For these reasons, using a quantitative research approach to address the research questions of this study is the appropriate method to investigate the main concern of this study. Furthermore, the
quantitative research will essentially provide a fundamental connection between all empirical observations and the statistical expression of the quantitative relation between the two variables of the current study.
available resources. Owing to the complexity of measuring the variable of the progression of English proficiency in an accurate and an objective way, different methods should be used in order to measure all the possible aspects of all language skills that directly and indirectly affect the progress of the participant in English proficiency. That is why using an exam that tests the sub-skills of English very thoroughly is a necessity which will definitely be an advantage for the accuracy of the results of the study. On the other hand, measuring mathematical skills and logical thinking is not, by nature, as complicated as measuring the progression of a language. In other words, mathematical and logical abilities do not have as many sub-level as in English language. Nevertheless, when the participants are assessed several times during the year in different
mathematical skills, it will definitely contribute to delivering data that can accurately express the actual level of performance of the participants.
Data
The set of data used in the current study comes from a database from one of the upper-secondary schools in the Netherlands. The data concerns the scores of the pre-university students in English and mathematics throughout four years starting at 2009 and ending at 2012. The data was
completely anonymised for the privacy of the test takers. In the Dutch educational system, the VWO system consists of 6 years, and on the 4th year, the student chooses one of four profiles (1) Natuur en techniek (nature and technique) (2) Natuur en gezondheid (Nature and health) (3) Economie en maatschappij (economy and society) , (4) Cultuur en maatschappij (culture and society). Each of these profiles prepares the student to join certain majors in university in order to qualify the student for the preferred career which the student would like to do in the future. The evaluation system used to test both English and mathematics in the 3rd year of VWO is slightly different from the system used in the years from 4 until 6. The reason for this is that system on which the examination system for last three years of this diploma is built, is general system used across the country to ensure equality and fairness. Before these three years, schools are free to adopt the system they see is suitable for their students. This system has also to be approved by the ministry of education in the Netherlands as well.
Measuring English proficiency from 4th to 6th grade
In the upper-secondary educational system in the Netherlands (which is known as VWO), every student gradually builds up the final grade for each school subject throughout the whole year. Each figure that the student gets throughout the year and included in the final grade is called a school exam or (Schoolexamencijfer or SE). There is also another exam at the end of the final year called central exam (centraal examen or CE) which does also have a weight in the total grade of the student. Some subjects do not have a central exam (CE), and for these subjects, the grades of SE or school exams are considered as the final grade for this subject.
the final examination or (Centraal StaatsExamen or CSE). Therefore, every school in the
Netherlands has its own PTA system which means (Programma van Toetsing en Afsluiting) and this stands for (program for testing and evaluation). The PTA program of every school should be approved by the (DUO) the ministry of education in Holland in order to ensure that the school is covering certain aspects of each subject through certain amounts of hours and a specified number of tests.
The PTA program of the school from which I have obtained the grades of the students deals with the assessment of English through a set of tests that evaluates English language skills
comprehensively.
First: Reading and literature:
The evaluation of reading skill in English includes two tests: (a) Free reading test
In order to prepare for this test, students are required to read a number of books during the year, and afterwards they are assessed orally for their understanding of these books. The board of the school chooses a number of novellas both in Dutch and in English (2 novels in Dutch and 3 novels in English). The school offers a certain schedule which helps the students to organize their time and keep them on the right track. Students are required to read and understand the main events of the novel and they should be able to elaborate over the characters in the story. The evaluation of these readings is completely carried out in Dutch. In other words, the oral questions are asked in Dutch, and the student is required to provide all the answers in Dutch. And, providing answers in English will cause the student to get no points for this test. The reason for this is that the main focus of this evaluation is not assessing
production of language as much as assessing how good the student did understand the text itself. This helps the student to focus more on the events and what he has
understood from the text rather than too much focusing on forming good English sentences. Students are also required to provide a slight literary analysis for the events and the characters of the novella. The weight of this test to the final grade of the student is 17.5% of the total grade of the whole year.
(b) Final reading exam (Centraal StaatsExamen or CSE)
information. This ensures that students are evaluated in various ways through various reading methods. The exam is corrected by teachers from the school itself, and then it is revised again through a committee of teachers entitled by the minister of education to revise the correction to make sure that the procedure is accurate and fair.
Second: listening
In order to assess the skills of listening for the students at this stage, a CITO listening test is used to measure the listening skill. CITO stands for (Centraal Instituut voor
Toetsontwikkeling) which means (central institution for tests development). This represents 10% of the final grade of the whole year. The duration of this test is 60 minutes in which students are asked to answer different questions that cover almost all sub-skills of their
listening skills. The first kind of questions deals with selecting the relevant information which is the lowest level. Afterwards, they are asked to give the meaning of the most important information given in the listening fragment. After that, students are asked to draw conclusions depending on what they have listened to. They also listen to other fragments in which students are required to tell what the intentions of the speaker or the subtle message that he/she is trying to convey. That is why this test is quite comprehensive with dealing with listening skill.
Third: Speaking
For speaking and conversation skills, there are two different ways to evaluate students’ speaking and conversational skills according to which year the student is in. In other words, students who are in the final year are evaluated differently than the ones in the fourth or the fifth year.
- Fourth and fifth year:
Students in these years are required to prepare and carry out a conversation in front of the teacher. Students first need to form a group of three, and they are required to prepare a topic about which they will talk and discuss. They are required to have a meaningful discussion in which each student would have a different opinion so that they would have a kind of argument. The teacher basis his/her evaluation on three main criteria: (1)
pronunciation, (2) grammar and structure, (3) the strength of arguments and how well students have prepared for their discussions.
- Graduation year:
that is concerned with presentation is graded by the teacher and considered as their grade for their speaking and conversational skills. Students have 25 minutes to perform their
presentation, and they are assessed according to the same criteria mentioned before. The weight of this presentation from the final grade is 10%.
Fourth: Writing
For writing skills students are required to write different kinds of essays throughout their last three years. In their fourth year, students are required to write an essay about a topic of their choice. They have to manifest their knowledge about the conventions of writing essays, i.e. introduction, body paragraphs, and conclusion. For the fifth year, they are required to write a compare and contrast essay in which they are required to use connectors that show addition and contrast while abiding by the writing conventions. In the final year, students should write an argumentative essay which should not exceed 700 words. In this essay, students have to
demonstrate their knowledge about a certain topic and how to structure an argumentative essay properly. Moreover, they are required to state their opinion in the essay. They are evaluated on basis of the strength of their arguments and the language used. The duration of this test is 100 minutes, and students are obliged to perform the test on the computer. The weight of this mark is 10% of the final grade.
Measuring English proficiency for 3rd grade
In the secondary education for the 3rd graders of VWO, students are tested for nine times during the year, and each test evaluates a certain skill or sub-skill and contributes to the final grade of the student in this year. Firstly, students are tested in irregular verbs, and the weight of this exam is 6% of the final grade. The creative writing skill weighs 11% of the final grade. The school uses a course book called ‘stepping stones’ in which students are tested three times during the year with the weight of 10% each. The listening exam weighs 11%. Students also have to read an English novella, and they are tested in it through a written exam which represents 11% from the final grade. The last test in the year is a reading comprehension test with multiple-choice questions, and this exam is the remaining 20% of the final grade.
Measuring Mathematical abilities from 4th to 6th grade
“culture and society”. For mathematics C, it is a must for students who are willing to major in “nature and technology”, in which student has to go deep in all topics. This means that the student should choose only one level to take depending on what the students intends to major in later on at the university or any later study.
Testing Mathematics (A)
In this level of mathematics, students study 4 modules. Each module takes 6 weeks except for the last module which takes 9 weeks. At the end of each module, students are tested through a
written exam. The weight of the first three modules is 18% each, and the final exam weight is 26% of the final grade. Students are tested in statistics, algebra, mathematical hypotheses as well as rules of differentiating. 20% of the final grade is also based on the final grade of the previous year since the grades of the last three years are integrated together for the final grade of
graduation.
Testing Mathematics (B)
This level of mathematics requires the students to take four tests for each module. All of the modules take 6 weeks except for the last one which takes 9 weeks. The weight of the tests at the end of each module is worth 20% of the total of the grade of the whole year. The remaining 20% is determined through the student’s grade from last year. In these tests, students are tested in algebra, geometry, derivative and second derivative and other mathematical applications. Testing Mathematics (C)
For mathematics (C) students take four tests at the end of each module which last for 6 weeks except for the last module which lasts 9 weeks. The weight of the tests at the end of each module is different from the other levels of mathematics: the tests for first three modules are worth 18% of the total of the grade of the whole year, while the test of the last module is worth 26%. Like the other levels of mathematics, the remaining 20% is determined through the student’s grade from last year. In these tests, students are tested in statistics, algebraic skills, formulas and graphs and calculus.
Participants
group 6 and continued until their last year before joining university. These learners had been learning mathematics for a longer period of time which is 12 years. However, it is worth noting that they have been studying calculations (arithmetic) until they joined the first year of VWO (brugklas). This means that they have been studying mathematics for two years. The vast majority of the participants had not lived in an English-speaking country. All of them are exposed to all kinds of media which offers some considerable amount of English knowledge. Since it is a law for all Dutch schools, these learners were exposed to 4 hours of mathematics every week while they are exposed to 3 hours per week for English. Some of the participants chose for mathematics (A), others for mathematics (B), and (C) according to the profile choice starting from the 4th year. Because we are not testing any group differences, no group division is needed for this study. The number of participants is of a great importance for this study. The reason is that there are a large number of elements that affect the educational process other than the participants’ intelligence, IQ, their personal preferences or the amount of work they put for these subjects. These elements can be family problems, the effect of the teacher, or other social elements; these factors can cause a lot of noise that affects the outcome of the study which will not provide us with the pure effect targeted in this study.
Data analysis
The data collected represent the scores of 84 participants throughout four school years from 2009 and until 2012 in both English and mathematics. There are 35 participants chose for the profile ‘Economie en Maatschappai’, 18 participants chose for ‘Natuur en Techniek’, 15 participants chose for ‘Natuur en Gezondheid’, and 13 participant chose for ‘Cultuur en Maatschappai’ In order to investigate whether there is a correlation between the scores of these two subjects throughout four years, we are going to check first if the data for each year are normally
RESULTS
Differences between English and Mathematics
Differences between English and Mathematics in 2009:
The data gathered on the students in 2009 represents data that was gathered when they had not yet chosen their profile for their subsequent schooling years. Therefore, this data was interesting to analyze as a form of ‘pre-test’, as it was representative of students who had all undergone relatively identical classes up until this point.
One-way ANOVAS were run in order to test whether there were significant differences between the students, in terms of the profile they would go on to follow in the subsequent years. When investigating English grades in this year, there was a significant effect of future profile on English skills, F(3,80)= 3.04, p < .05. A subsequent post-hoc analysis using Hochberg’s GT2 revealed that only the difference between the highest scoring group “Natuur en Techniek” (M=7.026, SE= .154) and the lowest scoring group “Cultuur en Maatschappij” (M=6.336, SE= .159) was significant, p < .05.
When looking at Mathematics for 2009, it was found that future choice of profile had no significant effect on grades.
As for the correlation between the students’ performance of English and mathematics, a two-tailed Spearman rho Test showed statistically insignificant correlation between the two subjects.
Differences between English and Mathematics in 2010:
The same one-way ANOVAS were then run on the data gathered from 2010. There was a significant effect of profile on English grades, F(3,80) = 4.112, p < .01. A post-hoc analysis using Hochberg’s GT2 revealed that the only significant difference was to be found between the highest scoring group “Natuur en Gezondheid” (M=7, SE=.179) and the lowest scoring group “Economie en Maatschappij” (M=6.191, SE=.125), p < .01.
There was no significant effect of profile on Mathematics grades in 2010.
A two-tailed Spearman rho Test revealed that the English scores of all the participants of different profiles did not correlate significantly with their scores in mathematics. However, a two-tailed Spearman rho Test showed that the scores of the participants from the profile
Differences between English and Mathematics in 2011
There was a significant effect of profile in English grades from 2011, F(3,80) = 4.949, p < .01. A post-hoc analysis using Hochberg’s GT2 revealed that the only significant differences were between the highest scoring group “Natuur en Gezondheid” (M= 7.462, SE= .166) and the two lowest scoring groups, “Economie en Maatschappij” (M= 6.594, SE= .129), p < .01, and “Cultuur en Maatschappij” (M= 6.614, SE= .091), p < .05.
There was no significant effect of profile on Mathematics grades in 2011.
In order to investigate the correlation between English scores and mathematics scores the same two-tailed Spearman rho Test was conducted on the scores of all the participants regardless of the profile chosen. The test revealed a significant weak correlation between English and mathematics scores: r=0.224; p<0.05. Moreover, testing the correlation between both subjects among the different profiles, a two-tailed Spearman rho Test showed that the scores of the subjects for none of the profiles was proved to correlate significantly with one another.
Differences between English and Mathematics in 2012
When looking at English grades, it was found that there was a significant effect of major on English skills, F(3,80)= 3.431, p < .05. Subsequent post-hoc analysis using Hochberg’s GT2 revealed that only the difference between the highest scoring major Natuur en Gezondheid (M=7.019, SE=.169) and the lowest scoring major Cultuur en Maatschappij (M= 6.079, SE=.238) was significant., p < .05.
There was no significant effect of profile on Mathematics grades in 2012.
A two-tailed Spearman rho Test revealed that there was a significant positive correlation between English scores of all the participants of different profiles and their scores in
mathematics r=0.354; p<0.001. A two-tailed Spearman rho Test showed that the scores of the participants from the profile “Economie and Maatschappaij” showed a statistically significant positive correlation r= 0.338; p < 0.05 while none of the scores from the other profiles was proved to correlate significantly with one another.
Figure 1 shows the development of correlation between English and mathematics throughout the four years 2009-2012.
Gain scores 2009-2012
English 2009-2012
2009 and 2010 t(83)= 3.99; p < 0.001. There was also a significant mean difference between 2010 and 2011 in English scores t(83)= -4.79; p < 0.001. The difference of means between the scores of 2011 and 2012 also proved to be significant t(83)= 4.39; p < 0.001. Moreover, Table 4 shows the correlation results of the paired-sample T-test. These results show medium to strong correlations between the scores of the English throughout the 4 years.
Mathematics 2009-2012
Table 4 shows the mean differences between mathematics scores throughout the years 2009-2012. A Paired-sample T-test showed that there is a significant mean difference between the mathematical scores of the years 2009 and 2010 t(83)= 2.18; p < 0.05. There was also a
significant mean difference between 2010 and 2011 in English scores t(83)= -3.01; p < 0.05. The difference of means between the scores of 2011 and 2012 also proved to be significant t(83)= 3.47; p < 0.001. Furthermore, Table 5 shows the correlation results of the paired-sample T-test. There was medium to strong positive correlations between all years except for the years 2009 and 2010 which did not show significant correlation between the scores.
Gain scores for English and Mathematics among profile groups 2009-2012
One-way ANOVAS were then run to test whether or not certain profiles displayed significantly higher gain scores over the four years in either subject. The gain score for each subject was first calculated, but subtracting the 2009 grade from the 2012 grade; and then the ANOVA was run, with the gain score as the dependent variable and profile as the independent variable. There were no significant differences found between any of the groups in English or Mathematics. In other words, none of the profiles increased or decreased their overall grades significantly in
comparison with the other profiles between 2009 and 2012.
Table 2: Statistics related to the results of paired-sample T-test for English scores 2009-2012
Year Mean difference Standard Deviation Significance
2009-2010 0.352 0.808 0.00*
2010-2011 - 0.335 0.641 0.00*
2011-2012 0.278 0.581 0.00*
Table 3: The correlation of English scores among the years 2009-2012(gain scores)
Year Correlation Significance
2010-2011 0.708 0.00*
2011-2012 0.758 0.00*
Table 4: Statistics related to the results of paired-sample T-test for English scores 2009-2012
Year Mean difference Standard Deviation Significance
2009-2010 0.247 1.03 0.032*
2010-2011 - 0.194 0.589 0.003*
2011-2012 0.266 0.703 0.001*
Table 5: The correlation of English scores throughout 2009-2012
Year Correlation Significance
2009-2010 0.208 0.058 2010-2011 0.740 0.00* 2011-2012 0.628 0.00* 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 2009 2010 2011 2012
Development of correlation between English and mathematics throughout 2009 - 2012
Correlation between English and Math
DISCUSSION
The first research question investigated the relationship between linguistic abilities (represented through proficiency of English as an L2) and mathematical abilities for adult learners. It was hypothesized that there will be a positive medium to strong correlation between English proficiency and mathematics. This assumption stemmed from the controversy that circled
theories trying to explain human intelligence; whether or not there is a relation between different intelligences of human is an issue of an inherent disagreement between the two leading names in this field: Spearman (1904) and Gardner (1983). Each of them had a specific theory that
supported a different perspective in understanding and interpreting human intelligence. However, there was much more evidence as well as anecdotal observations that promoted that fact that there is relation between human intelligences than that supported the idea that human
intelligences are separated and not related. Due to lack of research studies that investigated the relation between English and mathematics for adult learners, there was an important reason for this current study to take place in order to provide some empirical evidence for the true nature of the development of the relationship between these two skills when L2 learners turn into adults. A set of data based on the results of English and mathematics of pre-university students was used to investigate the first research question through applying a set of t-tests, one-way ANOVAs tests, and Spearman rho correlation test. These tests revealed some expected and other unexpected results which are explained as follows:
Differences between English and Mathematics
The scores of the students in the year 2009 was considered as a ‘pre-test’ in order to be able to compare the performance of the profile groups before they have chosen their profiles, and to investigate if their performance in either of these subjects (English or mathematics) did have an impact on their choice of profile. Interestingly, there was a significant difference between the groups of students who would choose different profiles the following year. This significant difference was found only in English scores. The future-profile group ‘Natuur en Techniek’ scored significantly higher than the profile group ‘Cultuur en Maatschappaij’. The profile group ‘Natuur en Techniek’ particularly requires a higher level of mathematics, so students are obliged to study mathematics C because students in this profile are prepared for fields engineering which requires a good command of mathematics knowledge. This significant difference can be
explained that students how scored better in English, are expected to perform better in higher levels of mathematics. Therefore, it can be asserted that better performance in English may result in high potentials in mathematics performance while the lower profile group ‘Cultuur en
en Maatschappaij’. In 2011, the same profile group was significantly better than the profile group “Cultuur en Maatscjappij” as well as “Economie en maatschappij”; in 2012, it was better than “Cultuur en Maatschppaij” against the profile ‘Economie en Maatschappij’. It is worth noting that in the profile ‘Natuur en Gezondheid’, students are required to study the set of science subjects chemistry, physics and biology, which all involve, at different degrees, using
mathematical and logical thinking. These results interestingly manifest the role English played as a supporter and enhancer for the performance in subjects requiring logical and mathematical thinking. These results were indeed backed up by a number of earlier studies such as what Plomin (2012) had found out about the link between L2 problems and how it is linked with mathematical difficulties, which suggests that the better the participants are in L2 the better they would perform in mathematics. These findings were further backed up by what Barton and Neville Barton’s (2003, 2005) have found out in the relationship between the proficiency of English as L2 and the participants performance in mathematics. Morales (2012) could
successfully find an interpretation to this phenomenon through her research in which she could prove that bilingual children performed significantly better in mathematics and other cognitive tasks than the control group of monolinguals.
For a clearer look at the nature of relationship between proficiency of English as an L2 and mathematics, a set of correlation tests were conducted to investigate this point. Spearman rho test did not show any significant correlation between English and mathematics in the 2009 which is before choosing a profile. The reason for this might be the fact that students tend to perform rather randomly at least at the beginning when dealing with new system when it comes to
mathematics. In other words, the students are not very familiar the new level of mathematics that is different from previous years. Surely, the adaption to this new system heavily depends on individual differences so that they can get used to this new level. These random differences among the students might have caused their English results not to correlate significantly with mathematics scores. Another reason might possibly be due to the lack of motivation for getting high scores in the final exam. In other words, at this stage, students are aware that they only need to pass the exam for that year, and that their grades of this year will not count in their final grades in their diploma which would start the following year (4th grade).
As for the correlation between the two subjects in 2010, a Spearman rho test was initially
students are well aware of the important of English language in their field and that it is a prerequisite for having a good command of English communication skills. This might have had an impact on students’ performance and resulted in a positive correlation between their English scores and mathematics scores.
For the year 2011, testing correlation was similar to the way it was tested in the previous years. The general correlation between the scores of the two subjects regardless of the profile showed a significant weak correlation between the scores of English and mathematics. This reveals in essence that the better students scored in English the better they scored in mathematics regardless of their profile choice. Testing the correlation among the profiles revealed that none of the scores of the two subjects of the profile groups correlated significantly with one another. The reason for this is probably that the number of the participants for each profile was not enough to proper;y show the relation between the two subjects.
Interestingly, with the correlation test in 2012, Spearman rank-order correlation test showed that there is a low to moderate correlation between the scores of mathematics and English regardless of their profile, and this correlation was significant. However, only one profile group was proved to have a significant correlation which is ‘Economie en Maatschappij’ which is explained
through the number of the participants in this group which makes it more probable to get a significant correlation; this profile group formed the majority of the students. Figure 1 shows an interesting curve which represents the strength of the correlation between English and
mathematics throughout four years. Interestingly, the strength of the correlation started at a very low correlation, insignificant however, and ended with a moderate to low correlation which reveals some interesting facts. First, as students get closer to the more important exams, they naturally exert more effort, which is shown in the average results of their scores. The better students get in English, the better they perform at mathematics or the other way around. This was clearly shown in the development of the correlation between English scores and mathematics scores throughout four years (2009-2012). It is quite evident that the small number of
participants had a rather negative effect on reflecting the true magnitude of the strength as well as the statistic significance of the correlation especially when this group had to be split up into four different profile groups.
English and mathematics (2009-2012)
A series of paired-sample T-test was conducted on the scores of English and mathematics, each separately. The results of these tests showed an interesting link between the difference of means for English and mathematics. The scores of the participants from all different profiles showed almost the same mean difference between a year and the following year which reveals that there is an effect associated between the two subjects with the development or regression of either of these. The results of this test also revealed significant medium to strong correlations between the scores of each year. These medium to strong positive correlations reveal that the scores of the participants in a certain year tend to be quite similar in terms of progression to the scores of the following year.
Although the results that this study reveal may not be interpreted as a strong support for all the aspects that are hypothesized in this study, they give a clear indication to what kind of
relationship between two of the most important aspects of human intelligence: linguistic and mathematical skills. Moreover, considering the results of the current study within the context of similar studies, reveals that these results, not very strong however, give clear evidence to the supportive nature that bilingualism provides to other cognitive tasks and particularly,
mathematics or the other way around. For the years in which participants have to work for their diploma, the strength of the correlation of concern clearly increases throughout the three years after having chosen their profiles. This essentially manifests the effect that both of these subjects have on one another. More importantly, participants who generally perform well in science subjects such as physics, chemistry and biology, tend have performed better in English than others. This was shown in the significant difference in the means among the groups in which the participants of the profile ‘Natuur en Gezondheid’ have got the best scores in English than other profiles. It is also worth mentioning that the science subjects if this profile group seems to reflect the influence that they may have on either subjects (English or mathematics). However, it is not possible to draw any concrete patterns for the relationship between science subjects like physics, chemistry and biology and their relation to English and mathematics, given the small size, and it was not a research question addressed in this study. For the previously mentioned reasons, and based on the discussed results, it could be asserted that students who perform well in English, are also expected to perform well in other cognitive tasks, and particularly, mathematics. This clearly shows the relationship between two aspects of human intelligence, which was the second research question addressed in this study.
