The Relationship Between Oral Language And Mathematics Competencies In Elementary School

Relationship between language skills (oral language) and mathematical competencies (calculation)

Kolupski (2014) arguing that language and mathematics are concepts that must occur simultaneously as they work together to produce the same idea, but still there are differences. What this means is that mathematics has a certain language independent of everyday speech. Certain words, letters, and phrases, represent something very specific in mathematical language. When this new language is taught to students, it is important that the new language matches the new topic directly. That is, when students create knowledge, they are also developing the capabilities corresponding to language development. In this sense, Serio (2014), affirms that communication is "an essential process in the learning of mathematics. Thus, students are able to reflect and clarify their ideas, their understanding of mathematical relations and their mathematical arguments "(p.12). Communication is an integral part of an individual's ability to succeed in today's world. "Involving students in the discussion of mathematics can promote their active meaning-making" (p.13).

In addition, Butterworth (2005) and Alcalá (2002) agree in arguing that mathematics rests in a language. Mathematical language is the support and, at the same time, a constituent part of mathematical knowledge itself. We must bear in mind that although the semiotic aspects of mathematical learning are very important, mathematical activity goes beyond any linguistic, representational or symbolic activity. To think we do not rely on the objects directly, but we do it by helping us with symbolisations of objects (icons, graphs, drawing, etc.) through a necessary process of conceptualization; using, also, symbolizations of feelings, of intentions (words); making use, at other times, of the silent gesture. In short, we use symbolic creations as mediators, as resources, as tools to think and communicate. Therefore, Alcalá (2002, p.26), states that mathematical language in the classroom describes four types of symbols: Logograms: signs invented especially to refer to total concepts such as "+", "-", "x "," = "; Pictograms: geometric icons: signs of angle, square, triangle, etc.; Punctuation symbols: taken from the normal spelling: "," "()"; Alphabetic symbols: letters taken from the alphabet: "a", "b", "c", "A", "B", "C", etc .; The own terminology and typical expressions written and spoken: "three", "four", "ten", "greater than". Dowker and Nuerk (2016) indicate that linguistic influences in the processing of numbers are omnipresent. They occur at a conceptual, semantic, syntactic, lexical, or phonological level, among others. Linguistic properties affect not only the verbal representations of numbers, but also the representation of numerical magnitude, calculation, representation of parity, representation of values of places, even the early acquisition of numbers. Therefore, they postulate that numerical and arithmetic processing are not independent of linguistic processing. In this way, they distinguish several linguistic levels in which the numerical processing can be influenced: (1) Conceptual influences. Beyond singular phonemes, graphemes, words and sentences, linguistic structures are formed by linguistic concepts. The linguistic concept suggests that for almost every adjective, a non-derived form (unmarked) and a derivative form (marked) exist (for example, efficient and inefficient: the marked form would be with "in"). Numbers have several attributes, which can be distinguished in unlabelled form (e.g., large, even, divisible) and marked (small, odd, indivisible). As for the spatial organization example as "right" it is not marked "left" if it is checked; (2) Syntactic influences. Number processing in real-life situations occurs in natural language and is described by a grammatical number (that is, singular for "1" and plural for two or more things). The languages differ substantially in their use of the grammatical number. In some cases, the syntactic structure of a language influences the development of numerical comprehension and the spatial assignment of numbers; (3) Semantic influences. Word meanings also influence numerical or arithmetic processing.

The addition seems to be more associated with words like "more", "buy", "get", etc., while the subtraction is similar to words like "less", "sell", "give", etc. When the problems of text are presented in a way that makes these deceptive associations acquire worse results. This comes to highlight an interrelation between the meaning of the word and arithmetic operations; (4) lexical influences. In general, a transparent structure of the numerical word it seems to help numerical performance even for problems that do not involve numerical words They conclude that lexical influences affect arithmetic, but not in the same way as other linguistic aspects, (5) Phonological influences For these authors (Dowker & Nuerk, 2016) the phonological skills are not related to the mathematical operation itself, but to the verbal representations / manipulations of the number. On the other hand, focusing on more specific aspects of the language, Moll et al. (2015) showed that the verbal-symbolic numerical system is not only based on the pre-verbal system, it also depends on the language and general mastery of the skills. Therefore, children with language or reading problems run the risk of having arithmetic difficulties. Koponen (2008) indicated that there are at least two cognitive skills that could function as early indicators of increasing risk for calculation in both children with difficulties as in children without them: the ability to learn and recite sequences number of verbal words and the fluency ability to access long-term memory in order to retrieve verbal tags for visual stimuli. Hence, Moll et al. (2015) state that variations in school pre-skills, especially in language and executive functions, influence the development of specific precursors in the domain of arithmetic such as counting skills and numerical knowledge. Numerical knowledge, in turn, plays an important role in formal arithmetic learning once schooling begins. Consequently, the relationship between linguistic skills (oral language) and mathematical skills (calculus) is clear, so the arithmetic skills in elementary school are directly preceded by the number of verbal skills in childhood and these skills, to in turn, they are influenced by previous variations in oral language skills.

Other studies focus on phonological skills, for example, Lesaux and Vukovic (2013) suggest that phonological skills directly influence arithmetic skills, while language impacts on arithmetic skills through symbolic numerical ability. Therefore, in general verbal ability affects the performance of children by influencing the mathematical thinking that involves the symbolic number system, phonological skills seem necessary for the execution of arithmetic tasks. As a result, it may be that while the numerical sense provides the basis from which children can think mathematically, general verbal ability shapes the way in which children acquire numerical and quantitative symbolic skills necessary for mathematics. On the other hand, Barbosa (2014) puts a strong focus on the vocabulary analyzing the performance of deaf and hearing children of 5 and 6 years through experimental tasks that include various cognitive aspects related to the numerical conceptualization, concludes that one has to have vocabulary to remember with numerical precision larger quantities. According to this argument, the numerical vocabulary functions as a cognitive tool that helps the individual to control the cardinal information of sets with a large number of items. Therefore, it highlights the close relationship between language and mathematical concepts. On the other hand, Pedraja et al. (2015), as mentioned above, state that the month of birth influences academic performance. After analyzing the data of 25,887 students from 889 Spanish schools, extracted from the Program for International Student Assessment, PISA 2009, these researchers found that those students who were born in November and December were 85% more likely to repeat the course than those who were born in January or February. Furthermore, García and Hidalgo (2013) argue that students born in the third or fourth quarter, get between 20 and 32 points less than those born in the first quarter of the year (p.12).

In addition, giving some examples of their research in the second year of Pre-school Education (thus, with children of five years of age), they point out that at the end of the course, 20% of the children born in the last quarter of the year had needed educational reinforcement compared to 6.34% of those born in the first months. García and Hidalgo (2013) also observed that the difference is progressively reduced as the student becomes older, during elementary Education and the first part of higher education. Fernández and Rodríguez (2008), make reference to the Spanish section of the 2003 PISA survey, explain that although the idea that the level of intelligence of both sexes is similar prevails, there are small but persistent differences favourable to males in mathematical skills, and women in linguistics.

Moreover, girls tend to do better than boys: they repeat less and are more likely than boys to reach the last grade of elementary school. Therefore, they affirm that the probability that a hypothetical male student with mean values in all the variables has repeated, is 51% higher than in the case of another student with the same conditions but of the female sex. Following the same line of argument, García and Hidalgo (2013) justify that children score better than girls in Mathematics and Science while the opposite occurs in Reading. Therefore, based on the results previously presented, sex and month of birth are proposed as possible modulating variables of the relationship between oral language and calculus. Therefore, it is possible that the fact that one is male or female or that one was born at the beginning or end of the year modulates the relationship between language and calculus. That is why this relationship is analyzed from a contingent perspective.

Sample

A total of 13 children from 1st grade of elementary school in Huesca participated in the study. 5 participants were boys representing 38.5% of the sample and 8 were girls, representing 61.5% of the sample. Subjects diagnosed with learning disorders have been excluded, because they were not the objective of the present study.

Measures

Two standardized tests have been used. These were BLOC-SR ( Batería del Lenguaje Objetivo y Criterial ), Objective and Criterial Language Battery Screening Revised (Puyuelo, Renom, Solana, and Wiig, 2007) and TEDI-MATH, Test for the diagnosis of basic competencies in mathematics (Grégoire et al., 2015).

Hypothesis Testing

Descriptive results and correlations of the variables considered in the study are presented in Table 1 . Hypothesis 1 suggested that children who scored high in oral league would also score high in calculus. The results show that when we jointly considered BLOC-SR (oral language) and TEDI-MATH (calculation) and the additional tests of TEDI-MATH (TEDI_A), positive and significant correlations were found among the variables. Thus, BLOC-SR correlated positively and significantly with TEDI-MATH (r = .80, p <.01). In addition, oral language (BLOC-SR) and the calculation provided by additional tests of TEDI-MATH (TEDI_A) also showed a positive and significant correlation (r = .80, p <.01). Therefore, H1 is confirmed.

The hypothesis 2 proposed that the difference of the means in TEDI-MATH of the students that scored above the mean in BLOC-SR would be higher than the mean of the students that scored below. The students who score above the mean in BLOC-SR (M = 70.06) obtained a higher mean in TEDI-MATH (M = 82.39, SD = 7.85) than the mean of those who score below the mean in BLOC-SR (M = 48.20, SD = 31.01) (see table 02 ). In addition, students who score above the mean in BLOC-SR, obtained a higher mean in the calculation provided by the additional tests of TEDI-MATH (TEDI_A) (M = 85.65, SD = 4.65) than those who scored below the mean in BLOC-SR (M = 56.63, SD = 27.48). The results of the t test show no significant differences for the following variables: TEDI-MATH (t = 2.17, df = 3.17, p = .11), and TEDI_A (t = 2.10, df = 3.08, p = .12) due to that the variances are not equal. However, if the result of the Levene test had not been significant, these differences would have been significant for TEDI-MATH (t = 3.25, gl= 11; p <.01) and TEDI_A (t = 3.24, gl = 11, p <.01), respectively. Although the data are close to significance, they do not reach the required level. Therefore, although a certain tendency can be observed, H2 is rejected.

Hypothesis 3 suggested that the relationship between oral language and calculus (taken as a whole) would be different depending on the sex and month of birth. As can be observed in table 03 , there is a direct positive relationship between calculus and oral language (B = .33, p <0.5). However, in this study it is not clear that this relationship is moderated by sex, that is, it is positive in both boys and girls and the pattern of the relationship does not differ according to sex (B = .01, ns) (see figure 01 ). In addition, the sex variable did not show a direct relationship with BLOC (oral language) (B = -1.93, ns). Also, as shown in figure 02 , the relationship between TEDI-MATH and BLOC-SR, for children born at the end of the year (younger), the relationship was positive, although weaker than in children born at mid-year, and practically nil in children born at the beginning of the year (B = .05, ns). Although these results are not significant and therefore cannot be taken into account, they have been graphed to observe the trends. The results seem to indicate that younger children show a greater relationship between TEDI-MATH (calculus) and BLOC-SR (oral language), this could be due to the interference of other context variables that are more outgoing in elementary school than in children such as preference, attention, level of effort, etc. Therefore, H3 is rejected.

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