4-273 THE RELATIONSHIP BETWEEN LANGUAGE COMPLEXITY
AND MATHEMATICS PERFORMANCE Hartono Tjoe
The Pennsylvania State University
We investigated the extent to which number word structure might offer an insight to children’s development of early number sense. In conjunction with TIMSS Grades 4 and 8 mathematics scores of 60 countries, we selected the transparency base-ten structure as a criterion for linguistic complexity of the 33 spoken languages in translating numeral symbols into number words. Our findings showed, to some extent, that languages with no transparent base-ten structure had an advantage over those with transparent base-ten structure at the initial stage of mathematics learning but not as significantly at the later stage.
INTRODUCTION
International studies comparing mathematics achievements of children in the U.S. and those in other countries, especially in East Asia, indicated a persistent significant difference (Stevenson, Chen, & Lee, 1993; Torney-Purta, 1990). Researchers attributed to such discrepancy a number of affective and cultural qualities including beliefs, motivations, and study habits (Fuligni & Stevenson, 1995; Leung, 2006;
Newman et al., 2007; Wang, 2004). Little was known regarding the role of number word acquisition on young children’s mathematical understanding (Miller, Kelly, &
Zhou, 2005).
In this study, we examined the extent to which different languages might influence the development of early number sense. From a list of official languages of the countries participating in the Trends in International Mathematics and Science Study 2011 (TIMSS 2011; Mullis, Martin, & Arora, 2012), we surveyed the number word structure that linked numerals and word names. We were interested in answering the question of whether learning a particular spoken language might be a predictor of a child’s success in mathematics learning.
THEORETICAL BACKGROUND
Kindergarten was one of the most prominent grade levels where students brought with them to school the most heterogeneous mathematics skills from informal contexts (Cross, Woods, & Schwingruber, 2009). Prior to formal education, young children’s counting skills in particular ranged widely from little exposure to word names for numerals to simple visual manipulations of objects via number decomposition or place value approach (Cross, Woods, & Schweingruber, 2009; Syrett, Musolino, & Gelman, 2012).
Such a considerable variation had been seen in mathematical understanding, particularly the understanding of number words and number sense, of not only young children across the U.S., but also those in the U.S. in comparison with those in other countries, especially in East Asia (Stevenson, Lee, Chen, Lummis, Stigler, Fan, & Ge, 1990). While the latter on the whole were more successful in a number of mathematical assessments than the former, some researchers pointed out that the substantial difference in mathematical competence might not be a direct result of formal schooling or the superiority of the curriculum (Geary, Bow-Thomas, Fan, &
Siegler, 1993). Miller, Smith, Zhu, and Zhang (1995) indicated that this difference in mathematical performance might be more related to the differences in the number-naming system.
The acquisition of word names using a certain language had been shown to accelerate particular counting strategies. Ho and Fuson (1998) observed that Chinese-speaking children were more adept than English-speaking children at operating the number ten as a benchmark when performing addition tasks. Geary and colleagues (1993) found that when unable to immediately recall addition facts, Chinese-speaking children applied more abstract fallback strategies such as the verbal counting method, while English-speaking children applied more concrete fallback strategies such as the finger counting method.
To the extent that Chinese-speaking children were perceived more mathematically proficient than English-speaking children, earlier researchers, in addition to cultures (Leung, 2001), student self-beliefs (House, 2006), and parental beliefs and practices (Miller, Kelly, & Zhou, 2005), credited the persistent difference to the transparency of base-ten structure in Chinese language that was not immediately apparent in English language (Miller & Paredes, 1996). Unlike English language, Chinese language was noted to convey a more direct relationship between Hindu-Arabic numeral symbols and their corresponding number words as one might read them in a literal translation.
Chinese language consisted of only ten unique number words associated with numerals from 1 to 10, the combinations or variations of which constructed all number words associated with numerals from 11 to 99. These 99 constructions were done using the literal translation of base-ten structure. For example, the number word “shí-yī” was a combination of the number words “shí” and “yī,” which literally translated into “ten”
and “one.”
On the other hand, English language introduced unique number words for numerals 11 and 12, in addition to the ten unique number words associated with numerals from 1 to 10. For example, the number word “eleven” for the numeral 11 was neither a combination nor a variation of the number words “ten” or “one.” In total, English-speaking children would need to memorize not only two additional unique number words compared to their Chinese-speaking peers, but also another seven number words, whose constructions made use of a modified word “teen,” for numerals
These seven number words were mostly learned through rote memorization by English-speaking children, resulting in many not fully comprehending how those number words might be connected to their base-ten constructions (Fuson, Richards, &
Briars, 1982). Evidently, by the age of five years old, compared to Chinese-speaking children, English-speaking children were less capable of recognizing that the numeral 13, for example, might be equivalently viewed as “10 + 3” (Ho & Fuson, 1998). Such lack of understanding of the base-ten structure in the Hindu-Arabic numerals might be considered to be comparable to the lack of association between number words and number concepts of any typical two-year-old children (Wynn, 1992).
More generally, the base-ten structure was considered to be more consistent and transparent in Chinese language than in English language (Miller, Kelly, & Zhou, 2005). For example, the numerals 16 and 60 were read in Chinese language as “shí-lìu”
and “lìu-shí,” which literally meant “ten-six” and “six-ten,” or equivalently, “10 + 6”
and “6 × 10,” respectively. On the other hand, these numerals were read in English language as “sixteen” and “sixty,” which were comparable to “6 + 10” and “6 × 10,”
respectively. While Chinese language clearly operated under the natural base-ten structure sequencing each number word with its place value, English language reversed the natural order, especially, for some numerals from 11 to 19.
METHODOLOGY
We determined the classification of each official language of TIMSS participating countries according to the transparency of its base-ten structure in the manner in which numeral symbols were associated with number words. Out of the 50 and 42 TIMSS Grades 4 and 8 participating countries, respectively, 60 were identified as distinct countries that utilized 35 unique languages. With the exception of Danish and Georgian that did not follow either pattern, we identified two number-word-naming patterns from the 33 different languages.
We recognized the evolution of number words from 1 to 10 to from 11 to 19 and from 20 to 99. If the place value and word naming association of the Hindu-Arabic numeral symbols was naturally translated into a literal manner, then a language was categorized as the first word-naming pattern (e.g., Chinese language). If the place value and word naming association of the Hindu-Arabic numeral symbols was not naturally translated into a literal manner, it was categorized as the second word-naming pattern (e.g., English language).
Based on the word-naming pattern of its language, each of the 60 distinct TIMSS Grades 4 and 8 participating countries was associated with either the first or the second group. We performed the Grubbs’ test at 0.05 level of significance to recognize any extreme value of the TIMSS Grades 4 and 8 mathematics mean scores of the two groups in each group. We then analyzed the mean scores of these two groups using the t-test for independent means at 0.05 level of significance.
FINDINGS
We identified 42 and 16 countries that corresponded to the first and second group, respectively (see Table 1). Examples of TIMSS participating countries in the first group were Hong Kong–CHN and Yemen whose official languages were Chinese and Arabic languages, respectively. Examples of TIMSS participating countries in the second group were the U.S. and Spain whose official languages were English and Spanish languages, respectively.
In the first group, 33 countries reported a TIMSS Grade 4 mathematics mean score of 474.63 (SD = 80.32), and 33 other countries reported a TIMSS Grade 8 mathematics mean score of 465.09 (SD = 67.14). In the second group, 15 countries reported a TIMSS Grade 4 mathematics mean score of 525.07 (SD = 35.80), and eight other countries reported a TIMSS Grade 8 mathematics mean score of 480.25 (SD = 80.84).
First group Second group Language complexity Transparent base-ten
structure
Non-transparent base-ten structure Number of distinct
countries
42 countries (e.g., Hong Kong–CHN and
Yemen)
16 countries (e.g., the U.S. and Spain)
Number of unique languages
29 languages (e.g., Chinese and Arabic
languages)
6 languages (e.g., English and Spanish
languages) Number of
participating countries in TIMSS Grade 4
33 countries 15 countries
TIMSS Grade 4 Mathematics mean
score
474.63 (SD = 80.32) 525.07 (SD = 35.80)
Number of participating countries
in TIMSS Grade 8
33 countries 8 countries
TIMSS Grade 8 Mathematics mean
score
465.09 (SD = 67.14) 480.25 (SD = 80.84)
Table 1: Language complexity and TIMSS Mathematics performance
The Grubbs’ test showed that there was no outlier in each group at 0.05 level of significance. Children in the first group performed worse than those in the second group at Grades 4 and 8. The t-test for independent means showed that at 0.05 level of
significance, there was a significant difference between the groups at Grade 4 but not at Grade 8.
ANALYSIS
Our findings demonstrated that to some extent, children who learned number words using a language with a transparent base-ten structure did not necessarily have a linguistic advantage over their peers who learned number words using a language without a transparent base-ten structure. Indeed, the former did significantly more poorly than the latter at Grade 4. The trend persisted at Grade 8, although not significantly.
To a certain degree, this result contradicted the findings by Miller and colleagues (2005), who suggested that Chinese-speaking children benefited from the consistency and transparency of base-ten structure in Chinese language. This result also indicated that being born in a certain country that used a more transparent base-ten structure language might not effectively guarantee an early mathematics performance.
Restricting the TIMSS participants to include only Chinese-speaking countries (e.g., Hong Kong–CHN and Chinese Taipei–CHN) and the U.S. as selected in the study by Miller and colleagues (1995) did show that the former group was at a greater advantage than the latter group in mathematical competence, confirming their findings.
Nevertheless, the hypothesis by Miller and colleagues (2005), to some extent, did not appear to apply in general to children in the countries outside East Asia whose primary language was not Chinese language but had a similar transparent base-ten structure as Chinese language.
One counterexample was Arabic language. Arabic language was the official language of nine out of 50 and 11 out of 42 TIMSS Grades 4 and 8 participating countries, respectively. These 13 distinct countries were among the very lowest performers in TIMSS Grades 4 and 8 mathematics assessments. For instance, children in Yemen, who used Arabic language as their primary language, scored 248, which was the lowest score in TIMSS Grade 4 mathematics. This score was significantly lower than that of Chinese-speaking countries (e.g., 602 and 591 for Hong Kong–CHN and Chinese Taipei–CHN, respectively).
Likewise, their hypothesis did not generalize to children in the countries outside the U.S. whose primary language was English language. For instance, English language was the language of instruction for students in Singapore, which scored 606, the highest score in TIMSS Grade 4 mathematics. This score was significantly higher than that of the U.S. (541).
In contrast to the studies by Miller and colleagues (1995; 2005), the present study suggested, to some degree, that children in the countries whose primary language had no transparent base-ten structure performed significantly better than their peers in the countries whose official language had a transparent base-ten structure.
That is, English language, despite its lack of transparent base-ten structure, might not, or at least not mainly, be the primary reason as to why children in the U.S. consistently fared less satisfactorily than their peers in the East Asian countries in early mathematics performance. Still, it should be noted that the dominance in mathematics performance, which was significant at the initial level (e.g., Grade 4), became slightly diminished at a later stage of mathematical development (e.g., Grade 8).
CONCLUSION AND DISCUSSION
The present study examined the relationship between language complexity and mathematics performance. It sought to understand the extent to which number word structure of a certain language might shape children’s trajectory in mathematics learning.
To some extent, the findings showed that: (a) with the exception of its proximate variations (e.g., Japanese and Korean languages as the official languages for Japan and Korea, respectively), Chinese language was the only language with a transparent base-ten structure that delivered a positive advantage of early mathematics competence in comparison with English language or other languages with no transparent base-ten structure, and (b) languages with no transparent base-ten structure more generally had an advantage over those with a transparent base-ten structure at the initial stage of mathematics learning but not as significantly at the later stage.
It could therefore be inferred that language did not appear to play as a critical role in the process of acquiring mathematical understanding. The substantial difference in the mathematical development of young children in East Asian countries and the U.S.
might have been confounded by affective and cultural qualities as opposed to with linguistic aspects.
PEDAGOGICAL IMPLICATIONS
Pedagogical implications that examined young children’s various counting mechanisms and proposed an alternative counting framework that connected the concepts of numbers and numerals might be reconsidered based on the findings of the present study. For example, despite having been considered to be of superior quality, Singapore mathematics textbooks, when blindly approached, might not necessarily find an identical success in its adoption in the U.S. as one in its own natural implementation in Singapore (Ginsburg, Leinwand, Anstrom, & Pollock, 2005).
Similarly, concrete presentations of the base-ten structure of number words, for instance, using manipulatives such as base-ten blocks, might not be as well grounded, or even counterproductive, in an attempt to ameliorate the perceived weaknesses of languages with no transparent base-ten structure as previously suggested (Miller et al., 1995).
References
Bruce, B., & Threlfall, J. (2004). One, two, three and counting. Educational Studies in
Cross, C. T., Woods, T. A., & Schweingruber, H. (2009). Mathematics learning in early childhood: Paths toward excellence and equity. Washington, DC: National Academies.
Fuligni, A. J., & Stevenson, H. W. (1995). Time use and mathematics achievement among American, Chinese, and Japanese high school students. Child Development, 66, 830-842.
Fuson, K. C., Richards, J., & Briars, D. (1982). The acquisition and elaboration of the number word sequence. In C. Brainerd (Ed.), Progress in cognitive development; children’s logical and mathematical cognition (Vol. 1). New York, NY: Springer-Verlag.
Geary, D. C, Bow-Thomas, C. C, Fan, L., & Siegler, R. S. (1993). Even before formal instruction, Chinese children outperform American children in mental addition. Cognitive Development, 8, 517-529.
Ginsburg, A., Leinwand, S., Anstrom, T., & Pollock, E. (2005). What the United States can learn from Singapore’s world-class mathematics system (and what Singapore can learn from the United States): An exploratory study. Washington, DC: American Institutes for Research.
Ho, C. S-H., & Fuson, K. C. (1998). Children’s knowledge of teen quantities as tens and ones:
Comparisons of Chinese, British, and American kindergartners. Journal of Educational Psychology, 90, 536-544.
House, J. D. (2006). Mathematics belief and achievement of elementary school students in Japan and the United States: Results from the Third International Mathematics and Science Study. Journal of Genetic Psychology, 167, 31-45.
Leung, F. K. S. (2001). In search of an East Asian identity in mathematics education.
Educational Studies in Mathematics, 47, 35-51.
Leung, F. K. S. (2006). Mathematics education in East Asia and the West: Does culture matter? In F. K. S. Leung, K-D. Graf, & F. Lopez-Real (Eds.) Mathematics education in different cultural traditions: A comparative study of East Asia and the West (pp. 21-46).
New York, NY: Springer.
Miller, K. F., Kelly, M. K., & Zhou, X. (2005). Learning mathematics in China and the United States: Cross-cultural insights into the nature and course of mathematical development. In J. I. D. Campbell (Ed.), Handbook of mathematical cognition (pp.
163-178). New York, NY: Psychology Press.
Miller, K. F, & Paredes, D. R. (1996). On the shoulders of giants: Cultural tools and mathematical development. In R. J. Sternberg & T Ben-Zeev (Eds.), The nature of mathematical thinking (pp. 83-117). Mahwah, NJ: Lawrence Erlbaum.
Miller, K. F., Smith, C. M., Zhu, J., & Zhang, H. (1995). Preschool origins of cross-national differences in mathematical competence: The role of number-naming systems.
Psychological Science, 6, 56-60.
Mullis, I. V. S., Martin, M. O., Foy, P., & Arora, A. (2012). TIMSS 2011 international results in mathematics. Chestnut Hill, MA: TIMSS & PIRLS International Study Center.
Newman, J., Bidjerano, T., Özdoğru, A. A., Kao, C-C., Özköse-Biyik, Ç., & Johnson, J. J. (2007). What do they usually do after school? A comparative analysis of fourth-grade children in Bulgaria, Taiwan, and the United States. Journal of Early Adolescence, 27, 431-456.
Stevenson, H. W., Chen, C., & Lee, S-Y. (1993). Mathematics achievement of Chinese, Japanese, and American children: Ten years later. Science, 259, 53-58.
Stevenson, H. W., Lee, S. Y., Chen, C., Lummis, M., Stigler, J., Fan, L., & Ge, F. (1990).
Mathematics achievement of children in China and the United States. Child Development, 61, 1053-1066.
Syrett, K., Musolino, J., & Gelman, R. (2012). How can syntax support number word acquisition? Language Learning and Development, 8, 146-176.
Torney-Purta, J. (1990). International comparative research in education: Its role in educational improvement in the U.S. Educational Researcher, 19, 32-35.
Wang, D. B. (2004). Family background factors and mathematics success: A comparison of Chinese and US students. International Journal of Educational Research, 41, 40-54.
Wynn, K. (1992). Children’s acquisition of the number words and the counting system.
Cognitive Psychology, 24, 220-251.
