"Proportional Language in Mathematics: A Key to Developing Early Reasoning Skills in Children

A crucial part of mathematics, proportional thinking arises in many situations, such when you mix liquids or when you share properly. For this kind of reasoning to work, you need to know your language inside and out, especially for certain situations. As an example, in everyday life, if a recipe calls for two cups of sugar for four servings, then four cups would be needed for eight servings. "Double," "half," and "three times" are important mathematical terms in this field. Elementary school students learn proportional reasoning as a foundational ability for arithmetic, algebra, geometry, and statistics, among other more complex mathematical topics.

Having said that, proportional thinking might be difficult for youngsters. The proportional reasoning learning outcomes are not met by a large percentage of Flanders children by the conclusion of primary school . Little is known about how early primary school students' language abilities relate to their ability to reason proportionally, even though the role of language in children's mathematical development is becoming more acknowledged .

Young children may acquire the capacity to comprehend some proportional scenarios, according to preliminary research are only a few examples of the many studies that have examined the relationship between mathematics and language, despite the fact that they are taught independently in school. In addition to a broad vocabulary, children learn mathematical concepts like "perimeter" and "ratio" in a language-rich setting. In addition, knowing these particular words and the patterns of language they go with is frequently necessary for the construction of mathematical concepts.

Fuchs et al. (2002), Ostad (2009), and Willcutt et al. (2013) found that mathematics language impairments are a common comorbidity of learning disabilities. Early mathematics learning requires mastery of mathematics-specific language, according to studies (NCTM, 2006; Chard et al., 2008). Abedi and Lord  are only a few of the many research that stress the importance of mathematics vocabulary in predicting children's mathematical ability.

As an example, LeFevre et al. (2010) investigated how children's mathematical ability was correlated with their general and early numeracy-related mathematical vocabulary. Compared to generic language, they discovered that mathematically focused terminology is a better indicator of numeracy ability. Researchers studying early numeracy abilities should pay close attention to students' mathematical vocabulary, according to Purpura and Reid (2016), as this is a more immediate indicator of future success in mathematics than students' overall language proficiency.

In addition, Vukovic and Lesaux (2013) looked at 6–9-year-olds' mathematical competence in areas such as geometry, algebra, analysis, and arithmetic, as well as the correlation between language ability and mathematical performance. Their research showed that proficiency in a language is a predictor of success in data analysis and geometry but not in algebra or arithmetic.

A Language and Proportional Reasoning Exercise

The idea of proportional reasoning is based on the fact that two ratios, a/b = c/d, indicate a multiplicative connection between two variables that are subject to change (Vergnaud, 1988). To maintain equity, it would be fair to give four children eight cookies instead of two. Recognized by the National Council of Teachers of Mathematics (NCTM, 1998) as crucial for the development of numerous mathematical ideas throughout school, proportional reasoning is a significant aim in early mathematics education.

There has been a dearth of study on proportional thinking, in contrast to the abundance of literature on the link between language and broad mathematical results. There have been requests to investigate the use of mathematical language in proportional reasoning, despite the fact that some research has operationalized language using broad metrics such phonological awareness and vocabulary (LeFevre et al., 2010; Vukovic & Lesaux, 2013). (Purpura & Reid, 2016).

Proportional reasoning is an important part of knowing rational numbers, probability, linear algebra, and other topics, and it is also a strong predictor of formal fraction abilities (McMullen et al., 2016; Van Dooren et al., 2018). To put these ideas into words, one must master the language of mathematics. For example, the word "product" may indicate both a produced good and a mathematical result; this might cause students to become confused when trying to study mathematics, according to research.

The fact that children as young as five or seven years old can participate in tasks requiring proportional thinking suggests that this skill develops sooner than originally believed, according to research by Resnick and Singer (1993). Students may also find it difficult to differentiate between the mathematical and common meanings of words when mathematical terminology is used interchangeably with daily English. As a result, ensuring that youngsters acquire the academic and technical language skills necessary to comprehend mathematical ideas, such as proportional reasoning, is of the utmost importance.

Reference

Vanluydt, E., et al. 2022. The importance of specific mathematical proportional language for early reasoning

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