How the inversion property in number-naming impedes mathematical performance, potential interventions to minimize its impact.

Linguistic properties affect numerical cognition. It is well-documented that transparent number-naming systems, such as those found in Chinese, Japanese and Korean, support mathematical performance due to their explicit structure that highlights place-value concepts. However, less is known about opaque number-naming systems and their impact on math achievement. In this review, we present several studies that investigate a linguistic trait known as the "inversion property" and examine its impact on a variety of math skills such as transcoding, magnitude estimation, addition and addition-estimation among young children. The inversion property can be found in languages such as German, Dutch and Czech, and is defined as the phenomenon where the standard, descending place-value order of numbers is inverted in written and oral expressions. For example, referring to "32" as "two and thirty." We argue that the inversion property impedes mathematical performance, likely because it undermines place-value processing and burdens working memory. To limit its negative impact, we consider early interventions such as modifying number-names to become more transparent and using physical manipulatives to strengthen place-value concepts.