The design of mathematics testing accommodations for second language learners: semiotic exchangeability of translation and illustration pop-up glossaries in computer-administered tests

ABSTRACT We examined semiotic exchangeability in pop-up glossary translations and illustrations used as supports for second language learners (SLLs) in computer-administered mathematics tests. In a sample of 516 mathematics items, Grades 3–8 and 11, from a large-scale assessment program in the US, test developers identified terms that could be translated and terms that could be illustrated without altering the target constructs. In each item, we examined: number of unique words (w), number of unique terms identified for translation (t), and number of unique terms identified for illustration (i.) Of the 3,186 terms identified for translation or for illustration, only about one sixth were identified both for translation and for illustration. We observed statistically significant w and t differences attributable to the main effect of depth of knowledge and type of item and statistically significant i differences attributable to the main effect of type of item. The correlation of item translatability (T = t/w) and item illustratability (I = i/w) was low for all items combined but higher and statistically significant for some types of items and for greater values of depth of knowledge. We conclude that translation and illustration pop-up glossaries are functionally different sets of semiotic resources that support SLLs in different ways.