1. ANS Acuity and Learning Number Words from Number Books and Games James Negen, Meghan C. Goldman, Tanya D. Anaya and Barbara W. Sarnecka University of California, Irvine {jnegen, meghan.goldman, anayat, sarnecka}@uci.edu Summary “Which side has MORE dots?” Set Comparison Measured a child’s ANS acuity before intervention First ratios were very easy (3:1). The child could not go on until 8 very easy trials in a row were correct. Ratios got harder (until 10:9) Previous research has found that children with higher approximate number system acuity (ANS acuity) tend to have higher math achievement (e.g., Mazzocco et al., 2004), but it is not clear why. The present study examined the possibility that children with greater ANS acuity (see Set Comparison in Method) learn more number words from simple counting books and number games (see Intervention in Method). Preliminary results suggest that this is not the case; children with higher ANS acuity did not learn significantly more number words. Background Method Results Conclusions 4 weeks, once per week Number line game (below): spun a spinner and went either 1 or 2 spaces (control went to a color) Counting books (left): Read books where they progressively counted from 1 to 9 objects (control just pointed and named objects) Done once in Spanish and once in English for 40 Spanish-English bilingual participants Half were area-correlated, half are area-anticorrelated (example above) so that non-numeric cues were not useful Feedback was given after every trial (e.g., “Yes, that’s right.”) The approximate number system (ANS) gives us a rough nonverbal idea of how many items are in a set. The acuity of this system varies from person to person and generally increases from birth to adulthood (e.g. Halberda & Feigenson, 2008). Number-word knowledge, measured here as the ability to consistently make a set that matches a certain number word, is a critical early step in learning mathematics. It generally develops by learning the first four number words by themselves, then coming to understand how counting works and how the counting process organizes the number words to give them numeric meaning (e.g., Carey, 2009). These data are taken from a project trying to develop a way to teach number-word knowledge to low-SES preschoolers. Preliminary results suggest that children with greater ANS acuity achieve more in math through some other mechanism. They do not appear to have an advantage in learning number words from number books and simple number games, like the kind commonly available in preschool. These conclusions are limited by the fact that only 14 children fit the inclusion criteria for the most important analysis. A Bayesian analysis favors the null by a factor of 2.29, which is generally only considered very mild evidence. These children are also all low-SES, so the results may not apply to other populations. On the other hand, disadvantaged children should be on average the most sensitive to increases in useful input, since they are least likely to be getting useful input from other sources. We also chose to give the bilingual children input in both of their languages; it’s not known if this is the optimal strategy. “Can you give him THREE oranges?” Give-N Measured a child’s number-word knowledge before and after intervention Asked for “one” through “six” Done in both Spanish and English for bilingual participants, higher result used in analysis Intervention English read and played twice for 7 additional English-speaking participants Average time of about 20 minutes per session Preliminary results suggest that children with greater ANS acuity did not learn more from the counting books and number games. 23 children were excluded for ceiling performance in Give-N before the intervention (17), failing to perform significantly above chance in the set comparison task (2), and/or re-testing at a lower level of number-word knowledge (5). 24 children remained: 14 experimental (4;1 – 5;1, mean 4;9) and 10 control (4;3 – 5;1, mean 4;8). 12 children learned at least one number word (4;1 – 5;1, mean 4;8, 8 in experimental) and 12 children did not (4;4 – 5;0, mean 4;8, 6 in experimental). The difference in set-comparison performance (i.e., ANS acuity) was not significant when looking at both conditions, t(22) =.39, p =.7, nor just the experimental group, t(12) =.73, p =.48. A Bayesian analysis favors the null by a factor of 2.29.