# What Have We Been Up To?

Below are a few sneak peaks at what we have been working on in the lab!

Your time and effort over the years have helped progress and enhance our research!

** Approximate Number Sense **

This study involves measures of approximate number sense (ANS), which is the ability to accurately compare quantities without using typical symbols used in mathematics. This study aimed to examine the relationship among approximate number sense, math achievement, and general cognitive ability using two different twin samples. It explored genetic factors as well as both shared and non-shared environmental factors. Shared being an aspect of the environment that twins have in common, and non-shared being something that differs between their environments. In both samples, the results suggested that individual differences in approximate number sense ability were due partially to significant genetic factors. The genetic factors associated with approximate number sense were also shared with those factors that accounted for individual math skills. The majority of the correlation between approximate number sense and math skills was due to hidden genetic factors shared by both traits. Additionally, when general cognitive ability was included there was evidence of genetic overlap among all three skills, and most of the overlap was genetic.

** Math Performance Around the World **

Our researchers wanted to test if the association between the number line and mathematical performance of childhood was caused from genetics or environmental factors. We studied twins ages 8-15 years old from the United States, Canada, United Kingdom, and Russia. The results of the twins from the United Kingdom and Canada came back as genetic factors causing this association. However, for the twins from the United States we discovered it was environmental factors. We found that schools that grouped by ability level were linked to genetic factors. On the other hand, schools that were grouped with all learning levels were caused by environmental factors.

** Strategies Predict Mathematical Thinking **

Results from this study suggest that even in adolescence, the strategies that students use to solve simple addition problems are an important indicator of the way they are thinking about math in general. Of particular concern, adolescents who are still relying on counting to solve simple addition problems may also be struggling with broader math achievement in other areas like geometry, fractions, or algebra. Helping students with this strategy profile to move beyond counting by practicing math facts may be an importation direction for intervention.

** Predicting Math Achievement **

Data were collected from a same-sex twin sample at ages 12 and 15 (N = 150 pairs) as part of the Western Reserve Reading and Math Project. Participants were asked to identify where on a number line a series of numbers should be located. Researchers analyzed the responses to determine if the way in which accuracy on the task was described (i.e., difference between the correct answer and the answer given or closeness to a predicted pattern of responding) at age 12 changed how well they could predict performance on mathematical achievement measures at age 15. The results of this study suggest that while most adolescents are able to accurately associate number with space (assign a number to the correct place on a number line), some adolescents have not fully developed this skill. The variation in performance on this task was predictive of later performance on mathematical achievement tasks, from solving basic arithmetic to more advanced problems regardless of how accuracy was described.