The Importance of Number Sense to Mathematics Achievement in First and Third Grades.

Children's symbolic number sense was examined at the beginning of first grade with a short screen of competencies related to counting, number knowledge, and arithmetic operations. Conventional mathematics achievement was then assessed at the end of both first and third grades. Controlling for age and cognitive abilities (i.e., language, spatial, and memory), number sense made a unique and meaningful contribution to the variance in mathematics achievement at both first and third grades. Furthermore, the strength of the predictions did not weaken over time. Number sense was most strongly related to the ability to solve applied mathematics problems presented in various contexts. The number sense screen taps important intermediate skills that should be considered in the development of early mathematics assessments and interventions.

Early math matters: kindergarten number competence and later mathematics outcomes.

Children's number competencies over 6 time points, from the beginning of kindergarten to the middle of 1st grade, were examined in relation to their mathematics achievement over 5 later time points, from the end of 1st grade to the end of 3rd grade. The relation between early number competence and mathematics achievement was strong and significant throughout the study period. A sequential process growth curve model showed that kindergarten number competence predicted rate of growth in mathematics achievement between 1st and 3rd grades as well as achievement level through 3rd grade. Further, rate of growth in early number competence predicted mathematics performance level in 3rd grade. Although low-income children performed more poorly than their middle-income counterparts in mathematics achievement and progressed at a slower rate, their performance and growth were mediated through relatively weak kindergarten number competence. Similarly, the better performance and faster growth of children who entered kindergarten at an older age were explained by kindergarten number competence. The findings show the importance of early number competence for setting children's learning trajectories in elementary school mathematics.

Development of number combination skill in the early school years: when do fingers help?

Children's change over time in frequency of finger use on number combinations was examined in relation to their change in accuracy. Performance was tracked longitudinally over 11 time points, from the beginning of kindergarten (mean age = 5.7 years) to the end of second grade (n= 217). Accuracy in number combinations increased steadily during the time period while frequency of finger use declined. Correlations between finger use and accuracy decreased gradually, ranging from 0.60 in kindergarten to -0.15 at the end of second grade. Low-income children showed linear growth in frequency of finger use while middle-income children slowed down by second grade and even started to decline. Although girls and boys showed similar growth patterns in frequency and accuracy, boys used their fingers less often than girls and were more accurate. The findings indicate that finger use is most adaptive when children are first learning number combinations, but this benefit lessens over time.

Sequence effects in the United States Medical Licensing Examination (USMLE) step 2 clinical skills (cs) examination.

BACKGROUND: Systematic trends in examinee performance across the testing day (sequence effects) could indicate that artifacts of the testing situation have an impact on scores. This research investigated the presence of sequence effects for United States Medical Licensing Exam (USMLE) Step 2 clinical skills (CS) examination components. METHOD: Data from Step 2 CS examinees were analyzed using analysis of covariance and hierarchical linear modeling procedures. RESULTS: Sequence was significant for three of the components; communication and interpersonal skills, data gathering, and documentation. A significant gender x sequence interaction was found for two components. CONCLUSIONS: The presence of sequence effects suggests that scores on early cases are influenced by factors that are unrelated to the proficiencies of interest. More research is needed to fully understand these effects.

Contrast effects in the USMLE Step 2 Clinical Skills examination.

BACKGROUND: As with any examination using human raters, it is possible that human subjectivity may introduce measurement error. An examinee's performance might be scored differently on the basis of the quality of the preceding performance(s) (contrast effects). This research investigated the presence of contrast effects, within and across test sessions, for the communication and interpersonal skills component of the United States Medical Licensing Examination Step 2 Clinical Skills (CS) examination. METHOD: Data from Step 2 CS examinees were analyzed using hierarchical and general linear modeling procedures. RESULTS: Contrast effect was significant for the communication and interpersonal skills score, both within and across test sessions. The effect was found to have a nontrivial impact on the overall score. CONCLUSIONS: The presence of contrast effects suggests that scores for an examinee are influenced by the performance of other examinees. More research is needed to fully understand these effects.