Publication details

Assessment of giftedness using the Rasch Model: Test for Identifying Gifted Students in Mathematics (TIM)



Year of publication 2016
Type Appeared in Conference without Proceedings
MU Faculty or unit

Faculty of Social Studies

Description Test for Identifying Gifted Students in Mathematics (abbreviate to TIM) is a new unidimensional test with two parallel forms for assessment high ability in math for 3rd to 5th graders in the Czech Republic. The item bank composed of three facets based mainly on difficult tasks, which are not included in the school education in particular grades, but which can be solved with mathematical knowledge available to primary grades students. During one preliminary (n = 223), three pilot (n = 524) and one standardization (n = 797) data collection we conducted item analysis and we tested validity and reliability. Due to high test difficulty, skewed distribution and ordinal data structure we used Partial Credit Rasch Model (PCRM). We merged pilot and standardization samples into one dataset (and verified item fit using DIF analysis) and equated both forms trough common-item non-equivalent group design. Data fitted to PCRM, X2(31754) = 31773,88, p = 0,45. Test forms were strictly equivalent with no significant differences in the distributions, means or variances of latent traits estimates or differential functioning of common items (DIF). TIM showed strong unidimensional structure (checked using structural equating modeling and PCRM) with high reliability: Cronbach’s alphas and “over-all” IRT reliability above .85 for all grades and target population (gifted children), test-retest reliability of parallel forms after three months was .78 for the whole sample (Md = .79 for different grades). We proofed validity in many ways, for example: TIM distinguished gifted and non-gifted children very well (median of Cohen’s d was Md = 1.6, median of areas under curve AUC = .93), median of correlations with subtests of WISC-III was Md = .28 (-.20–.56), for WJ IE II COG Md = .28 (-.17–.49). Score in TIM was positively connected to teacher’s rating and school grades too (median of correlation Md = .47). Mathematical ability was also connected to visuospatial ability – correlation with Rey-Osterrieth figure was above .18 for quantitative, but non-significant for qualitative scores under DSS-ROCF scoring system, which is in concordance with other research. There were no difference between sex. We conclude that TIM is reliable and valid assessment tool for measuring above-average ability in mathematics. We also discuss how the Rasch Model can help with adaptation of TIM into other languages (Polish, Indian Turkish versions are being translated).
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