Rasch measures of number discrimination and reversal, and numbers in calculations for young children

Document Type

Book Chapter


Nova Science Publishers

Place of Publication



Russell Waugh


Faculty of Education and Arts


School of Education / Fogarty Learning Centre




Richmond, J. Waugh, R. F., & Konza, D. M. (2010). Rasch measures of number discrimination and reversal, and numbers in calculations for young children. In Russell Waugh (Ed.). Specialized Rasch measures applied at the forefront of education (pp. 85-102). Hauppauge, New York: Nova Science Publishers. Available here.


Number literacy is a very important topic and the Australian Government runs numeracy and literacy tests, administered through the State Education Departments, for all Year 3 (8 years old), Year 5 (10 years old) and Year 7 (12 years old) students. Results of these tests are reported to schools and parents with a view to ensuring that all children meet certain numeracy standards and that children who are ‘falling behind’ are detected early so that remedial work can be given. Rasch measures were created with the RUMM2020 computer program for Visual Discrimination of Numbers (VDN) and Figure Ground Numbers in Calculations (FGNC). The student sample was N=324 pre-primary and primary students in Perth, Western Australia, aged 4-9 years old. Data on 20 items for VDN and 28 items for FGNC, where each item was scored in one of two categories (wrong scored zero and correct scored one), were Rasch analysed to create two linear scales. Six of the initial 20 items for VDN were deleted due to item misfit statistics, leaving 14 items. Thirteen of the initial 28 items for FGNC were deleted due to item misfit statistics, leaving 15 items. The final data for VDN and FGNC were used to create two highly reliable, linear, uni-dimensional scales (Student Separation Indices of 0.75 and 0.95 respectively) where the items are ordered from easy to hard and the student measures from low to high on the same scale. The two scales showed no statistically significant interaction of student measures on item difficulties along the scale, meaning that there was good agreement about the item difficulties along each scale, and each scale was unidimensional. The item-trait chi-squares are respectively, χ² = 68.34, df=0.92, p=0.12, and χ² = 58.83, df=60, p=0.52. The fit residual statistics for each of the two scales was reasonable and the targeting was reasonable.