Diagnostic assessment of children’s proportional reasoning

A proportional reasoning item bank was created from the relevant literature and tested in various forms. Rasch analyses of 303 pupils’ test results were used to calibrate the bank, and data from 84 pupils’ interviews was used to confirm our diagnostic interpretations. A number of sub-tests were scaled, including parallel ‘without models’ and ‘with models’ forms. We provide details of the 13-item ‘without models’ test which was formed from the ‘richest’ diagnostic items and verified on a further test sample (N=212, ages 10-13). Two scales were constructed for this test, one that measures children’s ‘ratio attainment’ and one that measures their ‘tendency for additive strategy.’ Other significant errors — ‘incorrect build-up,’ ‘magical doubling/halving,’ ‘constant sum’ and ‘incomplete reasoning’ — were identified. Finally, an empirical hierarchy of pupils’ attainment of proportional reasoning was formed, incorporating the significant errors and the additive scale.