Traditional assessment methods are not always suitable for diagnosing learners' knowledge structures at different levels of their expertise. This paper describes an alternative schema-based rapid assessment technique and its application in the area of arithmetic word problem solving. The technique is based on an assessment of the extent to which working memory limits have been altered by solution schemas held in long-term memory. In an experiment (N=55, Grade 8), the average test time was reduced by a factor of 2.8 in comparison with a traditional test, with a significant correlation of 0.72 between scores on both tests.