Assessing problem solving in mathematics: Some variables related to student performance

A mathematical problem is defined here as a question not dependent on specific syllabus content, and one sufficiently new to the student such that it cannot be solved by a previously known method. With increased attention being paid to this type of mathematical problem solving at the primary school level, the need for reliable and valid methods of assessment has become more apparent. This paper reports the results of using a new problem solving test, developed for use in the upper primary school, with 371 students in Years 4,5 and 6 at government schools in Melbourne. Particular attention is given to the effects of year level, sex and the method of test administration on student performance for different types of items and different problem solving processes. The performance of Year 4 students was generally lower than that of other students, but differences were small for most items and processes between Years 5 and 6. Although most of the differences in performance between the sexes were not significant, the girls had higher scores than the boys for the total score, for all processes and for all items except the spatial item. The method of administration was important for performance, especially for the girls. The marking schedule developed enabled high intra- and inter-marker reliabilities to be obtained.