Abstract:
In the transition years, Grades 7 to 9, the shift from natural numbers to rational numbers
and the associated multiplicative concepts prove challenging for many learners. The new
concepts, operations and notation must be mastered if the student is to thereafter rise to meet
the challenges of algebra and more advanced and powerful mathematics. The multiplicative
conceptual field (MCF) groups together such concepts as fraction, ratio, rate, percentage and
proportion, all of which are related yet subtly distinct from one another, each with its own
challenges. Rasch analysis allows us to compare the difficulty of mathematical problems
located within the MCF while, on the same scale, locating the degree to which individual
learners have mastered the necessary skill set. Such location of problems and learners on the
same unidimensional scale allows for fine-grained analysis of which aspects of the problems
being analysed make one problrm more difficult than another. Simultaneously the scale gives
the teacher clear evidence of which students have mastered which concepts and skills and which
have not, thereby allowing more targeted assistance to the class and individual learners. This
paper illustrates the process involved in such analysis by reporting on results located within
a larger study. It is suggested that implementing Rasch analysis within the school classroom
on appropriately designed assessment instruments would provide clarity for the teacher on the
locations of difficulty within the problems used in the assessment and the relative degree to
which individual learners are achieving success at mastering the targeted concepts.
