Bar Model Scaffolding for Percentage Word Problems in a Year Five Classroom

Many primary pupils can carry out a calculation but still struggle to turn a word problem into a useful mathematical representation. This paper revisits a small classroom intervention in which nine Year Five pupils from a public primary school in Sarawak, Malaysia, learned to use bar models for percentage problems. Over eight one-hour sessions, pupils identified the whole and the relevant part, drew and labelled a segmented bar, translated the relationship into a calculation, and checked whether the answer made sense. The class mean rose from 31.48 (SD = 5.55) on the pretest to 94.44 (SD = 8.34) on the posttest, and the median rose from 33.33 to 100.00. All nine pupils improved. Both the Wilcoxon signed-rank test and the exact sign test indicated a clear pre-post shift (W = 0, exact p = .0039). Every score moved from 33.33% or below at pretest to 83.33% or above at posttest. To make sense of this pattern, we introduce the Verbal-Visual-Symbolic Representation Bridge, which describes how pupils may move from understanding the problem, to constructing a diagram, to writing a mathematical expression, and finally to checking the result. The framework is offered as an interpretation of the teaching process, not as a tested causal model. The findings must also be read in light of the small sample, lack of a comparison group, limited information about the tests, and a marked ceiling effect at posttest. Even with these constraints, the study shows the value of examining each pupil’s score pattern rather than relying only on a class mean. It also illustrates how the assessment itself can shape what can reasonably be claimed about learning.

bar model, percentage, primary mathematics, representational scaffolding, word-problem solving

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