Insight into early precursors of proportional reasoning is necessary to further our theoretical understanding of mathematical development and to guide early interventions. Although several researchers have suggested patterning as a possible precursor for proportional reasoning, there is little empirical evidence to support this assumption,…

This study illustrates how a diagnostic testing model can be used to make detailed comparisons between student populations participating in international assessments. The performance of Turkish students on the TIMSS-R mathematics test was reanalyzed with a diagnostic testing model called the Rule Space Model. First, mathematical and cognitive…