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This research applied quantile regression to exam the effects of student demographic characteristics (age, gender, parents’ socioeconomic status, immigrant status, family structure, language at home) on STEM education equity and change, using the 2003 and 2012 Programme for International Student Assessment (PISA) data. The study summarizes the principal findings on mathematics outcomes by highlighting and comparing, location shifts, scale shifts and shape shifts within and between 2003 and 2012. The results showed that the effects of many student characteristics were not constant across the mathematics outcomes distributions. This suggested that individual differences were valued heterogeneously across the mathematics outcomes distributions.