We identify common genetic variants associated with cognitive performance using a two-stage approach, which we call the proxy-phenotype method. First, we conduct a genome-wide association study of educational attainment in a large sample (n = 106,736), which produces a set of 69 education-associated SNPs. Second, using independent samples (n = 24,189), we measure the association of these education-associated SNPs with cognitive performance. Three SNPs (rs1487441, rs7923609, and rs2721173) are significantly associated with cognitive performance after correction for multiple hypothesis testing. In an independent sample of older Americans (n = 8,652), we also show that a polygenic score derived from the education-associated SNPs is associated with memory and absence of dementia. Convergent evidence from a set of bioinformatics analyses implicates four specific genes (KNCMA1, NRXN1, POU2F3, and SCRT). All of these genes are associated with a particular neurotransmitter pathway involved in synaptic plasticity, the main cellular mechanism for learning and memory.