Young children have been taught simple sequences of alternating shapes and colors, referred to as "patterning", for the past half century in the hope that their understanding of pre-algebra and their mathematics achievement would be improved. The evidence that such patterning instruction actually improves children's academic achievement is scanty. However, recent research shows that instruction on more complex patterns produces advances in both mathematics and reading achievement. Patterning instruction should change accordingly. Further research is needed to assess the cognitive mechanisms involved, which children benefit from such instruction, and the patterns that will produce the greatest gains.