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…

This document contains the fourth volume of the proceedings of the 30th Conference of the International Group for the Psychology of Mathematics Education. Conference presentations are centered around the theme "Mathematics at the Centre." This volume features 59 research reports by presenters with last names beginning between Kun and…