For the past 15 years I have been involved with research that seeks to understand how students can transition from more informal reasoning to more formal, mathematical reasoning. As part of this NSF funded research, we have developed curriculum to help students make this transition. In my current project our team is developing instructional materials appropriate for a first college course in linear algebra including the topics of (1) span and linear independence, (2) matrix multiplication and linear transformations, and (3) eigen theory, change of basis and diagonalization. Aspects of this curriculum have been used by our team since 2009 and have been used by professors in the United States and in Mexico. This talk will provide an overview of our linear algebra curriculum and the materials we have designed to help instructors implement this curriculum. In particular, I will give examples of how the research we have done and we continue to do effects its design.