Stepping Up to STEM Act of 2013 - Amends the Department of Education Organization Act to establish the Office of Science, Technology, Engineering, and Mathematics (STEM) Education within the Department of Education to administer STEM education.
Directs the Office of STEM Education to conduct an independent evaluation of the Department's STEM Education programs at least once every five years.
Establishes an Advanced Research Projects Agency for Education (ARPA-ED) within the Department to pursue breakthrough research and development in educational technology and to facilitate the effective use of that technology to improve student achievement.
Directs the Secretary of Education to award matching grants to state-based STEM networks or similar organizations of STEM stakeholders to increase students' achievement in the STEM disciplines in elementary and secondary schools and in out of school and afterschool programs.
Includes among grant uses:
Requires grantees to conduct periodic independent evaluations of their effectiveness in accomplishing those activities.
Prohibits the Secretary from: (1) endorsing or approving any STEM curriculum designed for use in an elementary school, secondary school, or institution of higher education; or (2) requiring a state, local educational agency, or school to adopt a specific STEM program or instructional materials.