Linking ideas, concepts, and disciplinary content is an underused yet effective educational strategy for fostering students' higher order thinking. A body of psychological research on analogical reasoning can inform the challenge of encouraging higher order thinking in schools. We focus in particular on the teaching of mathematics and highlight alignments between a psychologically based definition of higher order thinking and educational goals as described within U.S. mathematical practice standards. Finally, this analysis implicates policies for supporting students' higher order thinking including requiring assessments that capture these skills; disseminating assessment data meaningfully to help improve teachers, schools, or curricula; and designing professional development that draws explicit attention to these skills.