Two district curriculum specialists, Julie Spykerman of the Anaheim Union High School District, and Cathy Martin of the Denver public schools, talk about how they and their colleagues try to separate truth from fiction in judging vendors’ claims that their products align to the common core. Both of them rely on the guidance of outside organizations who are reviewing content, as well as the judgment of their own administrators and teachers.

Spykerman and Martin say they expect companies get beyond vague boasts about their products, and show their districts how individual lessons satisfy the common-core principles, and how students are likely to respond to the material …