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Most of the materials that teachers reported using regularly for their instruction during the 2015–2016 school year were not highly aligned with the Common Core State Standards

• About 16 percent of elementary mathematics teachers and 5 percent of secondary mathematics teachers reported regularly using materials with a high degree of alignment.

• Teachers in states that have not formally adopted the Common Core were not using highly aligned materials, by the authors' definition.

A majority of teachers were able to identify Common Core–aligned topics at their grade level

• At the same time, many teachers also indicated that many topics not aligned with the Common Core should be addressed at their grade level.

• Less than one-third of teachers were able to order two sets of standards from the lowest to the highest grade level, although most teachers could order at least one set of standards correctly.

Over one-third of teachers reported that their students engaged in various standards-aligned practices to a great extent

• On the other hand, roughly 20 percent of teachers reported asking students to look for and make use of structure or construct viable arguments, two Standards for Mathematical Practice emphasized by the Common Core.

• Teachers using at least one aligned main material more frequently reported their students engaging to a great extent in standards-aligned practices than teachers not using at least one aligned main material.
• Teachers with more vulnerable students were less likely to report engaging their students in standards-aligned practices than teachers serving less vulnerable students.