aeh, I believe the study stated they looked for "proficiency", using tests developed to measure according to common core standards.

The study provides Table 4 and Table 6 which are "cut scores developed for each grade level and content area" for "Proficient-ELA" and "Proficient-Mathematics".

The downloadable "data linking table" on this webpage (found by following the study's linked reference #15) shows four categories for each grade level:
Not Met, Nearly Met, Met, Exceeded.

This corresponds to "California set four levels of cut scores for ELA and mathematics" (resource 12 shows these to be 1, 2, 3, and 4) and "Wisconsin provided cut scores on ELA and mathematics at four levels: below basic, basic, proficient, and advanced.11 The state set proficient to indicate performance that was on grade level."

This seems to indicate:
Met = Level 3 = Proficient = on grade level,
and
Exceeded = Level 4 = Advanced = above grade level.

The article states, "a MAP test score that is equivalent to ninth-grade performance is in fact based on ninth-grade content knowledge and skills."