Poster #146 - Sticky Floors, Sticky Ceilings, and Where to Intervene: A Markov-Chain Analysis of Achievement Mobility

• In Event: Friday Poster Reception

Abstract

Achievement gaps are usually reported as snapshots of where students stand. Policymakers
deciding where to direct tutoring and other supports also need to know how students move
between achievement levels, and where in the distribution a change in that movement would
do the most good. I study this question in two parts. First, using survey-weighted student-
year transitions from the Early Childhood Longitudinal Study, Kindergarten Class of 2010–11
(ECLS-K:2011), I find that socioeconomic status is strongly associated with staying at the
bottom of the mathematics distribution (a sticky floor) and with staying at the top (a sticky
ceiling), while in the three middle states I detect no SES association with persistence. An
apparent SES advantage in the size of upward jumps disappears once achievement levels are
defined relative to same-grade peers; nearly all of it came from pooling score cutoffs across
grades, which counts ordinary growth as mobility. Second, I build a five-state Markov model
calibrated to 2022 NAEP Grade 8 mathematics and show that the long-run effect of the most
favorable shift in a state’s transition probabilities is proportional to that state’s population share
times its expected time to reach the target level. In the calibrated model, the lowest-achieving
state has the greatest leverage on both the Advanced share and the at-or-above-Proficient share,
and within the calibration family this result does not depend on the model’s unidentified time
scale. The results suggest that accountability incentives focused near proficiency cutoffs may
underweight the students for whom improved mobility has the largest long-run payoff, and that
growth metrics built on fixed cutoffs should be interpreted with care.

Author

• Michael J Zhang, Equity Learning
  Presenting Author