From the abstract: We sought to construct a vertical difficulty scale for the skill library in Freckle, a widely used online mathematics practice system. The scale would span kindergarten through grade 8 and permit direct comparisons of skill difficulty across grade levels. We fitted an Extreme Gradient Boosting (XGBoost) prediction model to 3 million practice sessions covering over 1,800 mathematics skills. We applied the model as a counterfactual, fitting it to the full population of students to generate a population percent-correct score for each skill in adjacent grades. We linked adjacent grades using Thurstone’s scaling method and validated the resulting scale against independently derived Rasch-based skill difficulties from Star Math. The two scales were strongly associated (Pearson r = 0.80), supporting the use of large-scale practice data to estimate comparable skill difficulties across grades. Citation: Bielinski, J. (2026, October 5–7). Using XGBoost to construct a vertically aligned skill difficulty scale [Conference presentation]. Artificial Intelligence in Measurement and Education Conference (AIME-Con 2026), Pittsburgh, PA, United States.

Star Reading and Star Math have been rated highly by the National Center on Intensive Intervention (NCII) as academic screening assessments. The Full Review is available online: <https://charts.intensiveintervention.org/ascreening>.

To develop Pathway to Proficiency reports for Maryland Star Reading and Star Math schools, we linked our scaled scores with the scaled scores from Maryland's achievement test. This technical report details the statistical method behind the process of linking Maryland's state test (MCAP) and Star Reading and Star Math scaled scores. The full report is available online: <https://docs.renaissance.com/R53629>.

To develop Pathway to Proficiency reports for California Star Reading and Star Math schools, we linked our scaled scores with the scaled scores from the Smarter Balanced achievement test. This technical report details the statistical method behind the process of linking Smarter Balanced Asessments and Star Reading and Star Math scaled scores. The full report is available online: <https://docs.renaissance.com/R44908>.

To develop Pathway to Proficiency reports for Washington Star Reading and Star Math schools, we linked our scaled scores with the scaled scores from the Smarter Balanced achievement test. This technical report details the statistical method behind the process of linking Smarter Balanced Asessments and Star Reading and Star Math scaled scores. The full report is available online: <https://docs.renaissance.com/R45817>.

To develop Pathway to Proficiency reports for District of Columbia (DC) Star Reading and Star Math schools, we linked our scaled scores with the scaled scores from DC's achievement test. This technical report details the statistical method behind the process of linking DC's state test (SBAC) and Star Reading and Star Math scaled scores. The full report is available online: <https://docs.renaissance.com/R53527>.

To develop Pathway to Proficiency reports for Oregon Star Reading and Star Math schools, we linked our scaled scores with the scaled scores from the Oregon Statewide Assessment System (OSAS) Performance (originally Smarter Balanced )achievement test. This technical report details the statistical method behind the process of linking OSAS and Star Reading and Star Math scaled scores. The full report is available online: <https://docs.renaissance.com/R53784>.

To develop Pathway to Proficiency reports for Connecticut Star Reading and Star Math schools, we linked our scaled scores with the scaled scores from the Smarter Balanced achievement test. This technical report details the statistical method behind the process of linking Smarter Balanced Asessments and Star Reading and Star Math scaled scores. The full tehcnical report is available online: <https://docs.renaissance.com/R53507>.

To develop Pathway to Proficiency reports for Delaware Star Reading and Star Math schools, we linked our scaled scores with the scaled scores from the Smarter Balanced achievement test. This technical report details the statistical method behind the process of linking Smarter Balanced Asessments and Star Reading and Star Math scaled scores. The full report is available online: <https://docs.renaissance.com/R53517>.

To develop Pathway to Proficiency reports for Hawai'i Star Reading and Star Math schools, we linked our scaled scores with the scaled scores from the Smarter Balanced achievement test. This technical report details the statistical method behind the process of linking Smarter Balanced Asessments and Star Reading and Star Math scaled scores. The full report is available online: <https://docs.renaissance.com/R53552>.

To develop Pathway to Proficiency reports for South Dakota Star Reading and Star Math schools, we linked our scaled scores with the scaled scores from the Smarter Balanced achievement test. This technical report details the statistical method behind the process of linking Smarter Balanced Asessments and Star Reading and Star Math scaled scores. The full report is available online: <https://docs.renaissance.com/R53434>.

To develop Pathway to Proficiency reports for Nevada Star Reading and Star Math schools, we linked our scaled scores with the scaled scores from the Smarter Balanced achievement test. This technical report details the statistical method behind the process of linking Smarter Balanced Asessments and Star Reading and Star Math scaled scores. The full report is available online: <https://docs.renaissance.com/R53326>.

To develop Pathway to Proficiency reports for Texas Star Reading and Star Math schools, we linked our scaled scores with the scaled scores from Texas' achievement test. This technical report details the statistical method behind the process of linking Texas' state test (STAAR) and Star Reading and Star Math scaled scores. The full report is available online: <https://docs.renaissance.com/R45735>.