Evaluating the Effects of an Algebraic Frequency Building Intervention for Students with Disabilities
One-minute algebra timings on a Standard Celeration Chart quickly made three students with disabilities fast and accurate, and the skill spread to new equations.
01Research in Context
What this study did
Three middle-school students with disabilities joined daily one-minute algebra timings.
They solved one-step equations like x + 4 = 9 while the teacher charted every correct and incorrect digit on a Standard Celeration Chart.
The study used a multiple-baseline design across students to show that gains appeared only after the intervention started.
What they found
Correct answers jumped up right away and errors dropped.
When the kids later saw brand-new equations, they still solved them quickly, showing the skill had transferred.
How this fits with other research
Newson et al. (2026) tried one-on-one AMPPS tutoring and saw only weak gains in computation. Enders et al. (2025) got stronger, faster growth by adding frequency building and minute timings, so the newer method updates the older one.
LeBlanc et al. (2003) first showed that breaking math into small precurrent steps helps students with disabilities. Enders keeps the small-step idea but swaps in speed practice and charting, moving from slow discrete trials to rapid fluency.
Laugeson et al. (2014) used computer graphic organizers to boost accuracy on one-step word problems. Enders moves from accuracy to fluent algebra performance and shows the same one-step structure can be brought to fluent levels with timed practice.
Why it matters
If a middle-schooler stalls on basic algebra, try one-minute frequency timings instead of longer worksheets. Chart the digits, aim for a steeper line, and watch the student meet new problems with the same speed. It takes one timer, one graph, and a few equations to start.
Want CEUs on This Topic?
The ABA Clubhouse has 60+ free CEUs — live every Wednesday. Ethics, supervision & clinical topics.
Join Free →Run a 60-second timing on five one-step equations, count correct and incorrect digits, and plot both on a celeration chart to see the student’s learning speed.
02At a glance
03Original abstract
Abstract Evidence-based instructional strategies in mathematics provide critical support related to academic achievement for students with disabilities. Many researched mathematics interventions focus on foundational and elementary mathematics skills, indicating the need for interventions for higher-level topics such as algebra. Current research on a core skill within algebra—solving equations—focuses primarily on the initial acquisition. To move students past acquisition, we must consider how interventions target behavioral fluency. Leveraging precision teaching practices, we evaluated a frequency-building intervention to improve the rates of three middle-school students’ correct responses to one-step algebraic equations using a multiple-baseline across participants design. Results demonstrate immediate and significant positive effects on students’ correct notations and drastic decreases in students’ incorrect notations. Students generalized skills to untaught problem presentations. In pre- and post-think-aloud, students moved from using trial-and-error methods to using systematic procedures to solve equations. We discuss how the characteristics of the intervention supported students’ overall improvement and discuss potential implications for both practice and future research. • Frequency-building interventions are effective in supporting students’ accuracy and speed in solving algebraic equations • Precision teaching, including the use of the Standard Celeration Chart, is a powerful system for guiding both research and instructional decisions • Fluent behavior in foundational skills can support generalization to new mathematical problems • Mathematics research broadly must incorporate timing to facilitate movement beyond the acquisition stage of learning
Behavior Analysis in Practice, 2025 · doi:10.1007/s40617-025-01082-9