Early Intervention in Component and Composite Skills for Arithmetic Decomposition
Teach place-value and facts first, then show how to combine them—first graders will use the break-apart strategy right away.
01Research in Context
What this study did
Six first graders watched short math videos and then practiced with a teacher.
The lessons taught place-value and quick fact recall first.
Next, kids rehearsed how to put those pieces together to break big addition problems into smaller, easier chunks.
The team used a multiple-baseline design across children to check if the skill grew only after teaching began.
What they found
Every child mastered the small pieces first.
Right after the combo lessons, all six used the break-apart strategy on new, harder problems.
They kept the skill the next day and used it with different numbers.
How this fits with other research
LeBlanc et al. (2003) did something similar years ago. They taught four story-problem pieces in order to older students with disabilities. Both studies show the same rule: teach parts first, then link them.
Ledbetter-Cho et al. (2023) stretched the video-plus-practice idea to kids with autism. Their students also learned fast and showed less stereotypy. The package works for neurotypical first graders and for students with ASD.
Newson et al. (2026) looks like a clash but is not. They tested a direct-instruction math program with struggling second and third graders and saw only tiny gains. The difference: their kids were older, already behind, and needed more review. Patterson’s kids were brand-new to big addition and learned the pieces before trying the whole skill. Same teaching style, different starting point.
Why it matters
If you teach kindergarten or first grade, run the same two-step plan. First, check that each child knows place-value and basic facts cold. Second, add short lessons that show exactly how to merge those pieces for two-digit addition. Use a quick video model and then let them practice with you. Do not wait for them to invent the shortcut—explicitly bridge the pieces. You should see new problems solved correctly the same week.
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02At a glance
03Original abstract
Abstract As early as first grade, some children are more likely than others to perform arithmetic using inefficient or other overt counting strategies. To partially address this problem, the primary investigator developed a skill hierarchy with procedures based on applied behavior analysis. The novel early-intervention program included a combination of instructional videos and live rehearsal to teach children how to decompose and accurately solve complex addition problems using only “mental math.” Six first graders who did not use decomposition strategies at baseline participated in a single-subject, multiple-probe across participants design. Participants first learned component decomposition skills to identify ones and tens place digits, add tens place values, and retrieve simple addition facts. However, despite mastery of these skills, participants did not use the composite decomposition skill spontaneously when presented with complex addition problems. The primary investigator then provided training on how to apply the component skills to the composite skill. Following training, participants immediately used the composite skill to solve random, complex addition problems with sums up to 198. Results suggest that, through explicit instruction informed by skill hierarchies, children who do not use broadly applicable and efficient methods of solving math problems may come to match their peers in more challenging, mathematics-related activities.
Education and Treatment of Children, 2025 · doi:10.1007/s43494-024-00136-x