Improving the Mathematics Performance of Second-Grade Students with Mathematics Difficulties through an Early Numeracy Intervention.

Bryant et al. (2021) ran a 20-week Tier 2 numeracy program. Second-graders who scored low on a math screener met in small groups four times a week.

Each lesson used direct instruction: fast-paced teacher modeling, guided practice, and quick checks. The team tracked both basic skills and story-problem solving.

Kids in the program outpaced peers on basic number sense tests. They could name more quantities and count faster.

Yet on word-problem tests the groups looked the same. Better facts did not spill over into better problem solving.

Bennett et al. (1998) showed that direct instruction can hit 100% accuracy when you teach one skill at a time. Their older multiplication-fact study proves DI still works; the new trial widens it to a full numeracy package.

Liu et al. (2026) also worked with second-graders but used stimulus-equivalence training instead of DI. Their kids quickly learned coin relations. Together the papers say: both DI and equivalence methods move math facts, but neither auto-fixes higher-order problems.

Subramaniam et al. (2023) watched K-2 self-contained rooms and saw only 61% of math time was real teaching. The Pedrotty trial shows what can happen when you protect a full 20 weeks of high-quality minutes.

If you run RTI or MTSS, use this package to lift basic numeracy fast. Just do not expect word-problem gains until you add a separate problem-solving layer. Block 15 minutes a day for facts, then teach attack strategies in another block.