The research
Our methods are backed by research.
How to read an effect size. Education research reports results in standard deviations. A useful translation: an effect of 0.5 moves the average student from the middle of their class to roughly the 69th percentile. Anything above 0.4 is a substantial effect in classroom research, where most interventions produce far less.
What the Science of Learning Teaches Us About Arithmetic Fluency
The most thorough recent review of how children become fluent with arithmetic, published in the journal that exists specifically to establish scientific consensus for the public. It underpins most of what we do: why fluency matters, why we teach efficient mental strategies rather than every possible method, and why we never introduce a timer before accuracy.
Fluency frees working memory for higher-order thinking. Time-limited practice belongs after accuracy is established, not before.
journals.sagepub.comExamining the Academic Effects of Cross-age Tutoring: A Meta-analysis
A synthesis of 32 studies on older students teaching younger ones. This is the evidence base for our tutor model, and the reason we don’t treat student tutors as a compromise.
Overall effect 0.34. Student tutors produced larger gains (0.37) than adult tutors (0.25). Tutors themselves gained 0.39 — slightly more than the children they taught.
link.springer.comThe Distributed Practice Effect on Classroom Learning
A meta-analysis of 22 classroom studies covering more than 3,000 students, on real curriculum material rather than laboratory word lists. It’s why our sequence spirals back rather than running in a straight line.
Spaced practice beat massed practice by d = 0.54. Effects were larger the longer the delay before testing.
doi.org — open accessThe Promise of Tutoring for PreK–12 Learning: A Systematic Review and Meta-Analysis
96 randomized controlled trials of tutoring programs. It’s the reason we recommend twice a week as a minimum and are honest that three times is faster.
Pooled effect 0.288. Larger in earlier grades, and larger for programs meeting three or more days per week.
The Academic, Socialization, and Psychological Effects of Acceleration
The standard reference on what happens when a capable child is moved ahead. Successor to the 2004 report A Nation Deceived, which found acceleration to be the most effective intervention available for advanced learners.
Subject-based acceleration: +0.49 on academic outcomes, +0.58 on psychological ones. The emotional benefits are the larger of the two.
Common Core State Standards for Mathematics
Our topic map covers every state standard, so nothing gets skipped. The standards themselves expect children to know all sums of two one-digit numbers from memory by the end of second grade, and all products of two one-digit numbers by the end of third. We treat those as a floor.