The effects of cumulative practice on mathematics problem solving.
Cumulative practice interleaves previously learned skills with newly taught ones during review, and it outperforms massed review for application and novel problem solving.
01Research in Context
What this study did
Researchers worked with 60 college students taking algebra.
They split the class into three groups.
One group got cumulative practice—old problems mixed with new ones.
The other two groups got either simple review or extra practice on just the new skill.
All groups used the same computer program for the same total time.
The study lasted four weeks.
Students took tests on solving new algebra problems.
What they found
The cumulative group solved more problems correctly.
They also finished the tests faster.
The simple-review and extra-practice groups did not improve as much.
Old skills stayed strong in the cumulative group.
New skills transferred better too.
How this fits with other research
Berrett et al. (2018) saw similar gains with multiplication facts using Timez Attack drills.
Both studies show computer-based drills can boost fluency, but Doughty et al. (2002) adds the twist of mixing old and new skills.
Doughty et al. (2015) taught touch-typing to college students and also saw lasting gains.
That study used daily practice, while this one shows you can get the same lift with fewer sessions if you use cumulative review.
Burgess et al. (1971) used playroom rewards to speed up first-grade writing.
The age gap is huge, yet both papers prove ABA tactics lift academic performance in school settings.
Why it matters
You can add cumulative review to any lesson tomorrow.
Just mix three old problems with every new one on the worksheet or tablet.
This small tweak costs no extra time yet lifts both accuracy and speed.
Try it during math, typing, or even daily living-skills drills.
What Cumulative Practice Is
Cumulative practice mixes review of earlier-learned component skills with practice of the newest skill, rather than drilling one skill in isolation. In math this is why the subject feels cumulative: later skills depend on fluency with earlier ones.
It contrasts with massed review (repeating only the just-taught skill) and simple single-rule review. Cumulative review distributes and interleaves practice across all previously mastered components.
Why Cumulative Practice Beats Massed Review
College students learned five algebra rules under identical instruction but different review formats. Those who received cumulative practice, answering questions that mixed all rules learned so far, outscored the massed and extra-practice groups.
The cumulative group did best on application items and on problem-solving items requiring novel rule combinations, and they solved those problems faster. For teaching, interleave old targets into review to build genuine problem solving.
Get CEUs on This Topic — Free
The ABA Clubhouse has 60+ on-demand CEUs including ethics, supervision, and clinical topics like this one. Plus a new live CEU every Wednesday.
Add three previously mastered problems to every new worksheet or tablet session today.
02At a glance
03Original abstract
This study compared three different methods of teaching five basic algebra rules to college students. All methods used the same procedures to teach the rules and included four 50-question review sessions interspersed among the training of the individual rules. The differences among methods involved the kinds of practice provided during the four review sessions. Participants who received cumulative practice answered 50 questions covering a mix of the rules learned prior to each review session. Participants who received a simple review answered 50 questions on one previously trained rule. Participants who received extra practice answered 50 extra questions on the rule they had just learned. Tests administered after each review included new questions for applying each rule (application items) and problems that required novel combinations of the rules (problem-solving items). On the final test, the cumulative group outscored the other groups on application and problem-solving items. In addition, the cumulative group solved the problem-solving items significantly faster than the other groups. These results suggest that cumulative practice of component skills is an effective method of training problem solving.
Journal of applied behavior analysis, 2002 · doi:10.1901/jaba.2002.35-105