What matters most here
| Rank | Practice | Grade |
|---|---|---|
| 1 | Fractions on the number line; small-group program for at-risk 4th graders (principle 11) | Evidence grade: Proven in classrooms Proven (Fuchs et al.(opens in a new tab)) |
| 2 | Worked examples paired with practice problems (principle 3) | Evidence grade: Strong Strong (Barbieri et al.(opens in a new tab)) |
| 3 | Mixed practice once each type is learned (principle 8) | Evidence grade: Strong Strong here; a 4th grade experiment found 77% vs 38% a day later (Taylor & Rohrer(opens in a new tab)) |
| 4 | Multiplication facts to automatic by end of grade 3, with daily practice (principles 1, 6) | Evidence grade: Strong Strong in principle; see Twelve Minutes at the Kitchen Table for the home routine |
Why fractions get top billing. Fifth graders' fraction and division knowledge predicted high school algebra, even after accounting for IQ, reading, and family income (Siegler et al.(opens in a new tab)). That's a correlation, but it is why the fraction trials matter so much.
A lesson in this room
Fact sprint. Teacher places 1/4 and 1/3 on a number line, thinking aloud about which is bigger and why. Split-page practice: solved example on the left, twin on the right. Mixed review set with problems from three earlier units.
Leader look-fors
- Number lines in fraction lessons
- A solved example next to new problem types
- Homework that includes earlier units
Stop doing
Teaching fractions only with shaded pizzas. Moving to long division while students still count multiplication facts on fingers.
Where the evidence runs out
The fraction trials were small-group interventions; whole-class versions are less tested.
Principles
Sources
- Fuchs et al. 2017, five fraction trials (opens in a new tab)
files.eric.ed.gov
- Barbieri, Clerjuste & Chawla 2023, meta-analysis of worked examples in math (opens in a new tab)
doi.org
- Taylor & Rohrer 2010 (opens in a new tab)
retrievalpractice.org
- Siegler et al. 2012, early predictors of high school math (opens in a new tab)
ncbi.nlm.nih.gov