Are we wasting our children's time by giving them more homework?

25,794 student-by-teacher pairs covering 12,897 eighth graders in NELS:88

US public school eighth graders, each observed in two sampled subjects with teachers who taught multiple classes

Economics of Education Review 30(5), 950-961; full text read from IZA discussion paper 5547 (March 2011). WITHIN-STUDENT, WITHIN-TEACHER FIRST DIFFERENCES - each student contributes two subjects and each teacher several classes, so the design nets out unobserved student traits AND unobserved teacher traits simultaneously. The other decisive design choice is the measure: homework is HOURS ASSIGNED BY THE TEACHER, not hours the student says he spent, because as the companion paper puts it, 'relying on hours spent on homework from the student reports is not as accurate and may yield spurious correlations because it may reflect unobserved variation in student ability and motivation'. An instrumental-variables check uses the teacher's report of whether the textbook supplies good homework suggestions, interacted with subject fixed effects; the authors concede 'in the absence of multiple instruments, we can not test the second condition', so the exclusion restriction is untestable.

Homework works in mathematics and nowhere else. Per additional weekly hour of ASSIGNED homework, with student and teacher fixed effects: maths +1.290 (SE 0.414); science +0.052 (0.630); English +0.179 (0.442); history +0.331 (0.460). The authors' own summary: 'only math homework has a consistently and statistically meaningful large effect on test scores. An additional hour of homework in science, English and history has little to no impact in our sample and moreover, there is no evidence for spillover effects across similar subjects.' The maths magnitude is real but modest - 'a one standard deviation increase in the amount of weekly assigned math homework is associated with a gain of 1.77 points in math achievement... slightly less than one-fifth of the sample standard deviation... one-fourth of the raw black-white test score gap between the ages of 6 and 13.' TWO WARNINGS BELONG WITH THESE NUMBERS. First, in the specification with student but not teacher fixed effects, more assigned SCIENCE homework significantly LOWERED science scores (-0.235, SE 0.090). Second, the maths coefficient moves from 0.270 to 1.290 - a factor of 4.8 - purely by adding teacher fixed effects, which is not the behaviour of a stable parameter. On nonlinearity: pooled across subjects there are diminishing returns (homework squared -0.103, SE 0.062), but 'there is little evidence for nonlinear effects of assigned homework once we allow for subject-specific returns'.

Low for the student's own traits and this is the point of the design - within-student differencing removes ability, conscientiousness, family and school in one step, and the homework variable is a teacher's decision rather than a child's behaviour, so it does not express the child's genotype at all. What survives is that teachers may assign more homework in subjects where their classes are weak or strong, and the teacher fixed effects address that only within a teacher.

Unreplicated as a design. Its maths-only pattern is echoed by Ozyildirim's TIMSS meta-analysis, where the pooled effect for mathematics is d = 0.358 against d = -0.009 for science, and by Cooper's finding that maths correlations slightly exceed reading. It sits directly against Jerrim and colleagues' precisely estimated zero at primary age using a comparable within-student design - the two are not in conflict if the age gradient is real, since one is grade 8 and the other grade 4.