Turns out the question of whether collecting and correcting homework produces more learning than simply assigning homework & not looking at it has been asked and answered.
Collect-and-correct wins hands down.
Classroom Instruction that Works: Research-Based Strategies for Increasing Student Achievement by Robert J. Marzano, Debra J. Pickering, & Jane E. Pollock
The average effect size for assigned-but-not-graded-or-commented-upon homework is .28; average effect size for graded homework is .78; average effect size for homework with teacher's comments or feedback is .83.
.83 is a very large effect size:
Effect size = (mean of experimental group - mean of control group)/standard deviation Generally, the larger the effect size, the greater is the impact of an intervention. Jacob Cohen has written the most on this topic. In his well-known book he suggested, a little ambiguously, that a correlation of 0.5 is large, 0.3 is moderate, and 0.1 is small (Cohen, 1988). The usual interpretation of this statement is that anything greater than 0.5 is large, 0.5-0.3 is moderate, 0.3-0.1 is small, and anything smaller than 0.1 is trivial. There is a good site that describes all this that is worth a visit for those really interested.
And, from Robert Coe, of The CEM Center:
Interpreting Effect Sizes
Provided our data have the kind of distribution shown in Figure 1 (a ‘Normal’ distribution), we can readily interpret Effect Sizes in terms of the amount of overlap between the two groups.
For example, an effect size of 0.8 means that the score of the average person in the experimental group exceeds the scores of 79% of the control group. If the two groups had been classes of 25, the average person in the ‘afternoon’ group (ie the one who would have been ranked 13th in the group) would have scored about the same as the 6th highest person in the ‘morning’ group. Visualising these two individuals can give quite a graphic interpretation of the difference between the two effects.[snip]
Another way to interpret effect sizes is to compare them to the effect sizes of differences that are familiar. For example, an effect size of 0.2 corresponds to the difference between the heights of 15 year old and 16 year old girls in the US. A 0.5 effect size corresponds to the difference between the heights of 14 year old and 18 year old girls. An effect size of 0.8 equates to the difference between the heights of 13 year old and 18 year old girls.
What is an effect size? A brief introduction
As far as I can tell, collecting and correcting (which would cost nothing to implement in a school district not collecting and correcting) is a far more powerful force for student achievement than small class size (which costs a bundle) or SMART Boards ($4000 a pop).
So --- bonne idée!
Class Size: Counting Students Can Help (pdf file)
Robert Marzano's book, which is published by the ASCD, is extremely well-known in the field of education.
HyperStat: Measuring Effect Size
The Effective Use of Effect Size Indices in Institutional Research by Christi Carson (pdf file)
Food for Thought by Howard S. Bloom (pdf file)
Statistical Power Analysis for the Behavioral Science by Jacob Cohen
What is an effect size? by Robert Coe
The Homework on Homework, Part One