kitchen table math, the sequel: collect and correct

## Wednesday, March 26, 2008

### collect and correct

The terrific Huffenglish blog, which I think Liz Ditz may have introduced me to, pointed me to research on homework.

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.

source:
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.
source:
Bandolier

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.

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!

source:
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
Evidence-Based Education
What is an effect size? by Robert Coe

The Homework on Homework, Part One

Independent George said...

I read the article on class size, but I'm skeptical. I'm not disputing the results, but they left out one detail which I think is important: ability grouping.

I suspect the effect of class size is likely to be much greater in a mixed ability-class (since the teacher essentially has to tailor the lesson for each individual student based on ability level). In a class where students have roughly the same ability levels, I would expect the effects of class size would likely be reduced. This completely changes the cost-benefit analysis of class-size reductions, since ability-grouping doesn't require additional staffing.

Lsquared said...

"collecting and correcting (which would cost nothing to implement in a school district not collecting and correcting)"

I agree that it would be better than smart boards, but I think it does/ought to cost something. That sounds like at least an extra 2 hours of prep time for your average math teacher (maybe 1 hour if you are increasing prep time by reducing number of classes, while keeping the same number of students per class). I teach 2 classes that I collect and spot check homework for, and it takes me an hour a day for that. A bare minimum is 1/2 hour per class per day.

Anonymous said...

"As far as I can tell, collecting and correcting (which would cost nothing to implement in a school district not collecting and correcting)..."

This reminds me of a story about Tom West, a program manager at Data General in the 1970s and 1980s. Some of his engineers had requested a logic analyzer to help in debugging a hardware problem on a machine they were building. He denied the request.

“An analyzer costs ten thousand dollars. Overtime for engineers is free,” he was supposed to have said.

Collecting and correcting homework when one isn't already doing so "costs nothing" in the same sense as Tom's refusal to purchase a logic analyzer. There *is* no monetary cost, but that doesn't mean that it is free. Either:

(1)the teachers *don't* do something that they were already doing (prepping for class?), or
(2)the teachers work unpaid overtime.

Both "cost nothing" to the school, but they aren't free.

[NOTE: In theory, the teachers could 'be more efficient.' But this can always be suggested for *any* change that requires more time from the teachers. Taken to its limit, the teachers could achieve everything they are currently doing in no time at all! I think we should restrict ourselves to the two choices above.]

-Mark Roulo

Catherine Johnson said...

I agree that it would be better than smart boards, but I think it does/ought to cost something.

I was thinking about my own district, where experienced teachers are paid 100K.

When we visited private schools all teachers either collected and corrected or gave daily quizzes, which they corrected, and all of those teachers were paid less than teachers in affluent suburban schools.

Catherine Johnson said...

“An analyzer costs ten thousand dollars. Overtime for engineers is free,” he was supposed to have said.

I love it!

Catherine Johnson said...

Right, of course, "collecting and correcting" isn't free.

However, from my perspective, it should be included in the instruction the community is already paying for.

Thus if the administration were to persuade teachers to begin performing this core function of teaching instead of leaving it to parents and tutors it would be "free" in the sense that taxpayers wouldn't be asked to increase pay for the school to collect and correct.

Catherine Johnson said...

Speaking of free, I finished Homework #94 this afternoon. Spent at least 20 hours over "vacation" working on quadratic equations & making worksheets for C. to review.

I've corrected every single one of C's homework assignments this year & had him re-do the problems he missed.

The district probably sees this as free labor but....there's no free lunch.

Catherine Johnson said...

IG - I think you're probably right about the effects of class size reduction versus homogeneous grouping.

Dana Huff said...

I thought you all might be interested in a second post: The Homework on Homework: Part Two. Thanks for the kind words!

Liz Ditz said...

And it is also a blog post (with more links) at Kitchen Table Math