Sunday, May 20, 2007

Class sizes, logical fallacies, and a solution

In his defense of smaller class sizes, Tim Eby offers the perfect example of a counterfactual argument - or, fallacy in this case.
As the student population of the OLSD grows, the growth in the special needs and at risk student population will most likely grow at an even higher rate. Given the likelihood of this then it's within those areas where increased staffing will help the District continue to provide a high quality education for all of our kids

-- Tim Eby at (bold emphasis mine)
A counterfactual argument is one where the conclusion is true if the antecedent is assumed true. We could easily switch terms, assume the opposite, and derive another true statement, though equally invalid:
As the student population of the OLSD grows, the growth in the special needs and at risk student population will most likely grow at a lower rate. Given the likelihood of this then it's within those areas where decreased staffing will help the District continue to provide a high quality education for all of our kids.

-- The counterfactual reply
Anyway, back to class size.

For fun, I'll commit a logical fallacy: the ad hominem. Eby quotes a passage from an Economic Policy Institute (EPI) report as if EPI is an unbiased observer to the Krueger/Hanushek debate on class size reduction. What Eby fails to mention is that the EPI board is comprised of representatives of the nation's largest unions; including, as expected, Edward J. McElroy, President, American Federation of Teachers.

Of course, that alone does not invalidate the research of EPI. Nevertheless, one should be a little suspicious of conclusions drawn in a debate that is near and dear to the hearts of EPI board members.

Eby states that I supported my "own opinion on the issue of class size by using the controversial research of Dr. Eric Hanushek to back up (my) theory." Note the term controversial. Controversial is a loaded word. It can apply to that which has been challenged as easily as to that which is totally off-the-wall; think the University of Colorado at Boulder's Ward Churchill. Yes, Hanushek has been challenged, but by whom?

To refute Hanushek, Eby cites Alan B. Krueger of Princeton, best known for claiming that increases of the minimum wage in New Jersey and Pennsylvania resulted in increased employment. Talk about controversial, and maybe just a little off-the-wall. Oh, that darn ad hominem once again.

All of which still leaves Dr. Sanders unquestioned. Hmmm...

Keeping it simple: Seven hundred years ago, the English logician, William of Ockham, noted that, "Entities should not be multiplied beyond necessity." In other words; keep it simple. In that vein, the simple review of class size reduction is to note the dramatic reduction in class sizes during the last 35 years, reductions not met with improved academic performance based on the National Assessment of Educational Progress (NAEP) - the nation's report card.

Where class size reduction matters: Yes, both Hanushek and Sanders have noted that reducing class size can improve performance, but only under certian circumstances.

First, the definition of classroom disruption: Disruption occurs anytime the flow of instruction stops. This can be the result of behavioral issues, poor classroom management, or by a student asking a question to which all the other students already know the answer.

Hanushek and Sanders noted that disruptions due to heterogeneous classes (classes with students of all abilities) cause reduced learning in the aggregate: the questions of the slow learners reduce the achievement of all other students.

The solution: Simply reducing class sizes, while keeping heterogeneous classes, is not a solution to improving performance. Homogeneous groupings (classes of students grouped by ability), where extra intervention is provided to the classrooms with the struggling learners, provides benefits for all students. And, the extra intervention for the struggling learners can be offset by increased class sizes for the remainder.

So, you get reduced class sizes where it matters, without breaking the banks of the taxpayers. Simply reducing class sizes across the board only provides extra income for EPI board members … oops, the ad hominem again.


Anonymous said...

I remember homogenius grouping in all of my classes beginning in elementary school and continuing ad infinitum. It was a more effective way to learn than the p.c. heterogenous model we currently follow. Nowadays we try to make everyone feel good, but our achievement is poor. What is your suggestion to turn this tide? Specifically, how should the school explain to parents of children with special needs that we're going back to the Bluebirds and Redbirds in reading? A majority of that group viciously cling to the concept of least restrictive environment. VICIOUSLY. Is there another interpretation to least restrictive environment?

Anonymous said...

"Advanced Placement" and "Enrichment" curricula have become the escape hatch for the gifted from the heterogenous classroom; but the middle band of the bell curve--the average performers, which is the largest denomination of students--continues to be disserviced.

John Shacter said...

The class size argument is even more off-base than the dispute between the quoted "experts" might lead us to believe.

It is a plain but rather suppressed (by teachers unions, education professors..) fact that Tennessee's massive Project STAR experiment showed that a 1/3 reduction in class size resulted in greater student gains, ONLY IN GRADES K & 1!
Believe it or not -- in grades 2 & 3, the LARGER classes showed up with greater gains -- but not enough to totally wipe out the prior results.

U.S. class sizes have always been among the smallest in the world. However, since that sweeping misrepresentation of the Project STAR results in 1990, we have further reduced our class sizes, spending BILLIONS to do so. The results?
Further deterioration of our students' achievements.

For more accurate presentation of the results, do not read the Project STAR report. (The data in the back of the original report conflicted directly with the conclusions of the Executive Summary of that same report!) Read instead the conclusions in Vanderbilt's special Peabody Quarterly by one of the senior advisors of Project STAR, prof.-emer. John Folger of Vanderbilt. He concluded, properly, that Project STAR results demonstrated that smaller classes did NOT pay off except in highly special situations, with special-needs students.

So what did we do in this great country? We wasted billions of dollars for still smaller classes and achieved no greater student achievements as a result. So much for "educational research."