Tuesday, October 18, 2005

Bigger Classes Are Better

If you talk to any politician and many educrats, they will scoff at the statement made in the title of this post. But there are several different advantages to bigger class sizes relating to teacher quality and teacher pay that often get overlooked in the political posturing known as educational policy. Smaller classes require more teachers, which drives down both the quality of teachers as a whole as well as their pay. The only people who benefit from more teachers are politicians who can claim they have done something for education and teachers unions who get more members. Larger classes, with high quality teachers, actually benefits both the children and the teachers.

Bigger Classes--Better Teacher Quality
The larger the class size, the fewer teachers that need to be hired. A fairly obvious statement. Concurrently with the idea of fewer teachers needing to be hired is that, in a perfect model, a school system can hire more teachers with a desired level of quality.

The definition of teacher quality is irrelevant in this model. No matter how a community defines a quality teacher, usually an amalgamation of education, experience, professionalism, and personal attributes, quality can be placed on a bell curve ranging from 1 (the poorest quality) to 100 (the highest quality). The peak of the curve would be about 75. Assuming you have a large enough population of potential teachers, all teachers would fall onto that curve.

If you must populate your school districts teacher population from people on that curve, you obviously seek to attract the highest quality--those at the upper end of the curve. However, the number of high quality teachers, defined as those with a quality score of 85 or better is finite and usually will not suffice to adequate man you schools. Thus, the more teachers you need, the lower the quality score you have to accept as teachers.

If your desired quality score for teachers is 80, there are far more potential teachers with a quality score below 80. If you have a school district of 10,000 students and a desired student teacher ration of 20:1, you have to fill 500 teacher positions. If your potential teacher pool is 1500, statistically, only 150 teachers would have a quality score of 90 or better and another 200 with a quality score of 80-90. You can then hire 350 teachers of desired quality, but still have to hire 150 teachers with less than desired quality. However, if you find that a desired student teacher ration is 25:1, then you have to hire 400 teachers of which only 50 are of less then desired quality. Finally, if you think 30:1 is a workable ratio, you need only hire 334 teachers--which means that all teachers are of the desired quality.

Of course, the argument for smaller class sizes is that students are able to get more individual attention, but if the individual attention is of lesser quality, are we really helping our students? Take this hypothetical: Teacher A (quality score of 75) and Teacher B(quality score of 90) each teach a 60 minute class of with the exact same lesson plan of 30 minutes of lecture and demonstration followed by 30 minutes of equally divided individual attention to students. Teacher A's class has 15 students and Teacher B, 30 students. In a strictly mathematical sense, using Class Learning Points (CLP)=Time(T) times Quality Score (Q) divided by class size (N) Teacher A would achieve more quality points (150) than teacher B (90). However, teacher quality includes a multiplier for the additional amount of useful information imparted by the teacher (U). The scale for useful information runs from 0 to 2, with 1 being average the amount of useful information imparted by an average teacher. Thus Teacher A (average at quality score of 75) has a U score of 1 and Teacher B a U score of 1.6. (1.6 is derived by Teacher B being 60% closer to high end of the scale than Teacher A based on quality score.)

Thus, if you alter the formula to be CLP=TQU/N, teacher A still have 150 learning points and teacher B has 144. Still teacher A has more learning points, but the marginal difference is much smaller, particularly when considering Teacher B is able to achieve nearly the same result with double the class size.

The next part of the lesson calls for individual attention. Obviously Teacher A can spend twice as much time with his students than Teacher A can with her students. But again quality and the useful information multiplier changes things. If each individual student learning points is represented by the formula SLP=Time (T) x teacher quality points (Q) x useful information multiplier (U). If teacher A spends 2 minutes with each student, the SLP is 150 for each student. Teacher B, if she spend 1 minutes with each student has an SLP for each student of 144, again not a significant difference considering teacher B has spent only one minute with a child.

By the way, if you reduce teacher B's class to 28, all differences between Teacher A and Teacher B are reduced. Re-compute all the stats above and you will see the difference.

Bigger Classes Means Bigger Paychecks for Teachers
Most school funding is based on a formula of state, local and federal monies calculated on a per student basis. The national average is about $7,500 per pupil in total expenditures. Nationwide, at 56 percent of that per pupil expenditure on is spent on teacher salaries and compensation, which for simplicity sake I will combine into one figure. Using these we can compute an average salary level.

In our hypothetical 10,000 student school district, our school budget is $75 million. Of that $75,000,000, 56 percent is $42,000,000 to be spent on teacher compensation. If we took our student teacher ration of 15:1, we need 667 teachers, whose average compensation in our $42,000,000 budget would be $63,968 in salary and benefits. By contrast, if we have a 30:1 student teacher ratio, we need 334 teachers, whose salary and benefits package would be $125,748 or nearly double the amount. Assuming a $20,000 benefits package cost, including insurances, vacation and other benefits (not an unreasonable number), bigger class sizes would mean that teachers would, on average, make a six figure income!! Even increasing the benefits package would yield a high five digit income--on par with what they should be making.

In addition to higher pay, you have higher quality teachers and would be attracting higher quality individuals.

Is the above model a little simplistic and based on irrational perfection. Perhaps, but the basic argument is the same. Smaller class sizes reduces the average quality of educators, no matter how quality is defined because there is a finite number of high quality teachers in any pool. With smaller class sizes comes the need for more teachers, which means lowering the minimum level of quality. As demonstrated above a teacher of above average quality, teaching more students can achieve the same level of learning as a teacher of lower quality teaching fewer students. If we desire high quality teachers, why not have them teach more students.

But it is the pay differential where we see the real benefits. The difference between a 15:1 student teacher ration and a 30:1 means half as many teachers, which effectively doubles their salary, assuming no other spending changes. Higher salaries attracts better teacher candidates which in turn increases student learning. Until we break out of the political groupthink that smaller is always better in schools, we will never see the kinds of achievement we expect.

Snacking at Jo's Cafe
Now Stuck in the OTB Traffic Jam

1 comment:

Crista Renouard said...

Somehow, I don't think the money saved by fewer teacher would end up with the leftover teachers... it would probably be put to tax cuts. This means that the really talented teachers would ultimate teach in the private market, not in public schools. Or am I just being negative?