It Sounds Right, Is It?

Disclaimer: My opinions, not necessarily anyone else’s.

It’s common to read or hear “sound bite” statements that seem valid and authoritative. But, we need to ask ourselves if they really are valid.

For example, this statement was recently posted on an online comment board in regard to Salem schools.

“As for the schools I repeat the reason costs should be lower is because enrollments are declining, less students less teachers, that is Math:”

We really should ask ourselves questions like, “Do fewer students really lead to fewer teachers, lower costs and lower taxes?”

The statement has an appealing logic to it. It uses mathematics to support it and math is a science, so it must be correct. Common sense says that if the money we spend on schools is to educate students and we have fewer students … it should cost less money. The problem is that the statement is too simplistic and not necessarily correct. You can do your math correctly, but still get an incorrect answer if you don’t interpret the problem correctly.

Yes, there is a mathematical relationship between the number of students in a school district and the number of teachers needed to educate the students. It is not a direct relationship; it is a complex relationship among several variables. Decreasing enrollments don’t necessarily result in decreasing numbers of teachers, costs or taxes.

Over the past five years (2007 to 2011) enrollments in Salem have declined by nearly 1,100 students and the number of employed teachers has decreased by 32 teachers. If the previous statement were true, costs and taxes should have gone down. Why didn’t they?

First, it is true that a large portion of the school district’s budget is spent on teachers. The school district is a service organization. Its function is to provide education and teachers are, after all, the people who provide the service.  We need the right number of teachers to cost effectively provide that service. Too many teachers and we are not cost effective, too few teachers and we are not cost effective. We waste money either way, but too few teachers is a lot more damaging to our goal, providing education, than the other.

Here’s where the math, though correct, can lead you astray.  If we’re going to use numbers to talk about student-teacher ratios, let’s use the N.H. Department of Education’s (DOE) numbers. These numbers, though mathematically correct, can be misleading. They accurately compare one school district to another because the numbers were calculated the same way for everyone. You can tell which districts have relatively high student-teacher ratios and which have low ratios, but not how many students are really in a typical classroom.

The DOE numbers for districts our size in southeast New Hampshire range from 11.1 to 14.7 students per teacher. The DOE number for Salem is 13.8 students per teacher. If you divide the students enrolled by the teachers employed, the math is correct. But since students are whole people, call it 14 students per teacher.  It would be unusual to find a classroom in Salem with 14 or fewer students in it, except for kindergarten or high school Advanced Placement classes. What we can say is that Salem typically has more students per teacher than school districts around us.

Mathematically, you’d be tempted to say that if we decrease our enrollment by 14 students, we should be able to decrease our teaching staff by one teacher, since our ratio is 14 to one. The math is correct. The assumption is wrong. Here’s why.

The actual class sizes in Salem vary from a low of 12 students to a high of 28 students in the elementary schools, grades 1 through 5. The schools typically have classes in the 18 to 23 student range. There are 6 elementary schools. If elementary enrollments were reduced by 55 students, last year’s decrease, you might be tempted to say, based on DOE numbers we could eliminate four teachers (3.9 actually). The math is correct. The assumption is invalid because the number 14 is not actually the typical class size, but an average. Additionally, the assumption that the groups of 14 students would be in the same grade and in the same school is invalid.

If the assumptions are invalid, you may not be able reduce any teachers. If the class size drops only a few students in different grades, in different classrooms spread out over six elementary schools; you will still need a teacher in every classroom. The high school and middle school have the same issue, lots of students in lots of different classes taught by lots of different teachers;  reducing the enrollment by a few students in each classroom doesn’t mean you can reduce a teacher. So in regard to our largest expense, a reduction in enrollment doesn’t necessarily cause a comparable reduction in teachers/costs/taxes.

There are other reasons enrollment reductions don’t necessarily lead to expense reductions. A significant part of what we need to spend money on isn’t connected to student enrollments. The buildings, all eight of them, cost the same to heat and light regardless of the number of students in them. The cost of insurance, snow removal, and building maintenance don’t directly reduce based on enrollments. School buses follow the same relation as teachers; you need a bus whether there are 60 students on it or 50 students on it.

Enrollments in the district dropped substantially with the departure of Windham students from the high school. Salem voters made that decision years ago, knowing taxes would increase when the Windham students left. The tuition Salem received from Windham exceeded the cost for Salem to educate Windham students. The enrollments dropped, but so did the revenue we received from Windham. As the enrollments declined so did the subsidy and the difference was added to the Salem taxpayer’s tax bills. Costs might have gone down, but our share of the costs increased.

Our state legislature has lowered state expenses and state taxes. Unfortunately, they’ve done that by shifting some costs to the local communities. Enrollments may have gone down, costs might have gone down, but the local taxpayer is now paying costs that used to be paid for by the state, so our costs increased.

Has the cost of running your home gone up? Have the costs of insurance, heating fuel, gasoline and electricity increased for you? The district buys those things too, so the district’s costs have increased on things that aren’t related to enrollments.

So, when you read or hear a statement like, “As for the schools I repeat the reason costs should be lower is because enrollments are declining, less students less teachers, that is Math:”  don’t just accept it; question it, think about it and try to decide just how accurate and valid the statement is. It might be valid, it might not. You decide.

Send comments or questions to pmorgan@sau57.org .