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In nearly every public school district in the U.S., one can observe the following pattern: There are fewer middle schools than elementary schools. And there are fewer high schools than middle schools. (And the count of students per school goes inversely as the count of schools.)

But why is this the case? Is there any explanation for this based on economic principles?

For example, why is the reverse not the case? Why are there not fewer elementary schools than high schools, let's say?

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    $\begingroup$ The pattern seems to be one of school districts being willing to make older children travel further. There is also greater subject specialism among high school teachers, which brings more benefits from larger (and so fewer) high schools that you might not see with the more general teaching in elementary schools. $\endgroup$ – Henry Oct 3 '16 at 16:51
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    $\begingroup$ A very interesting Q, but it'd be great if you could back it up with stats. In particular, students for each grade level. For example, one thing I'm thinking is: If elementary schools (usually) span 6 years, middle schools (usually) span 4 years, and high schools (usually) span 2 years, then we'd immediately have (at least part of) the explanation for why # elementary > # middle > # high. $\endgroup$ – user18 Oct 4 '16 at 2:36
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Two relevant economic principles are:

Economies of scale: These are a more significant issue for middle and especially high schools which have a greater need for specialist teachers, as others have pointed out, and also for specialist facilities such as science labs with supporting technicians. Such teachers and facilities would tend to be under-utilised in small schools, resulting in higher costs of provision per child. Elementary schools, on the other hand, rely more on generalist teachers so can operate efficiently on a smaller scale.

Based on a survey of literature on scale economies in education, Andrews, Duncombe & Yinger (2002) found “some evidence” that the optimal size of elementary schools was 300-500 pupils while that of high schools was 600-900 students. The reason for identifying an optimal size (rather than concluding that larger is always better) was that large schools can also have disadvantages, such as more bureaucracy leading to lower student and staff motivation and less parental involvement. Note that these optimal ranges were based on studies focusing on the US: different ranges might be optimal elsewhere given different school curricula and different staff salary levels.

Travel costs: Older children are more likely to make their own way to school, while younger children are more likely to be accompanied by a parent. Hence the costs of travel to school, for a given journey, and including not only fares and/or fuel costs (if any) but also and especially the opportunity cost of a parent's time, tend to be greater for younger children.

More formally, family behaviour can usefully be considered within the framework of a household production model in which households derive utility $U$ from commodities $Z_i$ which they “produce” using inputs consisting of market goods $x_i$ and/or time periods $T_i$. Becker (1965) writes this as (p 495):

$$U = U(Z_1,…,Z_m) ≡ U(f_1,…,f_m) ≡ U(x_1,…,x_m; T_1,…,T_m)$$

The $f_i$ are the “production” functions, although the term production is used here in a somewhat specialised sense: Becker gives the example of the commodity sleep being “produced” via input of a home, a bed and time. Households aim to maximise utility subject to constraints on both income and time (albeit there may be scope to trade off income against time by adjusting hours spent in paid work). Within this framework a child’s education can be regarded as a commodity produced using time spent in school, doing homework and travelling to and from school, and perhaps market goods (school fees if applicable, fares or fuel costs if required for travel). A longer journey to school will imply a greater input of time, with a consequent lesser availability of time for other commodities and therefore less overall utility. Crucially, this effect will tend to be larger for younger children who are more likely to be accompanied by a parent, whose time should also be counted as an input. Moreover in some cases a parent’s time on a twice-daily school trip will reduce their hours of availability for paid work, again resulting in lower overall family utility. Hence families, seeking to maximise their utility, will have a strong incentive to try to ensure (via voting or campaigning) that public schools for younger children are small and numerous so that travel times to school are generally short, and less incentive to do so for schools for older children.

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Interesting question..... I attended public schools at all three levels and they were less than a mile from where I lived --- the elementary school and the high school were less than half a mile away, and probably also the junior high school (as 7th through 9th grades were called). The most conspicuous difference between the way things were done in elementary school and the ways things were done in those later schools is that in the latter, we went to five or six classrooms during the day whereas in the former we remained in one classroom, except for physical education. To me, that latter difference suggests a possible reason why there are fewer: You need teachers specializing in teaching English, some specializing in teaching science, some specializing in social studies, some in math, some in industrial arts, etc. Say three math teachers are employed in a junior high school: if you split it into six junior high schools you'd need a larger number of teachers. But if six elementary schools are merged into one, you'd still have the same number of teachers.

However, I'd have to say I haven't studied the problem, so I reserve the right to alter this view if I learn more.

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Government policy.

This video explains the Federal Government's (FHA) rules for making loans to developers during the Great Depression gave preference to things called "neighborhood units." Neighborhood units had to center their design around an elementary school.

So developers followed suit and designed their neighborhoods according to the FHA guidelines.

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    $\begingroup$ This is really interesting, but why don't high schools also correspond to "neighborhood units"? $\endgroup$ – Giskard Feb 8 '20 at 11:49
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I think that there are a number of reasons why elementary schools are much smaller than high schools.

Young children tend to cope better in smaller groups. In addition, teachers can only manage only so many at a time.

For the most part, elementary school teachers teach a variety of subjects other than an art, music and phys ed teacher, etc. They don't have teachers for each subject. This enables elementary schools to be smaller so towns can afford to build them closer to where the children live.

Middle schools have more specialization and this increases greatly in high school (clubs, competitive sports, bands, science and computer labs, etc.). The school population has to be larger to support such activities. With larger population, the curriculum is greatly expanded and there is a greater need for teachers in specific subjects (English, math, science teachers, vocational programs, etc.). It an economy of scale.

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You have asked the kind of question I can only imagine would very likely be interesting, as well as, thought provoking for many people.

I think there is a simple answer to your question as to why there are more elementary schools than they are Middle and High Schools. I believe the answer also applies to the idea that there are less middle schools than there are high schools.

In my opinion, the reason this is so is because it is based upon the student's education level. A Kindergartener will require more attention from the teacher as well as the teacher's assistant (hereinafter: TA).

In elementary school we have brand new students. They don't really know how to think for themselves. They have no general education knowledge like the Middle and High school students. The older kids have begun to get a feel for what it means to not need near as much One on One interactions between student and Teacher/TA.

Elementary students are for Ripe for having their heads filled with information. I remember when I went to grade school back in the early 1970's we didn't have a teacher's aid until high school. If my memory serves me well, I recall the majority of the assistants at the school were in fact students at the school. Very few Assistants during those years were actually adults like you'll see more of in Elementary School.

So, I assert the need for more one-on-one interaction between the elementary student and the teacher/TA is in my opinion the most likely reason why there are statistically more public elementary schools than their are either Middle or High School's. The same would apply to there being more middle schools than there are High Schools. Middle school children are still in the "latter-early or middle development in their educations so they will require more one-on-one time with the Teacher/TA than will the High School students, as a general rule.

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  • $\begingroup$ Can you clarify how more schools creates more one-on-one time with the teacher? In my area the class size is roughly the same for all types of grade schools, even though there are more separate buildings for elementary schools. $\endgroup$ – user3067860 Mar 31 at 16:48

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