FAIRER STATE SCHOOL AID FORMULA FOR IOWA K-12 SCHOOLS
Website www.iowalive.net/fairerschoolaidfunding.htm introduced learning curves to school aid funding on 2-14-13 and gives a very practical approach to applying learning curve theory and economies of scale to public schools, discussed herein. It should be viewed before proceeding. Economies of scale definition: a proportionate saving in costs gained by an increased level of production.
The existing State school aid formula gives no consideration for larger schools achieving economies of scale. This results in unfairness for smaller school districts and lower operating efficiency (34%) in the 8 larger districts. Iowa’s smaller school district’s average operating efficiency is about 42% for comparison—which means Iowans get a better return on their investment in the smaller schools.
The discussion and recommendations below result in improved fairness in the school aid formula and the opportunity to re-prioritize and reallocate monies made available by this improved fairness—to substantially improve student achievement, school operating efficiencies and Iowa’s economic climate as well. Any funding approved for an experimental pilot preschool program--should come from this source. Economies of scale involve the use of learning curve theory and learning curves—which should be used to improve the school aid formula. Mathematicians and statisticians should be advised that the learning curves shown below are simplified straight line learning curves--to facilitate adaptation to school use. Since the quantities start at 500, this is a reasonable approach. An exponential learning curve can be applied on down the line—as refinements are justified.
A learning curve is an analytical way of describing something everybody knows—the time needed to do a job goes down with experience. The formula and school curve in the following chart applies learning curve theory to Iowa public schools and makes good sense because schools are indeed institutions of learning—and as such, should learn most readily from experience. The proposed school curve in the chart shows very, very little learning is achieved (only 6.6%)—from 500 to 30,000 students taught, but it is at least a start in the right direction. The 85% learning curve routinely used for moderately complex jobs in industry, is shown in the chart for comparison only. Steeper learning curves, 80% and lower, are used for more complex jobs.
PERCENT OF INCREASED FUNDING RECEIVED PER STUDENT = Y = B + M*X WHERE B = 100.013197 & M = -0.00021935394 X = TOTAL ENROLLMENT (Y RANGES FROM 100% FOR 500 STUDENTS OR LESS TO 93.4% FOR 30,000 STUDENTS IN THE SCHOOL CURVE)*
By comparison, industry commonly uses the 85% learning curve in the chart, which would reduce the 30,000 quantity percentage above from 93.4% (for schools) to about 34%.—which represents 66% learning This shows the above school learning curve is very, very generous to the larger Iowa school districts. The industry learning curve is used on jobs done by people who don’t usually have college educations.
To fairly apply the school learning curve to Iowa K-12 schools, existing funding to the larger school districts should be reduced to the percentages calculated with the formula. For example, use of the formula would give a school having 10,551 students--97.6988% of the existing per-certified student funding.
In addition, it is suggested that future State funding increases be distributed according to the formula shown in the chart. For example schools having 500 students or less would get 100% of the per-certified student funding increase. A school having 10,551 students would get 97.6988% of the per-certified student funding increase. A school having 32,100 students would get 92.97197% of the per-certified student funding increase.
As a further example, if a 2% school funding increase were approved by the legislature—a school district having 500 or fewer students would get the full 2% increase. A district with 10,551 would get .976988 x 2% = 1.95398% increase. While other experts in the field, and perhaps many others, will say this is overly generous to the larger school districts, it is at least a start in the direction of achieving more fairness and at least some economies of scale--in the larger districts.
LEARNING CURVE FACTORS
Some major factors causing economies of scale that apply to schools are as follows.
Larger schools are in powerful position to negotiate better outcomes with parties such as suppliers, labor unions, financial institutions and government. When purchasing raw material, larger schools can obtain better trade discounts by bulk purchasing. They can, if they want to, negotiate lower wages because people are eager to work at larger organizations even at lower wages (not below minimum wage of course). Financial institutions such as banks are more willing to offer loans (bonds) at lower interest rate to well-established schools having large enrollments. Teacher training etc. can be done much more efficiently at larger schools.
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