The Truth About Apportionment

[I'll add more here when I get some data but I wanted to get this out before the holiday.]

Imagine three married couples went out to eat and split the check the following way:  The husbands split half the bill in proportion to the assessment on their respective houses.  The wives split half the bill in proportion to the number of school children they have.  Then the state gives each couple a different amount of help depending on how poor they are and how many kids they have.  Whatever's left is what each couple has to pay.

It's a crazy way to split the check.  But if you substitute "town" for "couple" and "equalized valuation for the town" for "assessment on a house" and "number of students enrolled from the town" for "number of children" that's how we pay for schools.  That's apportionment in the Oyster River Cooperative School District.  The basic agreement that makes the cooperative work is this apportionment formula to divide up the bill. It's half by town valuation, half by number of students per town, with the state aid then subtracted by town.

Apportionment is a touchy topic, guaranteed to tick everyone off.  Everybody thinks their town is getting shafted by the apportionment agreement.  I'm not going to get into whether it's fair to split the bill this way.  The coop's going to be around for a while and the apportionment formula is unlikely to change so it's occasionally worth learning about. My plan for keeping emotions calm is to make this pretty dry.  Warning: partial derivatives ahead.

The reason to bring this up now is that Business Administrator Caswell calculated that Madbury's local school tax millage will increase 6% if the current budget goes forward (3% operating increase).  The school board is all in a tizzy now about poor Madbury.

I'm going to descend into math soon, but before I do let me summarize the main conclusion.  The upshot of it is that at least part of Madbury's big increase is that they had some sort of audit and lowered their total valuation.  Considered in isolation, this will have the effect of lowering Madbury's local school tax, as half the bill is allocated in proportion to their valuation.

Nonetheless Madbury's millage will increase, since their decreasing amount of taxes is divided by an even faster decreasing total valuation.  But even though their millage is going up, their taxes are going down and the taxes of Lee and Durham have to go up to compensate.  So don't feel sorry for Madbury.  But don't feel that smug either -- I believe since 2010 Lee and Durham have both lowered their assessments as well, though I thought I saw Lee had gone back up again. Madbury's perhaps just a bit late to the party.

OK, the nice stories about dining out are over and we're going to look at the formulas.  You might want to skip to the Results section at the end.

Apportionment Formulas

There's going to be a fair amount of definition and math, but it pays off in the end.  I'm going to try to minimize notation, so it's going to be a bit terse.  You may have to refer back to the definitions to know what the variables are.  In general I'll use small letters for variables for individual towns (so there are three instances of each small variable, one for each town) and caps for variables that refer to the district as a whole.

The apportionment formula is

t = (s+a) B/2 - w

where

t is the tax, the local property tax in dollars to be divided among property owners in a given town

s is the share of students enrolled from the town
    s = <number of students from the town> / <total number of students in the district>
    s_Lee + s_Durham + s_Madbury = 1

I think s is calculated from the October 1 attendance numbers, so you can help your town's taxpayers out by keeping your kids home that day.  That's probably a bad idea. I think previously I recommended you send your sick kid to school that day as state aid is partly determined by the number of students that do show up.

a is the share of (equalized) assessed valuations from the town

   a = <equalized valuation of town> / <total valuation of district>
   a_Lee + a_Durham + a_Madbury = 1

Let's define v and V

v =  <equalized valuation of town>

V = <total valuation of district> = v_Lee + v_Durham + v_Madbury

So a = v/V

B is the budget,
   B = <total appropriations> - <non-state revenue>
   B is the gross amount to apportion among the towns.  The local school property tax collected from owners and the state aid to towns all add up to B.   B is essentially the tax impact in the budget goal.

w is the state aid to the town in dollars (w for town).

The formula t = (s+a) B/2 - w is pretty simple.  Each town's share of B is the percentage p

p = (s+a)/2

That says that each town's share of the total bill is the average of its share of the students and its share of the property value.  The bill is divided before each town's state aid w is subtracted, and the net is the tax t to be divided among town property owners.

You can view s as the capitalist component - each town splits half in proportion to its student share, a lot like paying tuition for those students.  The socialist component is a - the towns splits that half in proportion to its real estate valuation.  Of course within a town the bill in split among property owners in proportion to real estate values, so even s is socialist.

You could imagine the coop funded by a district-wide property tax, with the district as a fully united entity with the budget funded by a property tax proportional to assessed value irregardless of town.  The other option has the district billing the towns in proportion to the students from each town, like tuition.  Our district is a fifty-fifty compromise among these two.  Then the state gets to put its hand on the scales.

Since the total tax t is divided among the total town valuation v, the millage m is

m = t/v

There may be a detail about equalizing the valuations across towns that I'm leaving out here.  Other things I'm not sure about include how the state aid is calculated and why the state tax rate differs between towns.

After apportionment, you can look at the pie two ways, with and without the state.

Let's call f the fraction of the budget B each town's local school property tax really pays.  Then

f = t/B

f_Lee + f_Durham + f_Madbury won't add up to one because the state aid has been subtracted out.  If you set f_state = sum(w)/B, then the four of them would add up to one.  It's a pretty good approximation to think of f as a nine slice pizza pie, with Madbury getting one slice, Lee and the state two slices each, and four for Durham.

Without the state it's a seven slice pie, Madbury, Lee, Durham forming the geometric sequence 1, 2, 4.

Putting our equations together, we can write t, a town's total local school property tax to be collected, a few different ways:

t = mv = fB = (s+a) B/2 - w = (s +v/V) B/2 - w = pB - w

Sensitivity Analysis

The apportionment formulas take as inputs:

 B, the budget to be apportioned
 s, the share of students per town
 v, the total valuation of each town
 w, the state aid to each town

The formulas output:

t, the local school property tax collected and paid by each town
m, the millage rate for dividing t among property owners in the town

What we're interested in here is how the outputs tax and millage change with each of the inputs.  Let's focus on the percentage change in the output for each percentage change in the input.  The share of students s is already a percentage, so for that one we have a percentage of a percentage.  A 1% change means the number of students in a town goes up 1%.   Technically, they're not new students moving into the district but just changes within the district, but that's a detail that doesn't matter much.

At this point most sane people would make a spreadsheet and play with the inputs to see how the outputs change.  That's what I did.   Scroll to the end to see the spreadsheet.

But I also did the somewhat less sane step of treating the whole thing as a physics problem.  What we want to know is how each output changes when you change one input a little bit and hold all the other ones constant.  Let's determine the factors such as %t/%B, which when multiplied by a given percentage change in B tells you the percentage change in t. 

Let Δx be a small raw change in x.  Then the percentage change %x = Δx/x.  For small Δx we can approximate the change in the dependent Δy = (∂y/∂x) Δx.   For ease in typing, from now on I'll write the partial derivative using d as in dy/dx.    I'll also use a space after a fraction to indicate multiplication by the fraction; without the space it's multiplying the denominator.  I'll also indicate x squared as x^2. 

We're interested in sensitivity factors of the form %y/%x, the number you'd multiply the percentage change in x to get the percent change in y, keeping all other inputs constant.  Using the partial derivative we compute:

%y/%x = (Δy/y)/(Δx/x) = x/y Δy/Δx ≈ x/y dy/dx.

Let's start with how the percentage tax increases with each percent increase in the budget B, %t/%B.  

t = pB - w 

dt/dB = p

%t/%B = B/t dt/dB = Bp/t = p/f

This says a one percent change in the budget leads to a p/f percent change in the town tax.   f  is smaller than p because of the state aid, so p/f works out to 1.2 for Durham and 1.4 for Lee and Madbury.  I suppose I should pause here and emphasize that these are significantly larger than one. The more (relative) state aid the town gets, the bigger the magnification.   It's not so bad because it's offset by the state aid.  It's exactly offset (meaning the effective factor is one) by increases in w as far as they go, but only that far.  Once the budget percentage increases beyond the that of state aid, the taxpayers feel the brunt of the full p/f ratio, and that hits harder in the towns with proportionally more aid (Lee and Madbury).

The millage rate changes percentage-wise by the same p/f factor.  To see this, write

m = t/v = (p/v)B - w/v

dm/dB = p/v

%m/%B =B/m dm/dB = Bp/mv = p/f

The last part comes from t=mv=fB.

There's no difference between the sensitivity factors (sometimes called "loads") on total tax and millage for all of the input except v.  This is because when the valuations stay constant, all the changes in the tax paid are reflected in the millage.  Since changing v changes the tax base, the millage and tax factors change differently when changing v.

As the issue at hand is Madbury lowering its valuation, let's do %t/%v and %m/%v (the hard case).

t = (s + v/V) B/2 - w

Useful math facts:       d(v/(v+k))/dv = k/(v+k)^2                   d(1/(v+k))/dv = -1/(v+k)^2

Big V is the sum of the v we're interested in and the other two town's v's. Let k = V-v the sum of the total valuation of the other two towns, treated as constant in this partial derivative.

dt/dv = B/2 (V-v) /V^2

%t/%v = v/t dt/dv = v/t B/2 (V-v)/V^2 = vB/2tV (1-v/V) = a(1-a)/2f

The load a(1-a)/2f  gives the percentage tax increase for each percent change in v.  It ranges from .3 in Durham to almost .6 in Madbury.  It's positive, which means by lowering v a town reduces its taxes t.

It's an odd-looking factor. a(1-a) is the fraction of the valuation from the given town times the fraction of the valuation of the other two towns combined. It's maximized when a=1/2, which Durham comes pretty close to. But the f in the denominator is the fraction of the budget the town pays, which is also maximum for Durham. The f wins out, so Durham's factor is smaller than Lee's and Madbury's.


Now let's look at the most difficult case, how the millage changes with valuation.

m = t/v = [(s + v/V) B/2 - w]/v = (sB/2 - w)/v + B/2V

dm/dv = (w - sB/2)/v^2 - B/2V^2

Here we're looking at a percentage change in a millage which is already a kind of percentage, but that seems to be how people look at it.  It usually makes sense as the millage is proportional to your property tax when the assessments stay constant.

%m/%v = v/m dm/dv = v/m [  (w - sB/2)/v^2 - B/2V^2 ]
             =  w/mv - sB/2mv - vB/2mV^2 
             = w/t - sB/2t - vB/2mV^2

Each one percent change in a town's valuation changes the millage by the complicated factor above. Let's meditate on the terms a bit.

The first term w/t is the relative contribution of the state compared to the local taxpayers for a town's portion of the local school tax.  It's around .4 for Madbury and Lee and .2 for Durham. The more the state kicks in, relatively speaking, the more a town benefits by lowering its valuation.

The next term, -sB/2t is the ratio of sB/2, the amount the town pays because of its student share, and t, the town tax after state aid.  You'd expect the student share to be more than half of t but less than all of t, and indeed this part comes in at -.5 for Durham, -.7 for Madbury and -.8 for Lee.  The negative sign means that the more students the more the millage decreases when assessments go up.

The last term -vB/2mV^2 is pretty wacky.  v/V is a so we have aB/2mV.  aB/2 is the money the town owes due to its share of property value.  That's oddly compared to mV, which is the given town's millage applied to all the property in the district, so is approximately sum(mv)=sum(t)=B-sum(w), the total local property tax collected in the district (the budget less the state aid).  That's adjusted up or down depending on whether the given town's millage is above or below average.  The term comes in with a negative sign, coming in at -.2 for Lee, -.4 for Durham and -.1 for Madbury.

Actually what I should have done is what I did below, eliminate m by substituting t/v.

-vB/2mV^2 = -B/2t v^2/V^2 = -B/2t a^2

which is perhaps slightly more sensible.

Adding it all up, we get the factor of percentage change in millage for each percent change in town valuation as -.6 for Lee, -.7 for Durham and -.4 for Madbury.  The negative sign means for 10 percent off their valuation, Madbury increases its millage by 4% even while (as we learned above) decreasing its local school property tax by 6%.

I noticed doing the table that the difference of the two loads, %t/%v - %m/%v, is always one.  (Since one will always be negative if the other is positive, this means the absolute value of the factors sum to one.)  This means that the difference of the percentage changes in tax and millage will be the percentage change in valuation.  For example, a 10% decrease in Madbury's valuation leads to a 6% reduction in tax and a 4% increase in millage.

To prove this, let's start with some intermediate results in the above formulas:

%t/%v - %m/%v = v/t B/2 (V-v)/V^2   -    v/m [  (w - sB/2)/v^2 - B/2V^2 ]

It works out nicely when t is in all the denominators, so let's change v/m = v^2/mv = v^2/t.

%t/%v - %m/%v = Bv(1-v/V)/2tV - (v^2/t [ (w - sB/2)/v^2 - B/2V^2 ] )
                           = (Bv/2V)/t - (Bv^2/2V^2)/t - (w - sB/2)/t + (Bv^2/2V^2)/t
                           = [ (s + v/V) B/2 - w ] / t 
                           = t/t
                           = 1 

This rather surprising fact means all the comments about %t/%v and %m/%v apply to the other, only in reverse.  What we've shown is

a(1-a)/2f - (w/t - sB/2t - vB/2mV^2) = 1

I could have gotten here way more directly, I realize now, if I had only written t for the numerator when taking the derivative:

m = t/v = [ (s + v/V) B/2 - w ] / v

dm/dv = v^-2 [ vB/2 (V-v)/V^2 - t ]

%m/%v = v/m dm/dv = v/m v^-2 [ vB/2 (V-v)/V^2 - t ]
              = 1/mv [ ... ] = 1/t [ vB/2 (V-v)/V^2 - t ]
              = vB/2t (1/V - v/V^2 ) - 1
              = 1/2f (v/V - v^2/V^2) - 1
              = 1/2f (a - a^2) - 1
              = a(1-a)/2f - 1

Finishing up the other inputs, let's next do %t/%s, how taxes (and millage) change with student share. As s is already a percentage, %s is a percentage change in percentage.  This is confusing but you can think of %s=.01 as meaning the town (approximately) increases its student enrollment by 1%.  In Madbury this means its share of students s would change from 15.51% to 15.67%.   %s is probably mostly from the difference in towns between incoming K and first graders and outgoing twelfth graders, with shocks and perhaps trends according to whichever town is deemed more desirable to families with school children moving in.

t = (s+a) B/2 - w 

dt/ds = B/2 

%t/%s = s/t dt/ds =  sB/2t = s/2f 

This says for a one percent change in the town's enrollment you increase local tax by sB/2t = s/2f percent.  That term already appeared above with a negative sign in %m(%v).  It's the town's share of the enrollment tab, and that gets compared to t, the local tax from the town.  It's also s/2, the percentage of the budget the town pays for students, divided by f, the fraction of the budget the town pays in local property tax.  The load works out to .8 Lee, .6 Durham, .7 Madbury.

One left: %t/%w

t = pB - w

dt/dw = -1

%t/%w = w/t dt/dw = -w/t 

Here we get the factor w/t we've seen before, this time with a negative sign.  Recall w/t is the relative size of the state's contribution to the local taxpayer's contribution to the town's share of the budget.  Here it's -.2 for Durham and about -.4 for Madbury and Lee.  It means if the state raises its support 10% to Madbury or Lee that would cut taxes 4% in the happy town, but a 10% raise to Durham only cuts taxes 2% there.  (It's symmetrical -- state cuts are felt more deeply in Lee and Madbury than in Durham as well.)

Results

I'll repeat the variables in case you wisely skipped to here.  The apportionment formulas take as inputs:

 B, the budget to be apportioned
 s, the share of students in each town
 v, the total valuation of each town
 w, the state aid to each town

The formulas output:

t, the local school property tax collected and paid by each town
m, the millage rate for dividing t among property owners in the town

Here's a spreadsheet with the actual FY15 numbers.  We're in FY16 now and talking about FY17 budget now for elections in February and March.  I haven't used those numbers since I couldn't find them.  Maybe after Thanksgiving.

Here's the sensitivity table shows how for each one percent change in an input parameter (if all else stays constant) what percent change to expect in the output parameter.  The first three parameters when altered one percent change both the local tax and millage by the same factor as given in the table.  The fourth parameter, percent change in town valuation (%v) has a different effect and opposite effect on the local tax and the millage.   In particular a 10% decrease in Madbury's valuation, all else being equal, lowers Madbury's local school tax 5.7% but raises its millage 4.3%.

Again, the conclusion is a 10% decrease in Madbury's assessment leads to a 5.7% decrease in taxes and a 4.3% increase in millage there.



Let's look at the numbers from the last annual report:

Let's look at all the percentages first, starting with a and s.  Lee has 27% of the real estate in the district but 37% of the students.  Durham has the opposite tilt, and in Madbury it works out to about the same.  It's one reason the millage is higher in Lee -- less real estate to support more students.

The average of s and a make p, the proportion of the gross budget B that each town owes.  But each town gets a different amount of state aid, so in the end the actual fraction of the local property tax t/sum(t) works out much closer to the valuation proportion a.  This makes sense -- the purpose of the state aid is a progressive shift of the tax burden toward the richer towns.  Madbury gets a little more help because it has a lower state education tax, not shown in this post because I'm focusing on the local school property tax.

When you account for the state aid, the budget is divided into a nine slice pizza pie, f.  Madbury buys 1 slice, Lee and the state 2 each, and Durham 4.

The district reports p and a in the annual report so I computed s by working the average backwards rather than by researching the number of students from each town.

Now let's look at v/s, normalized so Lee is 1.  This is the town value per student, a measure of how rich the town is, i.e. how much real estate there is to support each student.  By this metric Lee is the poorest, which is really just to repeat what was said before -- they have 27% percent of the real estate supporting 37% of the students.  By this measure Madbury is 33% richer than Lee and Durham is 74% richer than Lee.

What's missing from this analysis is an understanding of how the valuations, student fraction and state aid varies over time.  That's more research than I can comfortably do on vacation, so stay tuned.

Congratulations Assistant Superintendent Todd Allen

I was at sea, but I still watched Wednesday's eventful school board meeting.  It covered new enrollment forecasts from the Long Range Planning Committee, the draft warrant including another loser field bond and news that the budget leads to a local school tax millage increase of 6% in Madbury.  I want to eventually talk about all of these, but let's start with the big news.

Oyster River High Principal Todd Allen was chosen as Assistant Superintendent.  He takes over for Carolyn Eastman, who recently resigned. Todd Allen has been a great principal at ORHS since he sorta lucked into the job after the bad board inexplicably rejected superstar candidate Justin Campbell in April 2011, leading to a student walkout. Then Oyster River Middle School Principal Allen was promoted, and now four and half years later he gets promoted again. Like many in the community I've known Todd a while now, and I am happy to congratulate him.  I'm sure he's going to do a great job.

Of course, now we have to find an ORHS principal again.  Superintendent Morse said a plan to fill the position will be presented at the next meeting.

Curriculum Development seemed to be most of Carolyn Eastman's job, and she seemed really into it. She'd wax on endlessly at the podium about Star or Atlas or Smarter Balanced or tools for measuring the alignment of the curriculum with Common Core.  I've always found the part of school board related to actual education rather tedious, but I was glad Assistant Superintendent Eastman was into it and would make sure it was right.  I guess we'll find out how Assistant Superintendent Allen sees the role.  I've been to a lot of school board meetings and I don't recall seeing Todd exhibit any particular enthusiasm toward curriculum development.  Maybe it happened while I was dozing.

Allow me to gripe a bit about the hiring process.  I actually knew someone who was applying, so I didn't try to get on the 15 member interview committee that included administration, teacher, staff and parent representatives.  I think most people would agree that it would have obviously been a conflict of interest if I was on the committee.  But surely everyone on that committee knew Todd Allen.  I don't know if he was the only internal candidate, but it's pretty likely that most people on the committee knew Todd and didn't know almost all of the other candidates.   Why is this not the same conflict of interest that I felt?

I guess what irks me is the superintendent wanted to do an inside search only all along.  The board and public pushed back and got a wider search.  But in the end the superintendent seems to have gotten the inside candidate he wanted.  Did I miss the hint on October 7th when he told us how Principals Dennis Harrington and Jay Richard never aspired to superintendency because they love being with their kids, but didn't mention Todd?  

I wish Assistant Superintendent Allen good luck and great success in his new position.

No $400K Insurance Discount Next Year

Premium Holiday Postponed

In more bad budget news, at yesterday's school board meeting Business Administrator Caswell announced there would be no "premium holiday" next school year.  We were expecting a $400,000 discount on health insurance premiums, about 1% off our $41M budget.  Last year we enjoyed a premium holiday of $500K and this year $400K.

The whole premium holiday system is the result of a judge's ruling our insurance provider LGC/Health Trust overcharged customers, including Oyster River and its staff, in the 2000s (NPR).  I recall LGC has to return over $50 million, including maybe $2M to ORCSD.  The plan is to dole it out over a few years.  However, according to Administrator Caswell, Health Trust just announced that their reserves were low and they would not be offering premium holiday payouts next year.

The district has been treating the premium holidays as found money to spend. Last year's $500K was the major funding for Moharimet Cafeteria project. The plan was to use this year's and next year's as $800K toward the new field. However, two weeks ago the news from Health Trust was the maximum guaranteed increase on premiums was 16.8%, which meant we'd have to budget for an additional $800K (2%) in premiums. (The actual increase is not determined until May.)

The premium holiday system creates a kind of slush fund for the district. The district budgets for the full maximum guaranteed premium, conservatively assuming the premium holiday will not appear. Since the payout is in the form of a discount, the district can then spend the money saved on other things and still stay within the total amount appropriated by the voters, which they are legally required to do. If they had to pay the full premium and were handed back a big check for the payout, they couldn't spend it, at least not beyond the voter-approved appropriation.

The administration and school board have been trying to shoehorn the new field into the annual budget. They were counting on the premium holidays continuing and a more modest health insurance increase, so this $1M hole in the budget that appeared over the last two meetings puts the field plan in jeopardy. As I type this the five hour budget meeting is going on, where a new budget (including the administration's recommendation for the field project) will be revealed. [11/6 update: Nope, apparently the field plan is still up in the air.]

Assistant Superintendent Search Progressing

Superintendent Morse reports that the district received two dozen applications for the Assistant Superintendent position.  A screening committee including five administrators whittled it down to 6 candidates to be interviewed.  Interviews are expected to be completed on 11/16 and after a review of references a candidate will be recommended to the board at the 12/2 meeting, two weeks later than originally scheduled.

ORESPA Contract Approved

The board approved the collective bargaining agreement negotiated with the custodians and secretaries union, ORESPA (Oyster River Educational Support Personnel Association).  The negotiated increases in the three year contract are 1.5% for the first year, 2.25% for the second and 2.5% for the third.  It was reported that ORESPA approved the contract as well, so now it goes on the ballot for final approval by the voters in March.

Nation's Report Card Out, Smarter Balanced Results Expected Soon

2015 NEAP
NH vs USA
click to enlarge

On November 12 the district expects the first results from Smarter Balanced, the Common Core assessments administered last spring.  Letters to parents will be sent home shortly after (electronically if they can work out the kinks).  The delay came from the state having to manually process the tests from a half dozen districts that chose the written version, rather than the online version we used.  

On a related note, the 2015 NEAP nationwide assessment reports, often called the nation's report card, are out.  Only 4th and 8th grade math and reading have been updated. NH did great, ranking 3rd for both subjects in 4th grade and 2nd for both in 8th grade out of all 50 states (plus DC and DoD schools).  So we're one of the best districts in one of the best states.   

In these four rankings, Massachusetts bested us 3 times, the DoD schools twice and Minnesota once.  I don't recall seeing the DoD schools in other studies -- if you exclude them we move up a notch twice, in particular to first in the country in 2015 8th grade reading.  The district has already spun some of these ranks as "tied for first." 

I pulled a couple of charts off the site, which I edited by adding the 2015 NH ranks among other things.  New Hampshire followed the national trend of a dropoff in math from 2013, and we had an especially sharp decline in 4th grade math.  In reading 4th grade stayed flat in line with the country, but 8th grade bucked the trend, increasing where the nation declined.  

It was a pretty short meeting, done by 8:20 or so including a 20 minute interval for non-public and non-meetings, so I'm going to wrap this up here.

$800K insurance rise puts field funding in doubt

At tonight's board meeting the superintendent announced that the district's "guaranteed maximum increase" on next year's health insurance premiums was 16.8%.  The guarantee is budget guidance from the insurance provider that the district receives every October.  The actual increase is determined in May (after the election), and sometimes comes in less, sometimes equal, but never exceeds the guarantee.

The 16.8% maximum increase is around $800,000, or 2% of our $41M budget.  The superintendent said he would present a plan that kept within the goal of a 3% operating budget increase at the Nov 5 budget workshop.

You may recall that two weeks ago the plan was to fund the $2.3M athletic field makeover this way: $800,000 from the LGC/Health Trust settlement, the $300,000 track fund, $650,000 from delaying some capital and technology spending and $500,000 new from the taxpayers.  The Health Trust settlement is actually an $800,000 discount for health insurance, $400,000 in the current fiscal year and a presumed $400,000 in the next.   This seems obviously neutralized by the $800,000 increase in the premium next year and so now the field needs another $800,000 to be built.

Actually it's probably less. Presumably the district had some percentage increase for health insurance in mind before this number came in.  I'll guess at least 5% ($240K, 0.6% of our budget), so they only have to come up with around $550,000 more for the field.  The Orchard Drive land sale, which was left out of the last plan, is probably good for at least $300,000, possibly more if Durham grants a variance.  It would require passing a more complicated ballot in March and the land sale actually closing to get the field.

You could then just ask the taxpayers for the remainder, changing the $500,000 (1.25%) new to $750,000 (1.8%).  If the board holds themselves to their recent honesty in budgeting, they would have to then report a 4.8% impact on taxes, which they would phrase as a 3% operating increase and a 1.8% ask for the field.  For that money you get full day K and a new field.

Of course the superintendent and board would probably prefer to do some more budget shuffling to pull another rabbit out of the hat to find the money for the field while keeping to their recently passed goal (4.25%).   Genuine cuts in education so they get their field would be unseemly and I think unlikely.

Though it really didn't come out at the meeting, it seems like the field really won't go ahead if the taxpayers vote no on the one-time money (my issue last time).  This isn't because the board realized their error and found their respect for democracy -- it's more that the staging plan, where the field is built over a couple of years, is impractical as it keeps the fields out of commission for an entire school year.

In other news, I mentioned at public comment that in addition to the field, the board should let the voters weigh in on Full Day K.  They discussed this at the table, with the superintendent's position being that curriculum matters were the purview of the board and do not require an election day vote.  Member Howland said the small increase (which he called around $60,000 annually) didn't rise to the level of a warrant article.  (I think he may be lowballing the impact, but I can't find the number right now.  Back of the envelope: going from 7 half day K to 6 full day K classes is an increase of 2.5 full time equivalents which has to be way more than $60K.)  The superintendent said there would be a half-day option, but indicated there would be no transportation at midday.  This is all subject to change when the committee makes its recommendation in December.

It was a short meeting, so I'll keep this short.  Lee and Durham said YES to the solar power project, and ORCSD agreed to take the 10% excess power, so Moharimet will soon be partially solar powered.  The district passed the child restraint policy and had an interesting discussion of medical restraint.  On a sad note, Principal Allen and the board remembered Martin Brewer, a high school literature teacher who passed away last week, honoring him with a moment of silence.

Field to be built even if voters say no

Last night the school board approved almost the correct financing plan for the $2.3M track and field project. Board Member Al Howland proposed a plan along the lines that I've been recommending: $800,000 from the LGC/HealthTrust settlement, the $300,000 track fund, $650,000 from delaying some capital and technology spending and $500,000 new from the taxpayers. Revenue from the Orchard Drive land sale is excluded from this plan, but could potentially reduce the amounts asked of the taxpayers and the capital fund.

Since the $500,000 warrant article is a one-time appropriation and not a bond, only 50% is required for passage on election day.  Four times in the past the field warrant has had over 50% voter support, but not the 60% required to pass the bond.

The main problem with the plan is that the district is planning to ignore the result of the vote and build the field no matter what!  It's right there in black and white: "If the warrant failed, the track would still be built."  To me this is completely unacceptable -- the field should be built if and only if a majority of voters approve it.  I believe a majority will, but if they're like me and told their vote doesn't count, they're going to get irate.

My email to the board

The seven member board, Superintendent Morse, Principal Allen and Athletic Director Parker spent around fifteen minutes discussing how to proceed if the voters vote NO.  Not one of them thought to say if the voters vote NO, we shouldn't build the field.  I was totally disappointed in all of them.

The school board still has time to change this detail of the plan.  I let them know how I felt with a public comment and an email.  You can email the board at orcsdsb@orcsd.org (which sometimes doesn't work) or email member Howland directly at ahowland@orcsd.org.  (Please be aware your email becomes a public document and goes in the public folder.  They black out your email address, so you don't have to worry about that.)

Here's the proposed list of the capital spending to be delayed.  The technology spending to be delayed was not specified.

In related news, the board approved the new budget goal.   I'm happy to report that the board is including all recommended warrant articles and all revenue in the budget goal, like I've been proposing for a while now.   This year's goal is to cap the growth in the total asked of taxpayers to 4.25%.  While that number seems high, it is honest -- in past years stuff was excluded to make the number look smaller. For your money this year you get a new $2.3M field and full day Kindergarten, two long standing goals.  It's probably best to think of this as a 3% increase and a one-time ask of 1.25% ($500,000) for the field.  (As I'm sure the district will tell you over and over, there's no guarantee that your particular school taxes will go up exactly 4.25% as the details of apportionment and state aid can make this number vary between the three towns.)

Job listing posted 2015 10 13

The board approved the superintendent's plan to start the search immediately with the goal of hiring a
replacement assistant superintendent during the school year.  He ignored a proposal from last meeting to immediately promote an interim from within and start the search for permanent replacement to begin in July.  The superintendent made a remarkable claim that in his experience ("in 24 years of doing this work...") it doesn't matter if the hire is for mid-year or the beginning of the school year.  As I personally know candidates who are committed to their job and would not think of leaving their current district in the lurch, I find the superintendent's statement quite hard to swallow.  He backed it up with a real red herring about principals wanting to stay principals, further tattering his credibility.  Dr. Morse did say at the table (it wasn't in the written plan) that the search committee would consider applicants that wanted to start in July not January.

The superintendent and Principal Richard talked about the move toward "standards based reporting" where students' report cards will no longer have the traditional A to F grades but instead a number indicating progress toward each of a list of "competencies."  This is basically the way grades have been done in fifth grade and for a year or so there's been a process in the works to expand this to sixth grade math, and I think arts and music and phys ed too.  There was a lot of apologizing going on for not informing the public sooner and louder.  The intent is to eventually do this across the board, all classes, all grades.  Parents, start your griping now.  Little Timmy's got a 2 out of 3 in factoring polynomials, meaning he's progressing toward competency.  Explain that to Harvard.

The board also approved for first read a controversial policy allowing child restraint and seclusion.  First read means it's not yet adopted -- they need one more vote (second read) to do that.  The board adopted a controversial policy that gives sub-committees wider latitude to carry out their charge without board micromanagement.  David Taylor predicts bad consequences -- stay tuned.

There was also a discussion of air conditioning the third floor of the middle school, which was unbearably hot at the beginning of the school year.  The conclusion was that this was impractical due to high ceilings, high cost and high electrical load.

Field Warrant Articles Proliferate

Summary of the complicated new plan to finance an ORHS track and field

New field plan

Two weeks ago I worried that the field plan wouldn't be presented to the voters as a separate warrant article (ballot question).  After yesterday's school board meeting I'm worried that there will be three or four warrant articles and the voters would have to approve all of them to get the field built:

1. The voters authorize the sale of the Orchard Lane property
2. The voters direct the proceeds from Orchard Lane to the field project
3. The voters direct the insurance settlement money to the field project
4. The voters approve the remainder of the field budget, either as a one time appropriation or a bond.

It's possible that some of these aren't needed or can be combined.  Even if the voters approve all this, it's still possible that the land won't sell (or fetch the expected $295,000) or the insurance settlement comes in less than expected.  Either way the field might not go forward.

As I stare at it now, it seems the worries about complexity are overblown.  I'm not a lawyer but I think we can get away with two warrant articles, one that authorizes the sale of Orchard Lane and one that lays out the budget and financing plan and asks the voters to approve the plan and raise from taxes a few hundred thousand additional dollars to complete the financing.  

A plan distributed
but not discussed

The plan has sources of financing that don't require warrant articles.  One was a delay of planned capital improvements, freeing up funds for the field.  This part seemed a bit hastily thrown together -- two weeks ago the amount was $600,000; at yesterday's meeting there was a plan handed out on the back table (that matched the one in the agenda) asking for $700,000 from this year's budget and $205,000 from next year's.  Then during the meeting the superintendent handed out and discussed another plan asking for $350,000 this year and next "as an example".

Board member Rotner ominously talked about delaying the spending on the middle school: "I think it looks really smart not to be putting money into a building that maybe three five whatever years from now we're not going to be using anymore."  What he seemed to be implying was us taxpayers had better get ready to pony up for a new middle school soon, I'd guess via a $30M to $50M bond.  Superintendent Morse quickly changed the subject, presumably because news of such a big upcoming expenditure might sour the voters on the field.  The cat's out of the bag now.

The school board and district leadership are still exploring field financing that requires a bond and thus a 60% YES vote.  Some think that asking to bond a significantly smaller amount than last year's $1.7M will lead to passage.  I personally think a bond virtually guarantees failure -- we've tried four times and failed to get 60% each time.  I don't think there's reason to think a lower number on the bond will matter much -- most voters will understand that however it's financed the field will cost $2.3M that otherwise would not be spent, so taxes would ultimately be that much lower if the bond fails.

The alternative is a one-time appropriation requiring a simple majority.  This is the solution that Board member Day favors.  So do I.  I suggested a $300,000 appropriation, which I'm predicting will have no trouble getting to 50% at the polls.  A budget like that requires about $700,000 to come from delaying capital improvements, assuming all the other money comes through as planned.

I don't get Dr. Morse's objection to the non-bonding solution: "it stages the project over two summers or delays the project until the summer of 2017."  To me the difference between a bonding and non-bonding solution is just the wording of the warrant article -- whether it says "bond" or just "raise and appropriate."  There's no reason for an extra year delay if you don't bond.  Staging is likely a bad idea as well -- they're looking into it.

There was a lot of discussion about the multiple warrant articles being too complex for the voters, lessening the chance of passage.  There were also concerns about what happens if some of the articles pass and others fail, so we fail to reach full funding.  I made a public comment suggesting the various warrant articles ask the voters for permission to move the funds to the Track Fund.  That way if we fail to achieve full funding this March we bank the money and get the rest of the way next March. 

The superintendent promised full transparency in the field financing.  Member Rotner urged the public to come to the next school board meeting, Wednesday October 7, 7 pm at Moharimet, to air their opinions on the plan before a presumed vote. 

There was one more odd thing that came up.  It turns out that the board could spend this year's insurance settlement on the field even though the voters did not appropriate the money.  Normally, even if the district gets extra revenue or finds a pile of cash in a closet, it still cannot spend more in a single year than the voters appropriated in March.  But technically we don't actually receive the insurance settlement money -- it comes as a discount on insurance, so we're able to spend the money the voters appropriated for insurance on something else.

After some site visits in Cambridge, the field committee came to an agreement on the fill.  You'll recall last year the community was divided over the use of tire crumb rubber as infill in the artificial turf.  The most vociferous combatants were UNH Professor Kevin Gardner, for tire crumb, and Dr. Bob Barth, against.   They were both on the fill subcommittee, and amazingly they came to agreement that EPDM, Ethylene Propylene Diene Monomer, was the fill of choice for us.   It was reported that the vote to recommend EPDM was unanimous in the eleven member committee.

Athletic Director Parker showed this model of the
turf and recommend fill at yesterday's meeting

The committee left the price off the slide -- an obvious omission.  At the meeting the cost was reported to be $260,000 more than tire crumb for the initial project.  This is $40,000 less than budgeted.  Maintenance costs were not reported.

While I'm griping about the slide, I'll descend into a spelling flame. "Affects" is a verb -- you want the noun "effects."  And "its" not "it's".  And a space before "degrees."  Call me naive, but I expect better from educators.

By the way, 3 to 10 degrees seems pretty negligible compared to some of the temperatures thrown around last year.  I remember people talking about 130 or 140 or even 170 degree fields when the surrounding temperatures were 80 or 90.  Maybe in cold New Hampshire this heat effect is mostly desirable.

The board voted unanimously to accept the committee's recommendation.

In other news, ORCSD was given a "District of Distinction" award by District Administration magazine for the achievements of our Sustainability Committee.  Chair Cristini Dolcino accepted the award on behalf of the committee with a statement.  A plaque commemorating this national recognition will hang in the SAU office.  The board also renewed the charge for the sustainability committee.

There was some controversy over the superintendent's plan to fill the Assistant Superintendent position from within the district.  Dr. Morse's chief concern was with filling the position quickly, so there can be some transition overlap before Assistant Superintendent Eastman moves on at the end of October. Board member Farwell persuasively argued that as a top notch district we need to select the best candidate from a broad pool of applicants.  Due to the unfortunate timing of Assistant Superintendent Eastman's departure, the best candidates have already committed themselves for the current school year.  Board member Klein suggested hiring an interim AS.  Eventually the pieces were merged and a plan formed: quickly promote a current staff member to Interim Assistant Superintendent while starting a search for a permanent AS who'll come on board next school year (in July).  This seems obviously the best plan to me.  It does have the downside that the interim person already has a job that will presumably need to be filled, also temporarily.  What the superintendent will do is anyone's guess as no vote was taken.

Field Fiat

At tonight's school board meeting Oyster River Superintendent Morse put forth a $2.3M plan that puts a new artificial turf field directly into next year's budget.  Last March the warrant article for the $2M project failed to get the required 60% of the votes.  State law dictates a 60% threshold is required to approve the $1.7M bond portion of the funding.  The plan presented tonight does not appear to put the field issue as its own ballot question, but as part of the large budget appropriation.

New field funding plan (the Goal should read "with NO Bonding")

The $2.3M budget is a $300,000 increase from last year's plan.  The additional money is intended to go into a higher quality fill than the rubber tire crumb fill in last year's field budget.  A committee is expected to give the board its recommendation on field fill by the next board meeting, September 16.   Now that I think about it, by skipping the bond the district saves $300,000 in interest, so this really isn't an increase over last year's field proposal.

The memo explaining the plan (right) claims "36 additional positive votes and the plan would have been approved" which is terribly wrong - 339 additional YES votes would be needed to switch the result.  (The vote was 1382 to 1147, 54.6%; with 339 extra YESes you get 1721 to 1147, 60.0%.)  "56%" isn't quite right either.  I conclude that the vote wasn't all that close and that any plan involving a bond is likely to fail.

The appraisal for the Orchard Drive Land came in at $287,000.  The disappointing appraisal was attributed (in a 130 page report!) to Durham zoning laws that prevent the parcel, which the district received as a gift in 1971, to be more than four buildable lots.  Board member Kenny Rotner, who also serves on Durham's Town Council, suggested the district seek a variance from Durham to improve the valuation.

The money from the capital account comes from delaying planned capital improvements, in particular a generator at the middle school and something else I can't remember.  The superintendent reports Facilities Director Rozycki enthusiastically supports the plan and sees little downside from the delay.  The district is about halfway through the backlog of $4M of building problems identified in early 2012.

The insurance settlement refers to ongoing payouts from a judge ruling LGC had overcharged customers (including Oyster River and its staff) for health insurance.   LGC's successor HealthTrust didn't have the money to pay the judgement in one shot, so it's being doled out a bit every year.  The plan puts two years' worth of the payouts toward the field.

The $300,000 track fund is mostly private donations collected over the last couple of decades and I think includes $50,000 the district itself has contributed.

At the last board meeting I suggested that instead of bonding $600,000 that the board just put it on the ballot as a one time appropriation.   I meant it to have its own ballot question, so the voters can register their choice.   The advantage of a one time appropriation is that it only requires a simple 50% majority.  Similarly, at tonight's meeting board member Denise Day suggested that the shortfall from the land sale of $300,000 be placed on the ballot as a one time appropriation.

I like the idea of including the question of the field as its own warrant article.  Four times in the past a majority of voters said YES but the majority never reached 60% so the bond always failed.   This time, if the same majority votes for a one time appropriation of around $300,000 (possibly less depending on fill costs) the article would pass and the project would go forward.

I'm less enamored with the idea of including the field in the large budget appropriation.  Opponents to the field would be forced to vote against the full budget to register their disapproval of the field.  Combined with the substantial number of voters who vote NO on the budget anyway, this might be enough to tip the balance into NO territory triggering the default budget and a whole to-do.  I'm not sure if the superintendent intended to do it this way, somewhat bypassing the voters, but it seems to me a very bad idea.   It's up to the school board anyway, which I believe will let the voters directly decide on the field with a simple majority vote on election day.



In other news, Assistant Superintendent Carolyn Eastman has quit, tendering her 60 day notice.  She's off to big-time greener pastures that she told me about but I didn't think to get permission to write about.   Her legacy will be how she proactively embraced Common Core and Smarter Balanced and moved the district to a comprehensive assessment system that quickly focuses teachers on individual students' needs.  I've gotten to know Assistant Superintendent Eastman over her three years here and I'm going to miss her very much.  Thank you for all your great work Carolyn.  Fortunately, Carolyn will still be a district mom.

Today was the first day of school and the superintendent announced that 381 students are enrolled at Moharimet.  Recall two years ago the overcrowding at Moharimet had gotten out of hand, with 407 students in a school with nominal capacity 389.   Back then I estimated it would be "two years before Redraw with Full Grandfathering got Moharimet down to capacity" -- score one for me.  This is in contrast to last November's Long Range Planning Committee report that forecasted 411 students would be enrolled at Moharimet today, off by a distressing 8%.  Board member Rotner asked that the LRPC look into the discrepancy.

Let's recall a quick history of how the board eventually settled on Redraw with Full Grandfathering, our traditional elementary imbalance remedy.   I think the distractions of tweets, lawsuits and almost full administrative turnover in 2011 & 2012 let the creeping problem go unaddressed, maybe even unnoticed, for a couple years.  It didn't help that the LRPC was forecasting a substantial 6% enrollment decline, with the December 2012 forecast for FY16 Moharimet (that's today) of 358.  Then the new superintendent spent an extra year getting everyone riled up deciding while the problem got even worse.   The superintendent liked a K-2, 3-4 split, a pretty bad idea that didn't really solve the problem.  It was soundly rejected by the community early on but the leadership inexplicably kept pushing it.

There's also news about the budget.  I'm happy to report that the board is considering my ideas to include revenue and not exclude certain expenses when setting budget goals.    But the real surprising thing to come out of the meeting is that the superintendent thinks he can fund Full Day Kindergarten and a new field and still keep growth below a nominal 3%.  I'm sure I'll write more as the budget develops so I'll just say good night now.

IXL math is confused about the order of the months and the days of the week

Oyster River News.  I haven't posted anything since the election.  There's a controversial and groundbreaking transgender policy that I think will be approved soon, and news that Mast Way and Moharimet have the same number of entering Kindergartners, 52 each -- usually there are 10 to 15 more entering Moharimet. Inequitably MW will have 3 classes of 18, Moh 4 classes of 13.


But I'm going to ignore all that for now and talk about online math.  My daughter is reluctantly doing some online math this summer in preparation for eighth grade algebra.  She's using IXL math, which is an online skill drilling system provided by the district.   She's up to eighth grade H 11 rate of change.

The questions all involve looking at a table or graph of a time series and calculating the rate of change of a quantity between two times by subtracting the earlier amount from the later amount and dividing by the time between them.

The time axis ticks are labeled by consecutive times.  IXL has no problem when time is a number, like seconds or years, but it has a skewed idea of the ordering of the days of the week and the months of the year.  For example, consider this problem:

The odd order of the days of the week makes this incomprehensible.  I suspect the problem is in their internationalization software where apparently they have the weekdays ordered alphabetically: Friday, Monday, Saturday, Sunday, Thursday, Tuesday, Wednesday.

Like the weekdays, the months are misordered alphabetically April, August, December, February, January, July, June, March, May, November, October as in:

The answer to this problem is 3, because August to December is considered one month in this ordering. (By the way, in my experience "3" is the most common answer to math test problems, so if you ever have to guess...)

Anyway, my daughter was pretty distraught over the whole thing. It really is a pretty awful bug that should have been caught.

Update: Monday, 8/17.  IXL quickly responded to my facebook post to their page.  (They don't make it obvious how to report bugs, so I tried four or five ways.)  "Hi Dean, good catch - this is definitely a bug we are aware of, and our engineering team is making it a high priority to fix it."  I'm impressed by their fast reply, and I hope to be impressed by how quickly they fix the bug.  Stay tuned.

Update 2: Mon, Aug 17, 2015 at 4:49 PM  Email from Joe at IXL support promising to have this fixed by tomorrow:

From: IXL Support <help@ixl.com>
Dear Dean,

Thank you for contacting IXL and bringing this to our attention.

Our engineers are working on this bug now, and this will be fixed by tomorrow. The days of the week and months of the year will then appear in the proper order again.

Thank you again for bringing this to our attention! If you have any additional questions, please let me know.

Sincerely,
Joe
IXL Support
help@ixl.com

That's pretty fast for a company to respond, and it's obviously written by an actual person familiar with the issue, so it seems they're really taking it seriously.  If they're resentful about me writing it up here, they're not showing it in the least. Good for IXL.

As of Monday 11:50 pm there is still no change.  I'll check tomorrow.   My girl also had a glitch in Math8 E8, maybe last Thursday, where the number line drawings were not rendering correctly, leaving a question about a garbled diagram. F5 refresh fixed things, if you tried it.  I checked it today and it seems to have been fixed -- at least I can't reproduce it.

Update 3: Thursday August 20, 2 am.  IXL has fixed the problem.  They sent me an email Tuesday saying they were testing the change, and some time in the last few hours they released it:

The question makes a lot more sense this way.  (And if you guessed "3" ... you're right!)  IXL did a great job responding to me and fixing the problem.  They weren't quite done by Tuesday like Joe said but it got done quickly but apparently not so quickly that other errors were made.  I'm impressed.  I especially appreciate how they didn't shoot the messenger.

OK, back to the original post.  Here's one of the explanations explaining why I was wrong counting Friday to Sunday as two days.




Apparently the good folks at IXL need to go back to their own first grade and brush up on a couple of skills.

I've reproduced this behavior on Internet Explorer and Chrome on Windows 8 and Windows 7, and on Safari on a Mac, and on Chrome on my Android. Haven't checked the app. I've only noticed it on Grade 8 H11. First grade S12 above seems to work fine.

Beyond the weird bug, I'm not sure the pedagogy here is all that great. If I was teaching rate-of-change, I'd focus on: (1) Rate, rate of change, and rate of increase all mean the same thing, how fast a quantity changes. This means how much a quantity changes per unit time, so it's always change in quantity divided by the time over which the change takes place. (2) It's always later minus earlier in the denominator, because that's the same thing as the time interval. (3) It's always later minus earlier in the numerator. This is very confusing to students until it isn't, and it is a recurring pattern they will use again and again in all future math and science so drill it in. (4) Rate of change means rate of increase, and a negative increase is a decrease. (5) As the time interval decreases, the rate of change approaches the tangent. (6) I would focus more examples on domains where rates of change play a large role, like physics. (7) The inverse operation, given a rate and a time interval calculate the amount, should be taught at the same time. I don't think IXL does a very good job on any of these.

So beyond the month names making Doug's budget below incomprehensible, I have other issues. I don't like asking students about "rate of decrease" which is the opposite of what the students are being taught to calculate. Furthermore, the past tense "was" is not right to refer to a budget for the future.

I started taking screenshots and captured 18 more: