Putting the math to work

Over at Funds for Learning, John Harrington has looked at the numbers and decided that the math for the Wi-Fi chimera works.  As usual, FFL is not wrong, but I don't agree with the analysis.  The math does work if the $150/student that we've been hearing about will be spread over five years.  So if every school gets $30/student/year, it will cost about $1 billion per year, just like the Chairman plans.

On to the problems.

1. The easy one: libraries.  If it will cost $1 billion/year to fund schools, how do we fund the libraries?  We're going to need a bigger fund.
2. $30/student/year?  ISTE clearly thinks it's going to be $150/student once every 5 years.  I'll do that math later.
3. The discount levels are a-changin'.  The rumor is that the Chairman's promise to "simplify discount calculations" means school districts will have a single discount level for all locations, based on the enrollment and NSLP totals for the district.  No more 86% districts.  How will this affect funding?  I don't know, but I'd guess that overall, it will lower funding demands; I suspect that 86% districts are more likely to move to 80% than 90%.
4. Who's getting their discount cut?  The last two columns show 1) funding at current discount rates, and 2) funding if all discount rates are cut 10%.  The only talk I've heard of cutting discounts is to make the top discount 80%.

Ooh look!  There's a table showing the number of students at each discount band.  I just can't resist numbers, so I dumped the data into a spreadsheet to play with.  You can download my spreadsheet and play, too.

I tried to get us to the new discount bands. I made some assumptions about rounding: applicants at 29% or below went down to 20%, 30% and above went up to 40%.  Beyond that, I rounded down on the 6, up on the 7, so 46% and lower became 40%, 47% and above became 50%, and so on.

I created columns for: 1) no change in discount, 2) everyone gets a 10% haircut, and 3) the matrix is the same, except the top discount is 80%.

I also created cumulative columns, so I could quickly see how much we'd need to cover all applicants at that discount rate and higher.

Looking at $30/student/year (if you downloaded the spreadsheet and are playing along at home, you can adjust the per-student amount in cell B2) with only the 90% group cut by 10%, the total demand is: $1.035 billion.  So we're short by $35 million plus whatever the libraries need.

Looking at the one-time $150/student:

1. If the only change in discount levels is to reduce the top discount to 80%, then we'll need $2.67 billion just to cover the 80% applicants.  
2. If everyone takes a 10% haircut, then with $1 billion we can probably fund all the 80% applicants (those would be the applicants who currently have a discount between 86% and 90%).  But we can't fund the 70% applicants (those with a current discount of (77% to 86%).  In fact, we'll need $1.8 billion just to cover the 70% applicants, so we can't fit them all in one year.  We'll need just over $1 billion to cover the 60% applicants.  After that it gets easier.

The math doesn't work using the current practice of denying all applicants in a discount band if there isn't enough money left to fund everyone in that band.  The FCC could always follow the rules, and pro-rate, but the howls would be considerable, especially if the 1-in-5 Rule is adopted.

The solution is to do what they should have been doing all along: if there isn't enough money left to fully fund the applicants in a discount band, go to the raw NSLP data.  Not enough funding to meet demand from 90% applicants?  Fund those applicants with 100% low-income kids, then the applicants with 99% low-income kids, and so on until the funding runs out.

The math shows me some challenges ahead.  We can't really say exactly what the challenges will be until we've seen the new rules, but one thing's clear to me: we're going to need a bigger fund.