Hogan orders more summer, gets an earful

When Gov Larry Hogan ordered public schools in Maryland to start the year after Labor Day and finish it by June 15, he was pummeled by superintendents, school board members, teachers, and a few others in the education field. He responded to critics by addressing their concerns in a memo. Most of it adopted the “he said, she said” style, but there was one response that addressed mathematics, and that’s what I want to talk about.

Gov Hogan (shades) and Comptroller Peter Franchot talk with reporters (Maryland GovPics / Flickr CC)

The assertion of “mathematical impossibility” isn’t an opinion; rather, it implies a proof has been put forth. That’s unlikely, unless the person who wrote the memo referenced above doesn’t know what mathematical impossibility means.

For example, the statement below is mathematically impossible:

No value for x in the universe will make this a true statement. That means it’s “mathematically impossible” that x + 5 = x + 6. On the other hand, the statement

is not impossible. For example, if x = 0, the statement is true. This is where the esteemed educators in Anne Arundel County may have become confused. If I force a “constraint” on the value of x, like saying that x can’t be 0, a statement that wasn’t mathematically impossible in an unconstrained world becomes mathematically impossible.

Now, we all know school systems have all kinds of constraints on their calendars. They can’t, for instance, have class on Saturday or Sunday. I don’t know why that constraint exists, but it’s a constraint (state law). They also have to provide days off for any days that many, many children are likely to miss, such as Christmas or Thanksgiving.

But the number of weekdays between Labor Day and June 15 in any random year is approximately between 201 and 205. Those are the minimum and maximum values for the next 10 school years anyway. State law requires 180 school days.

Assuming two days off for Thanksgiving and at least six days off around New Year’s Day, that leaves anywhere between 13 and 17 days for schools to schedule the days off. Given a 10-month calendar, that’s about one and a half days per month, in addition to Thanksgiving and Christmas.

One final note: School districts have to plan for snow days, and they usually allocate five days at the end of the year and hold those days in reserve. The executive order makes no provisions for emergency closures, so let’s say we have to come up with 185 days between Labor Day and June 15 and we therefore have between eight and 12 days to use outside Christmas and Thanksgiving. Work the problem. Which days off do you want your school to use?

It may be difficult, given an individual system’s constraints, but don’t fall for the logic that it’s “mathematically impossible.” If it were, I wouldn’t be able to come up with even one example of how it could be done, and I’ve written a little web app that will allow people to pick and choose which days off they would like to have between Labor Day and June 15 for the next 20 years.

Actually, it isn’t even difficult. I can in a few minutes, come up with several solutions. As in my 5x = 6x example, to prove that something isn’t impossible all I have to do is do it. So it’s done.

Voxitatis will feature content over the next few days to describe the fallout from the announcement of this executive order. It has drawn both fire and water from both sides, and we’ll get this sorted out soon enough.