Gall–Peters or AuthaGraph. The end.

[PeteD]

As for compromise projections, while the Winkel Tripel, or the Robinson are reasonable, another one that is readily available is the Van der Grinten, which basically perpetuates the flaws of the Mercator.

Yes, I suppose if you just banned the Mercator (or conformal projections in general) and schools switched to the van der Grinten, that would be a pretty epic fail for the legislation!

Is the main goal of the legislation to remove the Mercator (which I wouldn't find outrageous) or to promote the Gall–Peters (which I do)? Is the Mercator really still as ubiquitous as it once was? Is there any data on what projections are currently used in schools?

[daan]

Is the main goal of the legislation to remove the Mercator or to promote the Gall–Peters?

The original bill restricted use to either Gall–Peters or Authagraph. What got signed into law was watered down a little to permit other rectangular equal-area projections as well. I think we can conclude that the main goal was to force equal-area presentations, but that happened without acknowledging that there are a lot more choices.

Is the Mercator really still as ubiquitous as it once was?

No. It’s probably hard to find one in an American school classroom these days.

Is there any data on what projections are currently used in schools?

I don’t remember seeing any such studies “cross my desk”. ~~~~

— daan

[PeteD]

Is the Mercator really still as ubiquitous as it once was?

No. It’s probably hard to find one in an American school classroom these days.

In that case, I really see no justification for this ban.

[quadibloc]

While I agree that mandating schools only use one particular projection is a bad idea, even if the projection were one that was better than the Peters projection, if the legislature's mentality was such that this was the only kind of regulation they understood... then my proposal to them would be:
If the goal is to ensure children develop a mental picture of the world that is not distorted from the reality on the globe by the map they see on the wall, then world maps in the classroom (atlases should not be regulated; they use the Lambert Azimuthal Equal-Area commonly these days, which is an excellent choice) could be restricted to these projections:
An interrupted Sinusoidal in normal aspect
An Interrupted Bonne in normal aspect
Orthographic
All projections distort, because the surface of the sphere, unlike that of the cone or the cylinder, is not reducible to a plane.
The Sinusoidal and the Bonne are equal-area projections. But while they distort shapes, in normal aspect this distortion is entirely in the form of shear, and the precise quantity of shear, unlike stretch, is obviously and immediately visible on the map by looking at the graticule.
So a mental adjustment to the real shapes of landmasses on the globe is possible.
The Orthogrphic projection is like a picture of a globe, so a different sort of mental adjustment is possible, since the foreshortening of landmasses is again instinctively visible.
Thus, if your goal is to ensure that children have a mental image of the world that is not prejudiced by the false picture presented by the map projection that is present every day in the classroom, the way the Mercator has been criticized for doing, instead of choosing the Peters projection, which does show true areas, but gives a wrong idea about shapes, even if how we think about shapes is less important, choose an equal-area projection, the interrupted Sinusoidal, that is honest about how it distorts shapes, thus minimizing the false notions about the world that it might cause.

[PeteD]

If the goal is to ensure children develop a mental picture of the world that is not distorted from the reality on the globe by the map they see on the wall, then world maps in the classroom ... could be restricted to these projections:
An interrupted Sinusoidal in normal aspect
An Interrupted Bonne in normal aspect
Orthographic

Those aren't the projections that I would have chosen. I don't mean to say that my choices would be better than yours, rather that if we can't even agree on the most suitable projections, it goes to show that attempting to mandate certain projections is a bad idea.

The Sinusoidal and the Bonne are equal-area projections. But while they distort shapes, in normal aspect this distortion is entirely in the form of shear, and the precise quantity of shear, unlike stretch, is obviously and immediately visible on the map by looking at the graticule.
So a mental adjustment to the real shapes of landmasses on the globe is possible.
The Orthogrpahic projection is like a picture of a globe, so a different sort of mental adjustment is possible, since the foreshortening of landmasses is again instinctively visible.

I agree about the orthographic projection – my brain interprets it as a picture of a 3D globe, so the projection can't give me any wrong ideas about sizes or shapes. (It is, however, very difficult to discern details near the edges – assuming it's presented as two hemispheres interrupted at 20° W and 160° E, it's pretty much useless for Greenland, Iceland, the British Isles, Iberia, West Africa, Japan, New Guinea, Australia and New Zealand.) On the other hand, while I don't doubt that you can mentally adjust for the shear of the sinusoidal and Bonne projections, I can't.

[quadibloc]

On the other hand, while I don't doubt that you can mentally adjust for the shear of the sinusoidal and Bonne projections, I can't.

I do say that they have to be interrupted when used in a world map. Yes, if the shear is too severe, the map becomes unintelligible.
I could be wrong about the Sinusoidal; but it seems to me that (in normal aspect) the graticule gives information about what is going on with the shear, even to the extent of showing exactly how much shear is taking place - whereas, when a projection distorts shapes by stretching, or when it distorts sizes, there is no reference in the map that shows how severe the distortion is.

[PeteD]

I could be wrong about the Sinusoidal; but it seems to me that (in normal aspect) the graticule gives information about what is going on with the shear, even to the extent of showing exactly how much shear is taking place - whereas, when a projection distorts shapes by stretching, or when it distorts sizes, there is no reference in the map that shows how severe the distortion is.

Yes, that sounds right to me. I just meant that I personally can't mentally undo the shear based on that information from the graticule, and I doubt I'm the only one.

I do say that they have to be interrupted when used in a world map.

I suppose in that case there's not as much shear to mentally undo, but personally, I'm not a fan of heavily interrupted maps. Two-hemisphere maps are OK, but then an azimuthal projection or the Mollweide or Apian II would seem a better choice.