> The way I like to tell people this is, you know that thing where you want to take your kids or your students and make sure that they don't have to go through the same pain that you did to learn what you had learned? That feeling?

I am not yet convinced. Let me take the following example because I remember it well: I tried to learn about geometric optics and lenses. To do so, I downloaded multiple lecture PDFs from the internet and read them.

All of them started to explain lenses by describing how large the image of a real object is, defining focal length and such. Literally not a single one of them even defined what an image is. The whole talk about image size and focal length and magnification and what not was totally worthless because it was all based on the same fundamental word that had no meaning. In the end, I tried to make up my own definition that was consistent with all those PDFs, but it left me unsure if I got it right.

The "pain" was there, but there was no relief from it, and I am still convinced that that simple definition could have avoided it. If I were to teach optics, I would give such a definition, and I am still convinced that it would help with the pain.

The other example was one of those PDFs that showed a real object that was "wide" along the distance axis from the lens, and so by my understanding should have an image whose magnification changes along the distance axis, but the explanatory picture in the PDF showed equal magnification everywhere. Today I am convinced that this "explanatory picture" was simply wrong.

Again, there was "pain", no relief (because I could not be sure), and I am still convinced that a learner can be saved a lot of pain when you just exlucde factually wrong content from the learning material.