Elementary Geometry Nomenclature: why so bad?

Solution 1:

We also have, for example, add/sum/negation vs. multiply/product/reciprocal. As with natural language (be/is/was, go/went, speak/spoke), the oldest terms tend to be the most irregular, because they became established before the currently used structure emerged.

Solution 2:

I can't resist adding this, since it's been on my mind in recent months.

This vignette in the OP highlights part of a big problem with modern mathematics education: enshrinement of ideas and terminology as being written in stone. Another closely related thing is the unwillingness of textbook writers from departing from what has already been written. They apparently cannot dream of departing from the herd into more sensible pastures.

I acknowledge, of course, that it's necessary to select a vocabulary so that students can discuss things with you. For the sake of uniformity, teachers tend to stick with what they were taught, both because it is familiar and because other texts do it.

What this has come to in practice, though, is students being rigidly taught that "this is what you call it" along with the undertone that nothing else would be considered correct. As a result we have the patchwork of terminology to forcefeed children with.

I don't really think that this is a result of rigidity so much as it is an ignorance of what mathematics is about. The perception that mathematics is fixed or rigid causes teachers to treat it as such, whereas more mathematically experienced people recognize it is more like a canvas.

One annoying legacy of this insistance on sticking with tradition (that someone else mentioned in the comments) that (in the US anyway) we are stuck with thousands of primary school textbooks insisting that a trapezoid have exactly one pair of parallel sides. It has amazed me that there can be supporters of this position so entrenched, when their viewpoint flies in the face of the rest of the classification of quadrilaterals. (Another thing like this is insisting that kites have exactly two side-lengths, so that squares cannot be kites. This is more rare than the trapezoid thing, but it equally annoys me.)

This usually persists into the minds of secondary school teachers, and hence into their students' minds. Then, a student reaching college might discover that nobody in post-secondary education would entertain such a bad system, and they quickly have to relearn quadrilaterals according to the inclusive system. Or, more usually, the changes are just swept under the rug as stuff primary and secondary schools taught less than ideally.

Anyhow, it is difficult to see a good solution. Authors of textbooks are simply unaware of or unwilling to risk the transition to a 'new' system. Primary and secondary teachers apparently cannot (or will not) be persuaded en-masse that the 'new' system is more coherent and worth adopting.

But that's OK: it's not the worst problem education faces. Maybe overcoming these imperfections are important for developing mathematical minds.

Solution 3:

We need to get better at naming things and it should follow an understandable pattern for easy comprehension. When we're inconsistent with our nomenclature, it takes the fun out of learning.

Unfortunately, this problem goes all the way back to the numbers we use. Eighty-one is 8 tens and one, which makes sense, but explain "eleven" and "twelve". Then try explaining "thirteen" which is 3 ones and ten (which is backwards).

Where English has unique names for 11 and 12, Spanish has unique names for 11-15, then 16 translates to "ten and six".

Adding these poorly named numbers makes you do an extra step in your head. "Eleven plus seventeen plus eighty-one"? First you have to think about what these words mean, then rearrange their orders in your head by tens and ones, then add them.

Science makes you memorize the names of long dead folks (Ohms, Plancks, Coulombs,...) and computer programming is awful as well. (Did you know that in Unix, the command used to OPEN a file is "LESS"?)

Every subject has things which need new names.