Ok, let's see what we have to work with here. First of all, notice that
The teacher is terrible at her job. When teaching about "math" prefixes, she omits the most common math terms. Things that everyone knows - words like "Pentagon" (headquarters of the United States Department of Defense) is named as such because it has 5 sides - a common mathematical shape. But instead she teaches prefix "quint".
Of course she omits the other prefixes, such as "mono-" (monorail, monologue) and "du-" (duplex, duet). And, the most egregious of all, "quint" is written as "quince", which is actually a fruit and not a prefix at all...
Once she gets to 13, she forgoes the prefix "triskaideca-", as in triskaidecagon or triskaidekaphobia, and instead uses the word "dozen" which isn't even a prefix at all!
Another thing to note is
Just because she tried to use the term "baker's dozen" would not necessarily mean that she's a baker. I'm not a baker, can I not use that term to refer to anything? Should I not be allowed to use the term "nautical mile" or "metric Ton" either because I'm not a sailor or in manufacturing? Obviously something else must be afoot here...
Drawing on all these observations
Since we bear witness to how incompetent she is at teaching math, I would assume she would be just as incompetent at her other job. Since we also see that she used the word "dozen" as a prefix, and confused "quince" with "quint", I can only assume that her other part-time job is an English teacher!