Thank you for your comment, ShivamS. The GREs are required for almost all of the grad programs here at this US university, so this is why I mention this exam at all. My students want to apply to this university; I saw a learning gap and I am working to fill it. Isn't that what teachers do?
Thanks for the (mostly) warm welcome! I appreciate the thoughts, bobbym, and agree that problem solving skills are indeed in demand and marketable. Let me re-emphasize my job and it's purpose: I am not a math teacher. I am a language teacher who teaches the language of math to language learners who are already academically qualified for degree programs here at my institution. My class is called "Let's Talk about Mathematics." It is housed in the English Language Institute at the university, not in the math unit. My apologies for simplifying its content by calling it a vocabulary class, as this apparently gave an inaccurate picture of the course objectives.
I respectfully submit that your comparison ("That is sort of like knowing the difference between a predicate nominative and an object noun") is faulty, in that the goal of a language teacher is a student's ability to communicate, not their ability to name the parts of speech or diagram a sentence perfectly. Language teaching is nothing like the English classes we may have been subjected to in our grammar school years.
As for the SAT/GRE/GMAT discussion, the fact remains that applicants to degree programs must achieve certain scores on these tests in order to be considered for admission. Whether I agree with the test or the content or purpose of the test or how it was written/administered/interpreted is irrelevant to my purpose. In serving my students in an advisory capacity, I noticed that they were not doing as well on the math section as we would expect. These are NOT 17 year old high school kids. Some are professional educators with graduate degrees from universities in their home countries in accounting or engineering or math. Others are 20-22 year olds who have come to us to prepare for undergraduate studies. They are held to the same academic standards as any applicant to the university here, but they did not have the benefit of learning how we use language when "doing" math.
That said, here is a real-world example. I wrote a list of numbers on the board and told the students these are the scores from a recent exam. I asked them, "What is the mean of these scores?" After a pause, one student (who is a professor of statistics in her home country and is planning to pursue her PhD here), raised her hand and said, "It means 4 students got As, 8 students earned Bs, 7 students got Cs, and 5 students did not pass the exam."
Can you define "absolute value" by looking up "absolute" and "value" in a translator, even if you know what "absolute value" means in your native language? Search for "right triangle" in a translator and see if you get the geometric definition. If I told you the word for "parallelogram" in Thai, could you draw one? A language learner may know what "real," "rational," and "imaginary" mean in everyday (or, "real world," as you prefer to put it) English, but we know that they have very specific meanings in math, and knowing this meaning can make a huge difference when reading a math problem.
So my focus is to expose students to the many uses of math language (yes, including specific vocabulary!) that they might find on a standardized test.
I hope this clarifies my purpose. Thank you for any additional support/ideas you may have.
I am a teacher and advisor in an Intensive English Program at a major university on the East Coast of the USA. I found that many of my students were not passing standardized college entrance exams (SAT, GRE, GMAT) because, while they may have been academically qualified, they did not have preparation in the terminology the math sections require. So I created a math vocab course last semester to help fill in the gaps. I have run into some challenges, some teaching-based (appropriate textbooks/resources) and some student-based (language learners may not have the same math background).
I look forward to connecting with others in similar situations (if you are out there!) and with those who may have ideas that will help me strengthen this class for the coming semesters.