Math is Like a Language

Imagine students who learned a foreign language in high school entirely though speaking-listening roleplaying sessions, with the help of phrase books and babelfish when they needed it. A focus on scenarios that come up in tourism. No grammar, no memorized lists of vocabulary words and verb endings, no written work. Possibly from a teacher who wasn't fluent in the language.

Now imagine what would happen if these students took a college-level literature course in this language in which they were expected to closely analyze texts for diction and syntax and to write grammatically-correct and well-argued papers. Makes me think of my mom's Russian class in college. Since her grandparents spoke Polish, she tried to fake her way through Russian class by using what she'd remembered of her childhood knowledge of Polish (just written with the Cyrillic alphabet). She passed. Barely.

That's a decent analogy to what it's like in my gen-ed class. My students have taken years of math, and yet they don't know what the words mean, and they don't know the rules that hold things together. They can put symbols on the paper that bear a visual resemblence to the correct method but that don't make any sense. Worse than knowing nothing about the subject, they are full of bad habits that need to be unlearned.