I knew my students had language-related learning disabilities but didn’t know how that would manifest itself in the classroom. Many of these students hear words they don’t understand so often that they don’t like to make a show of it. They let the moment pass, acting like they understand what you’re saying and assuming they’ll figure it out later if it’s important. In time I began to notice signs that my students didn’t understand certain terms, but for a while I effectively ignored their vocabulary needs. My thinking was that with as many gaps as there were in their understanding, conceptual mathematical vocabulary didn’t rank highly on the list. I mean, they knew the most common vocab terms (add, subtract, multiply, divide, distribute [on good days], equation, etc.), so I tried to express new ideas in those terms. I did use more advanced vocabulary in class, but I heard myself saying those terms quickly, self-consciously, like I know this word means nothing to you so let’s just get it over with.
Finally, I was working one-on-one with a student (a high school senior in trigonometry, one of the highest math courses taught at my school) because she didn’t understand a homework problem. We read through the problem, I tried rephrasing it, breaking it into manageable pieces, but made no headway. Then she pointed to two words and said, “I don’t know those words.” She was dyslexic, so maybe it was a symbological thing. Maybe she knew the words but was confused by their written forms, so I said the words out loud: “Radius and variable? You don’t know those words? Do they sound familiar at all, like you’ve heard them before but can’t remember what they mean?” “No. I don’t know those words.” I know for certain she’d heard them before, multiple times, but the fact is that she had no recollection of hearing them, was aware of no meaning associated with them. Radius and variable. This is a student who has taken Algebra 1, Geometry, and Algebra II, and made positive impressions on her teachers. She should know the words radius and variable.
What a wake-up call. Maybe she’d had other teachers who, realizing what a jumble her command of language was, had decided to de-emphasize vocabulary, to get her to do the math without worrying overmuch about the words associated with it. Or maybe they’d given vocabulary the normal amount of emphasis and this was what that level of emphasis resulted in for students like her.
She had taken all the prerequisite courses for trig and had been able to “do the math” so well that teachers had given strong recommendations of her ability. But here she sat without even basic tools for expressing the math she had learned to do. She could neither produce the words on her own, nor recognize them when written and pronounced for her. She could not communicate the ideas she had worked to learn, and without communication, ideas wither.
Boy, was I wrong about the ranking of vocabulary in the hierarchy of important mathematical subjects. Getting these students to “do the math” without enabling them with tools for communicating the math is nearly worthless. After this, cumulative vocab-building ceased to be a dismissable time-drain in my class and became recognized as central to the students’ learning and reviewing. It absolutely takes time away from other pursuits. It is essential.