Very early during the school year, I write a statement like 2 < x < 7 on the board and ask my students in algebra 2 to read it. The most common response does not surprise me: “2 less than x less than 7″. It happened again this year, and I said: “that is correct, but now I would like you to think about what this statement says about some real number x”. There was a long pause, and someone said with a questioning tone “2 less than a number less than 7?”. “What else?” I prompted them, “what if you were to say something about this number to a seven-year-old?”, to which someone responded “x is a number between 2 and 7″. This was a good beginning to a classroom culture where we would try to find meaning in mathematics.
A discussion about meaningful reading of symbols is necessary to promote experiences in the classroom that might lead to understanding of abstract concepts. It is a difficult transition for most students. Prompting students to read the meaning in algebraic statements beyond the symbols is a challenging endeavor.
And, it can be rewarding. Following a lesson on sequences in the algebra 2 class, I asked the students to read a-sub-n = 3n + 2. A student replied: “this is the rule for the nth term of an arithmetic sequence with common difference 3 and first term 5.”