Due to the way a student did a problem I realized that she didn't understand the context of the letter x in the math problem. This lead to today's entry on this topic.
The students were carefully calculating the surface area of various sized boxes. The dimensions were listed such as 24 x 1 x 1 meaning 24 by 1 by 1. So when I spoke about multiplying the area for each surface, instead of writing 2 x 24 x 1 meaning 2 times 24 times 1 she wrote 2 by 24 by 1 and multiplied the numbers together.
When I asked her about it, she indicated she saw the x meaning by for dimensions as meaning times. I've used x in both situations as needed and never realized that some students, especially ELL students, may not understand the different contexts as easily as I might.
I stopped and thought about the meaning of X in the math classroom and realized it could be a variable, it could mean times, or it could mean by as in a 3 dimensional shape or even refer to a matrix. Furthermore, it really isn't until middle school or high school that students switch from using x to indicate multiplication to using * or parenthesis.
I get quite a few freshmen who have not been required to switch from x to * and they have difficulties when working with something like 2 times x because they instinctively write 2xx which to me is 2x^2. They also have difficulty with 2x meaning 2 times a number.
One way to cut down on the issue is to introduce the idea of using variables down in elementary and perhaps even get kids to change from using x to * when they want to show multiplication. If this is started down in elementary and reinforced in middle school, I might get students who are aware of the differences in meanings and can recognize the contextual differences.
This is part of being mathematically literate.