I work with Alaska Native students, most of whom are classified as English Language Learners because they are not considered proficient. These students are unwilling to try to define vocabulary in their own word. They do not use the words enough in their daily conversations either in class or outside of it.
I admit I am partially at fault. I have not required them to use the language in class. They need to use the words to develop fluency in the language of mathematics. I have not taught them to breakdown the book definitions so as define them into their own.
We know that there are three types of words students will run across in math. First are the general conversation words that you don't use in math. Words like Hello and Good bye. Second are the words you find in both general conversation and math such as constant or term. Finally are words that are specialized to mathematics such as derivative.
Students, especially ELL students, need to learn and practice the words. To I've come up with several ideas for additional vocabulary development.
First, I want them create their own word walls with those sticky note apps. Each word should have two definitions if possible The first being the mathematical one and the second being the general conversation. For instance, does the word product mean the same thing in both contexts? They should also have examples of the word in sentences in both contexts.
The second thing I want to do is to record thoughts, explanations, etc in a digital journal. I want to ask questions such as 1. "What does the 2 mean in 24 vs 3^2?"
2. "Illustrate 2x^2 and explain what it means using the drawing."
3 "Why does x^0 = 1?"
The third thing I want provide them with opportunities use the new vocabulary at lest 30 times in a 3 week period to help them remember it. I hope to have them use it in written or verbal form.
I plan to continue researching ways to increases literacy in my math classes so students improve their overall literacy.