When a student studies mathematics, they are learning a new language. Many of the words are familiar such as product, plane, or less than but the meanings are not.
All through school beginning in Kindergarten, teachers work on helping students acquire the necessary vocabulary to succeed in math but we don't always teach students how to write definitions in their own words.
When they see a definition such as "It is a decimal number that cannot be expressed as the ratio of two integers and neither terminates nor repeats", if they do not have a solid foundation in mathematical terminology, they will not understand it. If you ask them to define it in their own words, they might try to copy it and just change out one or two words or they might ask the teacher to tell them what to write.
The other day, I realized I'd never broken down the process of taking a mathematical definition and putting it into their own words. In fact, they made it to high school without learning the process and it appears teachers in earlier grades are allowing them to just copy material down verbatim without learning the process. I do not blame the teachers because many students will take the easier path and just copy rather than struggle to learn to use their own words.
I'm not sure if these students have a good vocabulary so they don't have enough words to put it into their own words. So I took time to demonstrate how I turn a definition into something more understandable. It was enlightening because some of the students paid close attention to the process.
Wednesdays are my word problem day. I take something out of the NCTM journals to work on with my students. This last Wednesday, the activity required students to know irrational, rational, integer, whole and natural numbers. I realized I needed to take time to help them learn to translate the definitions from math into common English.
So I took them through the above definition step by step to look at what each part meant. By the time we were done with the definition for irrational, they had a great definition, they understood. I do believe it is important for them to be exposed to the mathematical definitions but its also know what they mean in understandable English.
I admit, I assume they have learned this vocabulary in elementary and middle school but I'm finding they are being taught the processes but not the vocabulary that accompanies it. I've been working on finding ways to help with that.
Check back tomorrow for ideas on how to increase their understanding of mathematical words and expand their vocabulary.