Here, go and **read through this task from Illustrative Mathematics**. I’ll wait for you. Pay attention to the use of academic language in the task.

Here are the academic vocabulary words I noticed students would need to understand (in an academic sense) in order to be able to do this task without any support:

*table, random, data, scatterplot, selected, relationship, linear, equation, least squares regression, line, interpret, points, variability, estimate, expect, more than, less than, predicted, amount, more, less, residual, difference, calculated, plotted, corresponding, number, set, explain, determine, appropriate, describe, sample, diameter, plot, fit, area*

Students might not know some of these words and still be successful task as they can use the other words (including the non-academic vocabulary) in order to make sense of what those words mean. It could also be that through doing this task and talking with other students about it, they can learn some of the words that they did not know.

All of these words are important words for students to know and to be able to use in appropriate contexts if students are going to be able to participate in the wider mathematics community. We cannot strip language, either common or academic, from our mathematics classes and expect students to be successful. As Harold Asturias has reminded me a few times, in order to have complex ideas, we need complex language to describe those ideas.

On the other hand, we can be thoughtful and deliberate in how we introduce new words to describe ideas to students. Specifically we can:

- When students describe an idea but do not use the language a mathematician might to describe it, you can revoice their idea (or other students can) using the language that a mathematician might use, being careful not to introduce so many new words that students cannot piece together what each of them means.
- You can use mathematical problems with sufficient text for students to make sense of the mathematics and to use the context to make sense of the new words to which they are being introduced. Again, words should be introduced strategically because a page full of words students don’t know will
**sound like gibberish to them**. - You can introduce words through multiple contexts including text, words, visualizations, mathematical problems. This way students can make sense of what the word sounds like, would be used in a sentence, would look like if drawn, and how it applies to mathematical ideas.
**You can use the mathematical practices**to situate the language students need to learn within the context of the problems they are trying to solve.

What else can we do to help students use language to make sense of mathematical ideas?

Firstly, avoid unnecessary words that are used only by mathematicians, for example associative, commutative and distributive, especially when the explanations I have seen on teaching websites are garbage. Exception: matrix multiplication (“multiplication” is not the best term – there isn’t one unfortunately)

Secondly, use the proper terms. I am thinking of “u-substitution” in calculus. This is a “change of variable”.

Go back to “take out the common factor” and “expand the brackets (parentheses in the USA)”. Some of the attempts to make math more “mathematical” are leading to even greater confusion.

Yes, encourage them to learn and understand the use of the “proper” words, but while they are still having trouble understanding and explaining stuff in simple language the last thing to do is to burden them with “the proper words”.

I looked at the CCSS doc but could not find HSS-ID.B.6.b

The stuff looks like AP Statistics, and no student is going to be having a go at the quoted problem without having seen all the words before.

I taught Statistics for many years, from pie charts to factor analysis, and this problem is one of the worst ones I have ever seen. Poor kids!