Keeping an algebra vocabulary journal

A tutor wrote to me about this student:

K. is 15 years old...She said she struggles in her algebra class with the words and completing problems.

I reply: It's not uncommon for students to struggle with "academic English" even if their social English is flawless, because you just don't use phrases like "fill in the blank" or "solve for x" or "turn to page 104" with your friends, you know? In ESL world, we refer to social English as BICS (basic interpersonal communication skills) and academic English as CALP (cognitive academic language proficiency). Most language classes don't teach a lot of CALP, and low CALP is a big barrier to academic success. So we want to work on boosting K.'s CALP in algebra class. I'll give some suggestions for this below.

In addition, K. is learning algebra as she's learning English, which is hard to do. As much as possible, try to separate the math from the English so she can learn one at a time. How? Take some easier problems from a few chapters ago where she already understands the math and use those as contexts to practice English. The gist of your vocabulary lessons can be something like:

"Simplify is the English word that means do this action" and demonstrate the action of simplifying with some algebra problems (or other math problems) that are relatively straightforward and uncomplicated. Then, once she has an idea of what simplify means in English, help her simplify the more complicated problems in today's homework.

Throughout the semester, be on the lookout for CALP words and phrases that K. may not understand. I highly recommend having K. keep an algebra vocabulary journal, ideally in a physical notebook or ring of file cards that is specifically set aside for this purpose. Here, she can write words and phrases that she needs for algebra. For each entry, she can have example problems, notes in English, notes in her first langauge, pictures, diagrams, references to the textbook, or whatever will be helpful for her to understand what the word or phrase means. Encourage her to add entries during your tutoring sessions and also outside of tutoring sessions. Check her work to make sure she's defining/explaining the terms correctly. When you begin a tutoring session, ask if she's added to her algebra vocabulary journal, and if she has, check her entries and maybe have her demonstrate her understanding of the terms. Make whatever corrections are necessary, and make a point to encourage her taking ownership of her learning in this way.

She can continue to add to the journal for as long as she's studying algebra, and she should have it handy any time she's doing algebra (in class, working on homework, in tutoring, etc.) so she can refer to it easily.

The book tells me to 'simplify the equations.' I can't remember the word 'simplify.' Oh, I think I have it in my algebra vocabulary journal. *flip flip flip* Oh, right, that's what it means. Ok. Now I'm ready to tackle the algebra.

It's been a while since I did algebra myself, and I don't have an algebra textbook with me, so it'll be up to you and K. to find words and phrases that should go in her algebra vocabulary journal as you're working. Keep the focus on terms that are going to be useful for her, not terms you happen to remember from algebra class back in the day. Here are some ideas:

• solve for x

• write this in slope-intercept form

• evaluate

• simplify

• graph the equation

• x-axis, y-axis

• positive slope, negative slope

• absolute value

• slope (m)

• formula

In addition to keeping the algebra vocabulary journal, here are some other ideas to give her a boost, depending on her needs:

• If she sees "29", can she instantly say "twenty-nine"? If she hears "twenty-nine," does she instantly think "29"? Can she do this without counting?

If this is an issue, use cards, dice, or any random number generator to practice. The low-tech way to do this is to write the digits 0-9 on file cards three times, so you have three cards that say 0, three cards that say 1, three cards that say 2, and so on. Draw two or three cards at random and combine them to make a number (for example, if you draw a 2 and a 9 then you get 29). As she builds proficiency, use a timer and make it a game to see how many she can do in a minute.

• Can she look at 2x-3=x+2 and read "two ex minus three equals ex plus two"? If this is a problem, take some problems in her book and guide her in practicing reading them out loud.

• Practice these flashcards with her.

I hope that's helpful! As always, please get in touch with any further questions!

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