A system for helping language learners read mathematics

I have twice before now (here and here) pondered over the issue of how to help language learners past the reading of mathematics, particularly in a standardized testing environment.

Our school has implemented a system by Larry Bell termed UNRAAVEL, with posters in every classroom. Here’s the Math UNRAAVEL poster:

Underline the question
Now predict what you think you need to do to solve the problem
Read the word problem
Are the important words circled? (Especially the clue words?)
Apply the steps you chose to solve the problem
Verify your answer (Is it reasonable? Does it make sense?)
Eliminate wrong answers
Let the answer stay or rework the problem

I have tried to implement this in my classroom, with little success. Here are the issues:

1. The acronym is terrible as a memory aid. The first letter, U, suggests an immediate verb (Underline) which stands on its own without the rest of the phrase. The second letter, N, stands for Now, which suggests nothing at all. Recently, attempting to reconstruct the list from memory (and having taught it multiple times) I got only 5 out of 7 right; I’m fairly certain the students would do worse. A successful acronym would have every letter cued to a specific verb so students only have to remember single words.

2. It isn’t sensitive to misunderstanding by single word changes. To go back to Kate Farb-Johnson’s example:

“There were 90 employees in a company last year. This year the number of employees increased by 10 percent. How many employees are in the company this year? A)9, B)81, C)91, D)99, E)100

What if a student dutifully highlights “10”, but misses the percent? Optimally the student shouldn’t circle individual words, but the entire phrase “increased by 10 percent”.

3. It’s too much fiddly work. By “fiddly” I mean “stuff that’s part of the procedure that isn’t useful for every problem but we’re doing it anyway as part of the procedure.” Some math problems consist of only the question, so underlining the question followed by predicting what is needed (already observed) and reading (already done by the act of underlining) is overkill. Even when I hand-selected problems I felt rewarding to a lengthy process, the students rebelled and skipped doing most of the steps.

Going back to the employees problem, let’s see what could happen:

Underline the question: How many employees are in the company this year?

Now predict (etc way too long): Er … we’ll get numbers and we add them or something? With this (and many other math problems) there just isn’t enough information to do a prediction at this stage.

Read the word problem: With the aid being the question is underlined so we have the “punchline”.

Are the important words circled?: Problematic for reasons I already mentioned.

Apply the steps you choose to solve the problem: Taking the acronym literally, the student will have already chosen the steps by this point. Putting that aside, the process doesn’t provide the holistic understanding, the mental image of (or equivalent to) this:

Verify your answer: On this particular question past the point of answer to know what “reasonable” is, unless one happened to catch on rereading a missed important word (that one was previously ignoring because they forgot to highlight it).

Eliminate wrong answers: Wait, we are doing this now? On multiple choice tests even in a reading context doesn’t that come earlier?

Let the answer stay or rework the problem: The acronym’s the kicker here; students remember the “let the answer stay” part but not the “rework the problem” part.

So after a year of fussing and finagling, I have my own process, which I present here. It’s still “fiddly” by my definition, but it’s the best I’ve been able to summon so far:

Underline the question: Still not a bad starting point.
Read the problem: Prediction is one step too many.
Box words you don’t know: Half-baked psychology here, but the idea is to “contain” the tricky words, which may be entirely unnecessary to the problem. This can be coupled with a method of working-definitions-from-context.
Circle key phrases: NOT key words.
Diagram the problem: In my mind, the largest omission of Larry Bell’s original system. Not every problem needs this, but the ones that do are hurt by the reading-emphasis approach.
Eliminate wrong answers: Check earlier rather than later.
Rephrase if needed: From my blog experiments the most powerful technique seemed to be rephrasing.
Solve and verify: As a separate step, students never verify. I want them to have the impulse that every time they solve they also verify.

New acronym: UR BCDE RS

It doesn’t resemble a word (and probably is better for it because students don’t have to remember to misspell UNRAVEL) but it’s cute enough to use as a memory aid.

9 Responses

  1. Thanks for posting on this issue. I really want to find more ways to help students with reading word problems. Diagramming and rephrasing aren’t techniques I’ve taught before, but I’m going to add them to my repertoire now.

  2. This seems like a dilemma inherent in algorithmic problem solving.
    I’m having a tough time getting past the fact that most students would answer 100 to that question, and for all practical purposes, they’d be right.

  3. I’m having a tough time getting past the fact that most students would answer 100 to that question, and for all practical purposes, they’d be right.

    Not if I’m the 100th employee who doesn’t get a desk when they rearrange the cubicles!

    I’m really tempted to try to finagle your much improved acronym until it spells something, but I think that would probably involve dipping too deep into the vocabulary bin to help your target students. Maybe add an ‘A’ to fill out the ABCDE center section, like Read it All, or read it Again?

    • I’ve still been scratching my head over this one. To be honest optimally it ought to be shorter, not longer.

      One thing possible is to shuffle Eliminate and Rephrase:

      UR BCD RES

      Which sounds like something a text-messaging student could remember pretty well.

  4. Hi, Jason.
    I feel your pain. I teach primary kids in a multicultural setting, so I get non-readers and readers of other languages, etc. I’ve been using a process (stolen from my son’s math teacher) abbreviated to Dr. Ape. Draw, Restate, Answer, Prove, Explain/Extend. By drawing and restating (with hands on manipulatives), we really get to understand the problems. After that, the rest is easy. Check out http://web.me.com/Iainbro/105/Math_Performance.html and you’ll see some examples of how six and seven year olds replicated Gauss.

    What’s needed is less, not more. Simpler, not more complicated and all-encompassing.

    • Thanks for sharing!

      Keep in mind the above system is specifically geared for standardized tests, so extending would be overkill (especially on a timed test like the SAT).

      The length issue is part of my “fiddly” rant. I do think it’d be doable to cut the UR and stick with BCD RES. Part of the problem is there’s sometimes already a picture, but my just-passed-the-English-proficiency-test students aren’t able to shoot for Rephrase right away, so the box and circle steps give them something to do.

  5. Hi Jason.

    I think I need a Read-underline-read system for myself…

    I read only the title of the post, and then my eyes were drawn to the first box (the UNRAAVEL explanation) and I shook my head… I was so disappointed.

    And then I actually read straight through and saw that you agree.

    I wonder if there is a way to address my habit of jump-reading. I wonder how common it is.


    • I thought of making my title something ranty about Math UNRAAVEL, but I decided to keep it positive. I see how that could be confusing at a glance.

  6. […] A system for helping language learners read mathematics […]

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