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.