In my post “When vocabulary isn’t the issue” I got the impression it was difficult to “step inside the head” of a student who misunderstood that particular problem from a reading perspective, so I thought I’d give an example that has a better chance of simulating the experience.
This is a puzzle called Slitherlink. I gave it to my students and asked them to attempt to work it out simply from the directions, but out of 100 or so students only a handful managed without extra assistance. (They were given that the word “adjacent” means “next to”, so the vocabulary was not a problem.)
I have given this to adults who also needed extra explanation, so don’t feel bad if you’re unsure at first what to do.
Draw a closed loop by connecting dots. Each number in the puzzle specifies how many adjacent sides are included in the loop. A zero means no part of the loop passes next to that number.
Here are four sample puzzles of the type:
This example is less than optimal in that (unlike the last post) I know how to teach reading for understanding here, but still, I’m curious: did you have difficulty, and how did you extricate yourself? How would you teach reading the instructions to this puzzle?
Filed under: Education, Mathematics, Puzzles, Reading |
The Number Warrior 
“Closed loop” is maybe a non-standard usage of those words. “Loop” usually means curvy (like an oval or circle as opposed to boxy like a square or the example image) to most people and “closed” can be applied to doors, mouths, boxes, etc. but for most people I’d imagine “loop” implies that it’s connected again. I could see troubles there with even native-English speakers.
I can see how you could walk a person through it (maybe color coding the example with a blue 3 and the 3 adjacent walls also being blue, for example), but I’m not quite sure how to make the written instructions more easily accessible.
Also, as mathematicians we have to tread the line between accurately describing our object (“a right, circular cylinder”) and the usual understanding of an object (“a can”) that may be more easy to understand, but less accurate. My native English speakers have trouble with that sort of thing all the time (“Why didn’t you just say a can?”).
(I also don’t really understand the x’s in the example image.)
The xs are where (by logic) there can’t be walls of the loop.
Well, it doesn’t limit the ways that two dots can be connected. This is kinda implied with the sides statement, but not explicitly stated, So I could understand there being questions of whether or not a diagonal line is acceptable, particularly between dots where there is no number.
Good point!
If you all are curious, the directions here came from a puzzle website. For the puzzles I used a generator, because I couldn’t find 4×4 sized puzzles anywhere.
I’d rewrite those instructions backwards and connect it to something most of your students would already know – Minesweeper.
First explain that the numbers tell you how many straight lines are next to each number. “Like minesweeper, but with lines instead of mines.” Dang, that even rhymed.
Then add “Now the trick: the lines need to all join up into one big closed shape. You can add extra lines next to spaces that have no numbers.”
Do you think it might be helpful to try to get students to rewrite instructions themselves? I’m fishing here for ways to get students to handle this kind of (ambiguous, vaguely worded) writing when they don’t have a teacher with them.
The part that tripped me up was the sentence “Each number in the puzzle specifies how many adjacent sides are included in the loop.” I read the phrase “adjacent sides” and was immediately befuddled. Adjacent to what? To each other? If you have a single loop, don’t all of the sides have to be adjacent to other sides? I eventually figured out what was going on by staring at the example solution for a while.
For the record, I would phrase the instructions like this:
Your goal is to draw a closed loop by connecting pairs of dots with straight lines. Here’s the catch: a box containing the number N has to have exactly N of its sides filled in—no more and no less! So, for example, a box with a 3 in it has to have exactly three sides filled in. A box with a 0 in it can’t have any of its sides filled in.
Honestly, though, written instructions aren’t very helpful for a game like this. I think the best approach is to demonstrate the rules by doing some examples on the blackboard! If I couldn’t do examples live, I would at least give a solution and a non-solution, with explanations, on paper.
The point of all this is that on a standardized test, I will not be there to do rewrites, or run examples. The students need the ability to parse instructions on tests like the PSAT which, quite frankly, are often confusing and badly written.
Ohhhh! [Sheepish.] I guess I should have spent less time reading those instructions, and more time reading your posts. 🙂 Unfortunately, I don’t know much about the art of reading crappy instructions, although I’ve thrown in another two cents on the last post anyway…
Could it have to do with the Cognitive Miser issue they talk about here: http://blogs.discovermagazine.com/cosmicvariance/2009/11/04/are-you-a-cognitive-miser/
Not really. The cognitive miser issue is regarding someone who thinks they understand something and acts too quickly. This is regarding students who try yet don’t understand at all and are paralyzed.
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