This problem is from Engageny math. Here's the sheet I assume it appeared on. Grade 2 - Module 3.
Here's Andrew Gelman.
Speaking as a writer, and as a parent who spent a lot of time teaching my son and myself grade-school math, I don't like the wording at all.
"Sally did some counting" ---- the word "count" means count by ones, especially to a 2nd grade child.
Plus the question about why Sally did what she did invites commentary on Sally, not Sally's method.
Is there a way to ask this question that makes more sense?
And is there a reason to ask it this way -- to ask a student to analyze Sally's answer -- rather than to ask the student to use 1s and 10s to count up to 214?
I have to say .... offhand, I see no reason to ask this question this way.
I would much rather see this as a story problem about giving change.
Sally has pennies and dimes in her pocket.
Her friend Jane sells her a glass of lemonade for $2.14.
Sally gives her $1.77.
How many more pennies and dimes does Sally owe?
That wording doesn't produce the specific sequence, of course ....
What if you just said, "Count up from 177 to 214 using the fewest (whole) numbers you can. You can count by 1s or skip-count by 10s."
Here's a question.
Does "skip counting" by 10s only mean 10, 20, 30, etc.?
Can it mean 177, 187, 197?
Who would count by ones, switch to tens, then go back to ones? Too anxious to pass a 100-boundary by ones, have to skip over it?
ReplyDeleteThat is some really weird whistling-past-the-graveyard math reasoning.
(I'm only half kidding.)
Who would count by ones, switch to tens, then go back to ones? Too anxious to pass a 100-boundary by ones, have to skip over it?
ReplyDeleteThat is some really weird whistling-past-the-graveyard math reasoning.
(I'm only half kidding.)
The real answer, obviously, is that Sally's math teacher was an idiot.
ReplyDeleteThe test writer's English teacher was also an idiot, but that doesn't enter into the correct answer to the test question.
(I find that question an offense to good test design in many ways. I'd be willing to bet that there's only one officially correct answer, even though "Because she saw a butterfly" should be equally acceptable. I very much like the student's response, though.)
For those of us who haven't learned or taught
ReplyDeletemath this way ... what is the question trying
to get at? Because I have no idea.
-Mark Roulo
Hey Doug!
ReplyDeleteLong time, no see!
I've got an even better one to post.
Can't figure out the answer (and it's a first-grade worksheet, not 2nd grade)
This problem is supposed to teach place value .... counting by ones and skip-counting by 10s.
ReplyDeleteBut as I thought about it .... she could have counted up by any number at all. She could have "skip counted" by 37 and gone directly to 14....
This curriculum is supposed to be based in Singapore Math.
ReplyDeleteI would think if you'd want to show skip counting and place value relationship, you could do something some human might actually do -- like maybe starting with 10s, and then shifting to 1s when you have less than 10 left to go to your target number. That's even appropriate.
ReplyDelete"This curriculum is supposed to be based on Singapore Math."
ReplyDeleteI used Singapore Math through about grade 5 when teaching my own kid.
I'm a bit sloppy, but I don't remember anything like this.
In fact, I don't remember any "explain why you think XXX did something" questions.
In this case, I'd suspect "based on" means that same thing it does when a Hollywood movie is "based on" a book: We want to use the title because the title comes with some marketing value ... other than that, don't make any assumptions.
-Mark Roulo
Perhaps Sally is counting the coins in her piggy bank and converting everything to cents so she can have fun with larger numbers while deciding if she has enough for an ice cream cone.
ReplyDeleteThe purpose of the problem is to show that the number after 180 is 181, but that the student makes a mistake and thinks after 180 comes 190.
ReplyDeleteA better way to find out if the student knows the whole number after 180 is to ask: What number is one more than 180? How many more than 180 is 190?
These queations I posed are Singapore like questions.
Worse, students won't make this error. They do make errors across "zero" boundaries all the time, but not these. Twenty eight, twenty nine, twenty ten is a common error. Not knowing whixh ten xomes after thirty nine, because thirty doesnt aound quite close enoigh to three. Asking a student to "count by tens start at 37" often leads to 37, 38, 39, 40, 50, 60.
Scott Baldridge had a staff of hundreds? Helping him. That's the problem
He expects this to get better over the years. Too bad this kid isn't in stasis til he is done.
examine other beauties.
ReplyDeleteWe are about half way through second grade Singapore Math, Primary Mathematics -- you have to watch it these days because Math in Focus, based on Singapore's updated curriculum, not the version homeschoolers mean by "Singapore Math," is labeled Singapore Math, so is often what teachers mean when they say Singapore math. But yes, definitely in Primary Mathematics, you wouldn't get a question like this. You might be asked to break a number down into hundreds, tens, and ones, or to skip count by 2's, 3's, 5's or 10's from any random number to another one, but nothing this unclear.
ReplyDeleteHonestly, it is part of what I like about the curriculum. My (admittedly mathy) kid can work through a lot of it without much help, once we introduce the basic idea, because the questions are so clear.
I know this one has quieted down, but I am going to take a shot at defending the question. (To do this, I may be inventing a context that the problem doesn't provide. But maybe the classroom discussion did provide it -- or at least might have.)
ReplyDeleteSally already has a pile of 177 pennies. You give her another pile and ask her to count up to get her new total. She counted by 1's to get to 180, then she made groups of 10's and counted that way until she didn't have enough to make a full group of 10 at which point she reverted to counting by 1's.
So Sally is not actually confused at all. She is kind of math-y and clever. Math-y people create little strategies like this all the time. It would not be a bad thing to use a small portion of class time to encourage this kind of thing and show it to all...and we may be talking about a single item that took up say 2% of the math instruction time that week. But the internet does not know that so the problem becomes the target for math war artillery practice.
Anyone who comes into my classroom can see that I am pretty far to the direct instruction side of the spectrum. But it IS a spectrum. And the internet encourages this kind of selective mockery of things that are not as wrong-headed as they may seem out of context.
Having said that, 5x3 is still 3x5, dammit.
Phil
Phil, then it is still bad teaching. If this is homework, then the teacher is assuming that the classroom discussion provides the context, but honestly, even with college students, if it was discussed in class but unclear on paper, it will be unclear at home. With second graders, who are going to get help from parents, clarity is really important.
ReplyDeleteIf it had been put in terms of money or some other context where counting from 177 to 214 had some kind of motivation, I think it would be fine, but as it is, the answer given is as sensible as anything else.
You may be right, but I don't know...we weren't there when the lesson happened. If they modelled this kind of thing and then did it in groups and then watched a video and sent another home...well, you get my drift. Or if it was intended to be a challenge, maybe it was sent home with that warning: here's something that you may have to think about -- we will play with it more tomorrow. Or maybe you are right and the teacher does not know the answer or why they are doing this. Does EngageNY come with a key? I'd be curious to see the "official" answer.
ReplyDeleteI'm just saying that the item itself is not as inherently silly as people are saying. Whether it is taught effectively or not is a separate and important question but not one that the picture provides sufficient evidence to answer.
My point is, it was sent home. The minute it is sent home, it should be as close to self-contained as possible, because not every student will REMEMBER all that context. And this generation is particularly bad at that -- I say things and write things on the board (which they then photograph with their phones) and they still don't remember what I said. And this is with college students, not second graders.
ReplyDeleteWell this is second grade: I don't see why there needs to be more than 5 minutes of homework per night of any kind. But again, do we even know that this was "sent home" as an assignment? It just appeared as it is in my facebook feed...we don't know that it is even a student's work. Could be a subversive teacher or parent looking to make a humorous point about a math question that seems silly to them.
ReplyDeleteBut as for the students, yes, they do all need context and a cell phone won't do it.
Student: "I was out yesterday. Did I miss anything?"
Me: "Did you get the notes?" [...meaning: you borrowed good notes, transcribed them carefully, noting points of your confusion that you will come to extra help to ask about...]
Student: "Yeah, I got them. No problem" [...meaning: I took pictures of my friend's notebook. They are on my phone....]
As worded, there are several possible right answers--one of which the child gave (counting mistake). I was assuming they were looking for an answer that the problem was figuring out 177+37 or perhaps 214-177, in which case, the wording is pretty vague...
ReplyDeleteIt looks like a great problem to ask college students studying to be elementary teachers, but I'd reword the question to be: if a child successfully solved a problem by doing this, what could the problem be?