How important is it to learn how to explain how math problems are solved?

[nature girl]

My daughter (2nd grade) is better than I am at mental math, thanks to Singapore which we used before we switched to public school, and now Beast Academy. Because of this, and because in general she has an aversion to writing, she groans every time she's asked to explain her process, either in words or drawings. It seems like a waste of time to her, I guess, but I can't help thinking there must be some benefit to it or they wouldn't continually ask. (Her school uses Go Math, and there are one or two of these problems at the bottom of every worksheet.)

 

In general I see her point, it does feel like busywork. For example, if you can multiply or add numbers with carrying in your head, why do you need to draw pictures to explain how you've done it? Doesn't that negate the power of mental math? Is it just so teachers can follow their students' thinking, or is it a valuable part of their learning?

[Tanaqui]

Extremely important.

And some kids take longer to learn new concepts than others, or need more review later. What's "busywork" for one child is valuable practice and review for another.

[regentrude]

Absolutely vital.

Student who cannot explain how they are solving the problem and why they are performing every step have not actually understood the concept.

 

Now, making a student who has mastered a concept like multiplication explain every.single.problem with a picture is absolute overkill. But the student should have the ability to do so.

[nature girl]

Thanks...I've been pushing back in general against the school on homework, because she's SO exhausted after she gets home. I got the teacher to agree to let her do only one worksheet instead of two per night (as long as she's proven in class that she understands the concepts) and was considering pushing back even more, asking the teacher whether she could skip these problems. It's such a struggle...One of the problems asked how she was able to figure out a previous equation and she wrote, "By knowing math."  :closedeyes: Maybe I need to find a way of explaining to her why these sorts of problems are worth the time and mental energy...

[Tsuga]

Have her explain to her dollies or if she's not into dollies, an imaginary friend or a favorite book character.

 

That is the 2nd grade equivalent of having to explain what you did to management. You can also assume the same level of comprehension for the management and the dollies.

 

(Joking. I'm in management now. :D )

 

[EKS]

She should be able to explain what she's doing, and hopefully why she's doing it, orally.  She should not be required to do it for every problem.  The only reason that second graders in school need to be able to explain it in writing (pictures or words) is because of standardized tests and test prep.  

 

 

[nature girl]

She should be able to explain what she's doing, and hopefully why she's doing it, orally.  She should not be required to do it for every problem.  The only reason that second graders in school need to be able to explain it in writing (pictures or words) is because of standardized tests and test prep.  

 

 

The standardized tests ask them to do this? It seems like grading this sort of thing would be so much harder (and more subjective.)

[OneStepAtATime]

If she can explain it orally for one or two problems maybe the teacher would let you scribe her answer? At least sometimes?

 

And for what it is worth it can be hard to explain a lot of steps if those steps are often intuitive. She may do better if she had a vocabulary reference sheet and some example problems to refer to and maybe a step by step system of questions used systematically to help her figure out what to say, at least until it gets to be a smoother process.

 

For example, DH can take apart and put together tons of pieces of equipment or program a computer. He is abysmal at explaining what he is doing. He just KNOWS. He doesn't have to think through every single tiny piece of what he doing with actual words. When he has to explain to someone else he is having to try and link words to actions that he was not thinking of as words. He has to translate, for all intents and purposes. That makes it a slower, more tedious process. Perhaps that is part of what is frustrating your DD.

[nature girl]

If she can explain it orally for one or two problems maybe the teacher would let you scribe her answer? At least sometimes?

 

And for what it is worth it can be hard to explain a lot of steps if those steps are often intuitive. She may do better if she had a vocabulary reference sheet and some example problems to refer to and maybe a step by step system of questions used systematically to help her figure out what to say, at least until it gets to be a smoother process.

 

For example, DH can take apart and put together tons of pieces of equipment or program a computer. He is abysmal at explaining what he is doing. He just KNOWS. He doesn't have to think through every single tiny piece of what he doing with actual words. When he has to explain to someone else he is having to try and link words to actions that he was not thinking of as words. He has to translate, for all intents and purposes. That makes it a slower, more tedious process. Perhaps that is part of what is frustrating your DD.

 

 

This makes a lot of sense, thanks OneStep. I think that's exactly it, she doesn't think of the problems in words, just shifts the numbers around in her head (again thanks to Singapore...) and it happens so quickly she may not even understand fully how she's getting the answers. I think asking her to explain verbally is a great idea, especially because it'll be easier to scaffold and give her prompts. I'll see if her teacher is okay with me scribing. If we continue that way, over time it all may come more naturally to her...

[nature girl]

What's tiring her out?  Does she go to sleep right away?  If so, consider doing the homework after breakfast. If she doesnt have the handwriting stamina, you could scribe one worksheet for her.  

 

 

She has ADHD, and being forced into hours of desk time during the day is already so much more tiring for her than it would be for a neurotypical kid. By the time she gets home, she needs to let off steam...and then once we've had our walk or bike ride, it's almost impossible to get her back to the desk. She's just done. Mornings are even harder for her...(She's not a morning person.) The teacher has been very understanding and accommodating, so I'm guessing she'd be okay with me scribing. It's just been painful, seeing a kid who struggles so hard to control herself throughout the day feeling like that day has to be extended.

 

And it's only going to get worse as she gets older. But that's a stressful topic for another day...

[EKS]

The standardized tests ask them to do this? It seems like grading this sort of thing would be so much harder (and more subjective.)

 

Yes, they do.  This is at the heart of the problem with the Common Core.  The CC standards say that children are supposed to "understand" this and that.  Because of this wording, the tests are written to ascertain "understanding."  The most direct way to do this is to ask the student to explain her reasoning.

[Earthmerlin]

My daughter (2nd grade) is better than I am at mental math, thanks to Singapore which we used before we switched to public school, and now Beast Academy. Because of this, and because in general she has an aversion to writing, she groans every time she's asked to explain her process, either in words or drawings. It seems like a waste of time to her, I guess, but I can't help thinking there must be some benefit to it or they wouldn't continually ask. (Her school uses Go Math, and there are one or two of these problems at the bottom of every worksheet.)

 

In general I see her point, it does feel like busywork. For example, if you can multiply or add numbers with carrying in your head, why do you need to draw pictures to explain how you've done it? Doesn't that negate the power of mental math? Is it just so teachers can follow their students' thinking, or is it a valuable part of their learning?

My daughter uses Go Math as well & I personally don't care for the program all that much. I wholeheartedly agree with verbalizing one's thought process but I wonder if it folds into the classroom dialgoue. Discussing–that back and forth (building on one another)--is a truly important way to catapult students' development as mathematical thinkers and speakers. To me, in-class rich number talks provide the most bang for one's buck.

[bethben]

If she's doing GoMath, she may also be doing tests on the computer (if not now, probably later).  If they progress toward the computer testing (my dd is in 4th grade), she will eventually have to explain in words (no pictures because it's on the computer) how she got to her answer.  This process is going "really" well with children who have not been taught to type yet.  My dd's math tests take over an hour for less than 15 problems because they have them explain in words hen peck typing how they got their answer.  Knowing where this curriculum is going would make me advise that you have her write down how she got the answer.  Eventually, it will catch up to her if she doesn't get into the practice of being able to write down "why".  Go Math is one of the many reasons I am not sending my child back to this particular public school.  DD has come to the conclusion that she is stupid in math due only to this curriculum.  

[SKL]

I agree that it is often overkill at that grade level.  Huge waste of time if it's like what my kids were asked to do.

 

Can you suggest some shortcuts?  For example, when my kids were in primary, they learned to use one-stroke symbols instead of drawing pictures.  If they could explain it in words or numbers instead of pictures, they would do that.

 

Maybe you could get the teacher to agree to let your daughter do just one of the two explanations, since she understands the concepts well.

[Targhee]

Absolutely vital.

Student who cannot explain how they are solving the problem and why they are performing every step have not actually understood the concept.

 

Now, making a student who has mastered a concept like multiplication explain every.single.problem with a picture is absolute overkill. But the student should have the ability to do so.

Unless of course their conceptual skills outpace their communication skills. This was the case for my oldest. She later, like age 12, was able to explain, and went on to do AOPS classes with full written solutions (which she did ^really well*). So I guess I point it out to say that there times when mastery is there even if communication isn't. Though working towards explanation is very important (and something we worked on, gently but consistently, with oldest).

[eternalsummer]

The ability to explain it is important, the ability to sit through 10 problems of 5x7 drawing out little groups of 5 apples is not as important (educationally speaking - of course it may be very important for getting through school unscathed).  DS finds handwriting difficult and obnoxious and sees drawing sets of items to illustrate simple math problems to be an absolute waste of time (he also thought manipulatives were a waste of time), and because he can explain verbally how he does it, I don't worry about it.

 

But we took him out of school partially because of response to ADHD-type characteristics and the insistence on keeping his math skills as far back as his handwriting skills, so I'm not sure how to accommodate successfully in a PS setting.  Scribing is definitely a good idea if the teacher will allow it.

[Bluegoat]

I'm not convinced that this is actually something that comes very naturally to children at that age.  Partly because of their language skills and partly because of the level or type of math they are doing.

 

I remember asking my dd questions like that at that age, since the program said to - she looked at me like I was a complete moron and said that she got the answer because if you take x away from y you get z, and that's exactly what she had written thank you very much.  I eventually came to the conclusion that for the most part past where were using concrete markers, it was in the word problems where that kind of understanding became evident (or not).

 

I seemed to me that both my girls were closer to 12 before they could really put a lot of math ideas into language easily.

[Lecka]

I think you can definitely scribe for her. 

 

Then, when my daughter has these, a lot of times she will write something like "I added."  So -- it's not like you have to have some amazing answer.  I think it is more about getting kids used to just using words like "add" and "subtract" at a certain point, more than really explaining some mathematical process. 

 

I think if you talk about it more that is great, or if she has better answers that is great.

 

But I think maybe go more for just having her put something really simple and call it done! 

 

Is this homework-homework, or is this something that in theory would have been completed at school?  If it is "finish at home" stuff, I would really want to know what is going on at school, if it's something to address. 

 

"Finish at home" homework was always a sign of some problem with my older son, even though it would often not seem like much of a problem at all at home! 

 

If it is homework-homework, I saw advice recently to time how long it takes your daughter to complete, and if its longer than 10 minutes, maybe 15 minutes, or if she is frustrated with it, then go talk to the teacher.  The teacher may think it is taking all the students 5 minutes!  But teachers can't read minds to know how long it takes or if it is stressful. 

[Tanaqui]

If it is homework-homework, I saw advice recently to time how long it takes your daughter to complete, and if its longer than 10 minutes, maybe 15 minutes, or if she is frustrated with it, then go talk to the teacher.  The teacher may think it is taking all the students 5 minutes!  But teachers can't read minds to know how long it takes or if it is stressful.

 

The NEA and the National PTA both recommend a maximum of 10 - 15 minutes per grade level for ALL homework through the 8th grade.

 

However, some children will have different needs. Nature girl, I'm thinking on this - if your child has a formal diagnosis of ADHD, it may be possible to force the school to accommodate her homework needs. This might mean doing no homework, or having a hard limit on how much homework she has.

 

That is a separate issue from whether or not she should be doing this particular assignment.

[Bluegoat]

 

 

I can't easily show your comments, but my thoughts:

 

Yes, if something is totally natural I suppose it wouldn't need to be taught.

 

However there is also developmental readiness which you generally need before you can teach something with good results.  I don't think that I generally trust that curricula will have this just because they are popular  as many don't.  In this case, as some have suggested, teaching language to describe certain things could help a lot.  But I also wonder if readiness is an issue - I don't think it's just language that is getting better as they get older here so much as the ability to conceptualize real abstractions.

 

As far as killing two birds with one stone, sometimes that works but it can also hold back kids when their abilities are developing at really different rates.  I think it tends to work better in a homeschool environment when the teacher really can adapt the work to the needs and abilities of specific kids - in a classroom doubling up like that has a good chance of being a bad fit for some.  ETA: After all, many kids in grade 2 still need written and narrative output separated in language arts, where they fit together most naturally.

Edited January 31, 2018 by Bluegoat

[nature girl]

I don't see the work she does at school, I just see her balking at the work she brings home, but I'm assuming she has the same issue. This was happening last year as well, I remember her teacher saying she'd asked her to go up to the board and figure out how much a set of coins was worth and she got up to the board and just said, "95 cents." The teacher told her to explain to the class how she'd gotten the value and she said, "I looked at it and saw it was 95 cents." Somehow she couldn't (or maybe just didn't want to take the time to) break into words what she was doing in her head.

 

In a recent problem, the book asked them to add two numbers that required regrouping, and explain two ways of solving the problem. But she knew the answer within a second of looking at the numbers, so having to explain in words just didn't go over well. I'll be honest, I wouldn't want to do it either...it seems so annoying, and 10 times more for a kid who's been at a desk all day. (Funny story, a couple of months ago she gave me a sheet she'd written with 20 multi-digit addition problems, she wrote out an answer key and everything so she could grade it. So I did the problems and when I was done she said, "Okay, HOW DID IT FEEL to have to sit there and have to do the problems? When you saw it, did you want to do the problems or play? Really good point.. :) .)

 

I've gotten accommodations on homework, where she only needs to do 1 math worksheet and her spelling work rather than 2. It still takes 10 times longer than it should, because getting her to sit at her desk is a chore, and then she gets distracted after 1 or 2 problems and starts drawing pictures or hanging off her chair. Each problem goes very quickly, but with all the distracted time, the actual time at her desk takes much longer. If she could work non-stop, she'd be done with math in less than 5 minutes. I guess that's why I was hoping there was no reason to do those problems, because I'm sure she'd complain and dawdle less if she knew she could skip them.

 

I've asked her the past couple of days if she wanted me to scribe for her, and she told me she didn't want help...which surprised me.

 

[Lecka]

Do you know what a sample good answer would be?  If you did, you could write her a template to copy.

 

Like for adding coins, I don't even know, but I'm assuming they want something like "I added the coins from largest to smallest" or "first I added the quarters, then I added the nickels, then I added the pennies." 

 

If a lot of things with adding are going to be "first I added _______, then I added ______," that kind of template would really help my son to get started.  And I think over time it can be more engrained when it's the same template every time. 

 

Even "first ____, then ____" is a really useful all-purpose template. 

 

Or having a word box with "first, then, next, last, add, subtract, count, tens, ones," etc, words that might be used in an answer. 

 

Those are all things that they might have up on the wall in her classroom, too, I think it's good to have available at home, too. 

Edited February 2, 2018 by Lecka

[Lecka]

I also think -- at a certain point, I don't care how much time is wasted time.  At a certain point I think tell her teacher "I'm cutting her off at x time." 

 

I also think it might be a strategy to tell her "I am setting the timer for 5 minutes, if you can show a good effort for 5 minutes, I will let it be done."  Or -- give a long break instead of letting it be done, if that is what you want to do.  Or -- if you see it's going to be reduced work, maybe pick that she starts with the 3rd problem or something like that, so that she gets to the last problem if it is one where she could need more practice. 

 

I would just do this.  It's not right for it to take so long, it doesn't matter if your daughter is dawdling, it is still taking that time, and it is too much time, imo. 

 

Edit:  My younger daughter is getting into an age where she has homework sometimes, and I am so mad sometimes at how EASY it is for her.  She truly just sits and does it, no big deal.  It shouldn't be excessively more difficult, for any reason, than that, for any kid.  I did a lot for my older son as far as not having him doing things or scribing, and now ----- I even wish I had done more with seeing how easy it is for my daughter. 

 

It's more complicated if more practice is needed for a child to master the material, but it doesn't sound like that is the case here at all.  If practice is not needed to master the material, it is just ------ there is no reason.

 

Your daughter might honestly need less work to master the material, too.  She sounds like she is picking things up easily to me (my impression lol).  If she honestly needs less practice, then less practice can be what is appropriate for her!  The same way another child would need an amount appropriate for him or her, that might be more or less. 

Edited February 2, 2018 by Lecka

[Lecka]

When I did the timer strategy with my son, if I thought he was truly dawdling then I would pause the timer until he quit dawdling. 

 

I wouldn't do this if he was dawdling/thinking, which he does legitimately do sometimes.  And if he was just totally dawdling, I would probably just say "let's come back to this in a few minutes and try again." 

 

But it's amazing sometimes, when he knew there was a 5 minute maximum, sometimes he could actually get a lot done in 5 minutes! 

 

He had a lot of issues with things looking too long and imposing, it made it hard for him. 

 

You also might re-direct her more with more stuff like "let's see what number two says, can you tell me x (the first step that you supply to help her get started)," if stuff like that would get her back on track more quickly.  My younger son does really well with that kind of thing. 

 

My older son also had some nonverbal reminders at school, this is like tapping his desk or something, where there aren't words used which can be more distracting for kids sometimes.   

 

[Lecka]

It seems really simplistic but sometimes even trying things like covering up most of the worksheet with a blank piece of paper can help with focus. 

[Lecka]

I would say too, if she does seem like she likes the timer idea, watch her -- 5 minutes might be too long.  If you see her want to do it and have a good start, but then she is dawdling after 3 minutes, then make it 3 minutes! 

 

Or start with 3 minutes if you have any thought 5 minutes might be too long.  Then after a while you can say "you are doing SO good with 3 minutes, I'm going to make it 4 minutes now, I think you can do it." 

 

I have done very short times like even 2 minutes on some reading things that were very hard for my son and took a lot of concentration, he would have a thought process like he had to save some energy back so he wouldn't be totally depleted to zero, so he would hold back some.  But if he knew if he worked hard then he could really have a break, then it freed him to work hard and not worry about saving his energy.  He was only like that about a few things but when he was it made a big difference, and he really couldn't work hard for very long at all, but he could do very well in that short time. 

[nature girl]

These are really good ideas, Lecka. Thank you!!!

[Lecka]

A lot of my suggestions are suggestions I have gotten from teachers.  So if there is some strategy that works for her teacher at school, that is something you can ask her teacher. 

 

My older son and my younger son are different, and most of my suggestions are for my older son, she sounds like my older son.

 

But for my younger son ----- when he does dawdling type things, there is an attention part to it.  He might be a little lonely or need some emotional connection or reassurance or something more like that.  With him he DOES like the chatty "let's look at this," type stuff.  My older son is driven crazy by this a lot of the time, it is very, very distracting to him. 

 

But if there is any element of wanting to hang out, then you MUST have your hanging out be focused on "let's check out your homework" and not on "look, you're dawdling again, now you're hanging off the chair." 

 

If you back off to give her space while she is working, and then come closer when you notice she is dawdling, she might be a little lonely and want you to come sit with her. 

 

It just depends what you are seeing. 

 

My younger son loves any comments about "wow look how good you are doing."  Like -- to the point of ridiculousness.  That is how he does his best work with me ;)  If he's not getting attention for doing things good, he is pretty happy to switch to getting attention for messing around.