Hi,

New here, although I've been reading and appreciating these forums for the past several weeks! Hoping for some advice on this month's challenge.

DS ( just turned 7) has tested as PG, with exceptional math ability but overall quite balanced scores.

He's in second grade at a private parochial school, but in third grade for math. (Kindergarten was a great Montessori experience, we relocated and suffered through a very difficult private school first grade year and are so far, glad that he is happy and that we aren't getting weekly stresses from teachers, principal or son.)

However, math homework is a problem. Some of it is far too easy, but he typically does it without complaining. The problems are in two main areas. One is when the worksheet requires him to "explain how you got the answer." I'm hoping someone has a good way of coaching a kid who does the problems seemingly without thinking (I know he does think, but the speed is amazing.) on how to come up with an answer, preferably without crying and melting down. Or, do we need to talk about this with the teacher? I did hear something in a pre-start of school conference that troubled me, about how with this new curriculum "gifted" kids couldn't always answer how they did it... meaning the curriculum developers thought that was bad/the kids didn't know it and thus needed to be forced into doing so... I read conflicting information on this topic. He does have a solid foundation on relating concepts to manipulatives from his Montessori days, so it seems like backtracking at times to explain the process.

The other issue is that his math teacher has supposedly told him if something was "too hard" to just write that down. Bingo, instant out so he can stop doing homework and read or play... until we figured out what was happening and ruined his glorious plans. It appears that the "too hard" pages may be material he's not covered before. I've been giving him brief explanations and he can always do the work, other than the resistance to any questions that ask him to explain his work. He doesn't particularly like writing and his handwriting is sloppy. Not sure if that's connected or not to the resistance.

He told me last night that the pages he's been writing "too hard" on are assignments only he gets, that the other kids only get the ones he's been doing (he developed a keen sense last year of when he was getting additional, vs. appropriately different, work, so I tend to believe him). We're going to meet with his second-grade teacher and are going to get a connection to the math teacher to get to the bottom of this...

BTW, I apologize for the long-winded message!

Welcome ConnectingDots

I think the problem with not knowing what to write as an explanation to show how you did your math homework is a *really* common problem - it didn't come naturally to any of my children, two of whom are very talented at math and one who has struggled with learning new math concepts. With my kids, when it was early elementary, if I knew they knew how to do the work, understood the concept and it was simply easy enough for them to do the work in their head or without really thinking, I didn't worry about whether or not they wrote anything down for the "show your work" questions. This didn't go over well with some of their teachers, but I had to remind myself, this is only early elementary - unless this is preventing them from moving ahead with more challenging math, I just let it go and ignored the complaints from the teachers. I *did* always first ask my child why they were having a hard time with showing their work, and explained to the teachers what the issue was but if the teacher was sticking firmly with must-show-work I just stayed zen about whether or not that part of my child's homework was blank.

Re writing "too hard" - I would tell my kids that *I* wasn't going to let them write that, even if it was ok with the teacher. We haven't had exactly that issue, but we have had a few times when teachers tell our kids they can skip things that I as their parent think are important for them to learn/do, so we tell them they have to do it because we said so. Sounds domineering and non-child-centered.. but.. it's only a few things here and there

Re not particularly liking writing and having sloppy handwriting - if nothing showed as a concern in his testing, I wouldn't worry about it - all of that is fairly typical at his age. If you start to notice that he is slouching over his work, has an odd pencil grip, rubs his wrists a lot or seems to have much sloppier work than his classmates, then I'd wonder if something else was going on and if discomfort with handwriting was causing part of the reluctance to answer the problems. Having a child who was showing resistance to handwriting that was related to an undiagnosed (at the time) disability in K-1, the thing I noticed about reluctance to write was it was across the board on *all* homework, not just the "show your work" problems in math.

Best wishes,

polarbear

Polarbear -- thank you! We told him as soon as we discovered the whole "too hard" thing that it might be okay with the teacher, but not with us. He still thinks us patently unfair, of course, but so be it. However, he usually does his homework before we pick him up from school and has been trying to get past us by saying homework is done. Lovely.

He is extremely farsighted (corrected and making great progress thanks to a wonderful eye doctor). My guess is that he's not as coordinated on writing yet, given that he also struggles with tying his shoes. (He can do it, but dislikes it as they don't always stay tied.) We will watch for what you mention.

When DS was in 1st grade they had a short template that went along with the word problems. It was 4 fill-in-the-blanks (I don't remember the terminology used, but it was something like this):

data (4 apples, 3 apples);
word clue (the word(s) used in the story problem, like started with, gave, ate, etc);
operation (add, subtract, etc, what you need to do to solve the problem);
math sentence (4 + 3 = 7).

The teacher had this written underneath every single word problem, so it became a habit to read the story and fill in the blanks. The teacher must have had lessons on which words gave the clue to the operation.

The math was much too easy for DS, but since he had to fill in the template after each problem, he was forced to think a little about how he arrived at the answer.

As for claiming some of the math is too hard, I do think it's important to push a little on this. DS has fallen into the habit of quitting when the work gets challenging, and it's proven hard to get him to move even slightly beyond his comfort zone. Nip it now, because it doesn't get easier!

[nodding] Yes!

I also agree with KM-- both that it doesn't get any easier as they get older, and that you'll want to push a little on the challenge front.

I love KM's description of that teacher's method of encouraging students to tackle word/context-rich math problems systematically-- that is GREAT!


Math has been the subject of Battles ROYALE at my house, between two volatile and assertive PhD parents... and one self-determined, perfectionistic PG princess*.

* as in The Princess and the Pea Pi.

Thank you all! I was speaking with my mom this morning and she reminded me that some of this may be anxiety left over from last school year. He was doing the next year's math book, mainly with us at night, after his regular homework (yes, after things like two plus two) and there were some epic struggles, sometimes because he didn't want to do it, sometimes because frankly, the directions stunk and sometimes because his writing was poor and we or the teacher made him redo things we couldn't read. (Nice run-on sentence, eh?)

I love the methodology of breaking the problems down, too! He doesn't struggle with figure out word problems (yet), but it would give him a way to structure his work.

On the plus side, he did do the "extra or formerly too hard" page without being asked to do so by us. Unfortunately, he didn't fully follow the directions and so, we had another crying fest this morning when we reminded him he had to finish the work.

It seems like he should be happier about doing math work. Ugh!

We use rewards, rewards, rewards. I know some people don't agree with that approach, but it really works for DD. Otherwise she just complains that she wants to learn new math stuff but will really push back about sitting down and doing the work. We use anything from extra video game time to dessert (yes, I know but with her it's pretty much the only thing that is guaranteed to work.

Good luck!

Math instructions fail right out of the box when they say "show your work." It doesn't exist. There isn't "work" to show. It isn't that it happens so fast; it is that it comes together so differently between lots of connections in the brain. So, a gifted kid is forced to lie by answering something that says "show your work."

So "show your work" needs to be redefined, perhaps as "explain it for someone who doesn't have your skill." There are lots of ways of repackaging it: "if you had a tiny robot who could only move one number at a time, how would you instruct it to solve this problem" anything like that. It also helps to model explanations yourself. In a grocery store, I talk out loud converting to price per unit or price per ounce. I've also used the eating an elephant one bite at a time example. There are some mental math tricks that make large problems easy to solve and patterns that simplify things. If you start with something crazy large and show tricks, that may also get him to look at things as puzzles and not "problems." Like what is 9998 times 103?

DS7 has PG level math skills and mixed farsightedness (one eye is more extreme than the other.) He struggles with handwriting, but is praised for his explanations of what he does in math.

The "show your work" idea may be fine in theory, but in practice it just ends up being ritualized busywork.

I think Polarbear already gave some wonderful advice. I'll add my own perspective and experience:

Mathematics is its own language. Some children are native speakers of that language, and some are learning it as a second language. When you know math as a second language, you translate every math problem into your native language and solve it there. When you know math as a native language, you solve math problems without the need to translate your thought process into your spoken/written language.

When you ask a student to explain their answers in a language other than math, you are asking them to approach math the way MSL (Math as a Second Language) students approach it. Performing this unnecessary translation is an unnatural hindrance to mathy students, who often resist. It's analogous to asking a child to explain how they walk or catch a ball, and has about as much bearing on the actual performance of the task.

Personally, when I was in elementary and middle school, explanations weren't considered as important as they are today. It wasn't until I was in algebra that my teacher really wanted me to focus on showing my work and explaining my thought process. She wanted to make the point that my intuition wouldn't hold up to the more complicated problems, and we made a deal: I would try to solve a problem of her choice in my head in under a minute. If I solved it, I wouldn't have to show my work to get full credit, if I failed to solve it, an explanation would be required. In under a minute, my problems were gone. Perhaps there is some demonstration of rare mathematical insight that your child could perform for his teacher that would convince him/her that understanding a problem and being able to explain it in English to other people is not the same thing.

I've grown up to be an engineer, and when I think about math, I can't say I hear a lot of english buzzing around my head. I tend to think in pictures, but not where arithmetic is concerned. That's just recall.

I think that is a spectacular explanation, DAD22.

I had not one bit of trouble "showing work" in calculus and beyond-- but prior to trigonometry or solving simultaneous equations in high school mathematics, I was always sort of flummoxed by what was intended by that statement.

I preferred-- as a teacher of college chemistry, I mean-- to suggest that students should "demonstrate THEIR process" for an outside observer/reader so that the observer could replicate that problem-solving strategy.

That's basically the basis of scientific (and mathematical) communication at those higher levels anyway. It just happens that it's also convenient for catching errors in a pedagogical framework, too.

A quick idea on why having to show your work is an important skill; not sure how accurate it is, so I'd love feedback. If you want to be a computer programmer, don't you have to know how to translate a "word problem" into mathematical terms? Even if you intuitively know that Susie will have 7 apples after her friend gives her 4 more, computers are dumb devices that don't know this stuff. It seems to be that being able to show your work would be necessary for programming.

I realize not every kid is going to grow up to be a programmer, but at the elementary level, who can say?

The book "Upside Down Brilliance: The Visual Spatial Learner" gives interesting insights into kids who can solve complicated math problems but can't explain their work or show their steps. My 6 year old appears to be that way, although has an obvious fantasic visual memory and has about a 25-30 point gap between his verbal and performance IQs (performance being very high). I gave him some double/triple digit addition/subtraction problems with regrouping (he had never seen that before) and he figured out the answers very quickly, but his explanation as to how he solved them did not make any sense and was not the way I was trying to show him (i.e. you borrow a ten). I had to re-teach him but he still does not want to show his work regrouping, he just does everything in his head. His teacher is going to love that.

In terms of handwriting, my DS struggles a lot and part of the problem in math and showing work is that it just takes too much effort to write. His writing looks age appropriate for the most part, but he scores extremely low on tests of fine motor coordination, meaning he has to put a lot of thought/effort into writing (much more than other kids). DS was diagnosed with developmental coordination disorder. If you continue to have concerns, perhaps get an occupational therapy assessment and ask specifically that they test both for visual-motor integration and coordination. My DS is above average for visual-motor integration (so that has masked some of his problems) but on tests of just motor coordination (like the grooved pegboard) he is very poor.

Yes! This is beautiful!

I don't even know how to tell my kids how to "show your work" on something like subtraction. How did I get the answer to 7 - 4 = 3? Well, because 7 - 4 = 3. As DS used to write, "because it is the answer". And no amount of drawing apples or coloring circles is going to make it any easier. It's just going to annoy the pig.

DS is currently up to about 50% on showing his work in 8th grade math, from the looks of last night's homework. He had approximately every other step written down -- and it was mostly legible, which is something.

If problem solving is just procedural, like 8th grade algebra or anything easier, then "show your work" is not that critical. My DS often skips a few steps here or there, where he is used to the mental math.

But "show your work" becomes very important when kids start working on geometry problems. The thinking is no longer step-by-step. You really have to build the logic network by writing it out clearly.

it is a skill you will need later but why learn it before you need to.

Teachers would probably do everyone a favor if they instructed students to write solutions in a stepwise manner and then gave an example.

I have no idea how one would do this for 7-4=3, barring drawing 7 circles in step 1, repeating in step 2, crossing 4 of them out, and finally numbering 1, 2, 3 in the remaining circles. This seems silly, however.

Oh but Val that is EXACTLY what they want...

Dad22, beautiful explanation!

In our school, 7-4=3 would be shown as a "math mountain" with little circles drawn on both sides. All the teachers are very serious that the kids be able to show all their work, even for the simplest addition/subtraction problems. The curriculum is "Math Expressions" which I hear is a good math curriculum, but not for those kids who don't like showing work.

DAD22 puts it beautifully with his MSL analogy. Love it!

Personally, I would be sorely tempted to draw some inappropriate pictures for the tally to embarrass the teacher into providing real work. But that may just be my current snarky/sleep-deprived mood speaking. I don't actually recommend the strategy, but it's fun to think about.

All of these analogies and perspectives have been so helpful and thought provoking. DS has done the extra work without being asked, which is progress! I think we may wind up having to talk more with the teacher about all of this, but it sounds like we may not get very far. Common core and all that... vs. a different style of learning (I also appreciated the math as a second language analogy, that's sort of how DS describes it to us.)

Did find out there are no prescribed "right" answers, so that's something. Yet, if there is no right answer to "how did you do the work?" it makes me wonder what the point of asking the question is... ;-)

I was reading this thread when ds7 showed me his math homework. "Use the mental math strategies we learned in class today to solve the following problems. Show your work."

Just made me giggle and shake my head at the same time.

At the conference for DS7 his teacher said with Common core they insist that the kids write down explanations for each and every step. They will not let a child progress even tho they know the child can do all that silly stuff in his head. She was showing me his test where he didn't explain how one is able to count by 10s on a hundred chart. She knows that DS knows how to use the chart because all of his answers are right but since he didn't explain well too bad for him. This child of mine easily works on 4th grade math at home. Unfortunately there is only so much time to afterschool - the mind numbing boring stuff they do at school is exhausting for little ones.

OMG, AM Tuba! My DD had the same sort of instructions recently and the both of us were cracking up over it. (She came to me to show me. "REALLY?" is her usual comment in these situation.)

Because that the point it's too late. It's like teaching an old dog a new trick.

Yeah but at least by then there are some steps to write down. I don't really see a problem with waiting until there is more than one step.

But a lot of these posters had kids 6 or 7 years old. My daughter is in 6th grade so I do understand what you and the others are coming from. But really is there that much homework at that age? Is putting down the one extra step that big an effort? Another comment which wasn't by you is laughing with your kid about the teachers instructions. They may be funny but I think that's a bad habit to get in.

I think as others pointed out your explanation is good. My only observation though is that it sounds like Algebra was freshman year in high school for you. These days you can take Algebra as early as 6th grade.(or probably sooner)

Homework varies. Most nights it isn't too bad, maybe 4-5 worksheet pages. The issue really was trying to get him to show work in the prescribed way, when he was more than able to do math problems like 24 plus 39 in his head. So, in his mind (and mine), it was busy work and the methods they were trying to teach (i.e., filling in grids or arrays) were a true step backwards. The extra steps may not individually have seemed like a lot of effort, but yes, it does take time to fill in that many dots in an array (especially for a kid who dislikes writing). Time that could go to much higher level purposes.

That said, yes, he understands that if there is any question of the teacher needing to check his thinking, it makes sense to write down the steps. Now that the school has him in fourth grade math, we're not seeing the same level of frustration with this topic as we were when I first posted, fortunately.

I believe we started pre-algebra in 8th grade when I was in school, perhaps earlier.

Back in my day you just did what the teacher told you and didn't question it. The problem is and I'm not accusing you of this is the parent always seems to take the kid's side. In regards to the writing my daughter is the same way.

Why I brought the Alebra is she's in 6th grade taking accelerated algebra. My point in that was not to brag but things for kids now change quicker than back in the "old days". Suffering through the busy work doesn't last forever.

I'm not so sure about that. My 10th grader gets his share of busy work.

... as does my HS senior.

Just ask her how she feels about "Life Management Skills" class (a graduation requirement that has resulted in some real gems down in the ultimate bad homework thread...)

I am actually not taking sides, but rather, trying to think logically about the whole situation. My goal is to raise a thoughtful, free-thinking and logical child with the right respect for authority (rather than an automaton). Forgive me if that sounds harsh, but I have seen what happened when we cowtowed to a school/teacher, rather than paying attention to our child's learning needs.

BTW, I am old enough to have also done what teachers asked without question. That is, until middle school, when I had a teacher who thought showing Beatles movies for days on end (he was a big fan) without any lessons to be drawn from same made for a good social studies curriculum. That's the first time I rebelled, and also the first time my mother, a very intelligent former teacher not given to interfering, backed me up.

Oh, but it does. The busy work just gets ... busier. Like having to turn in an outline for a 40-pg research paper, when you're a person who doesn't outline. Doing the outline after the paper, just to have something to turn in, is busy work.

I come at these things from a different perspective, though, as my parents had no qualms about telling a teacher she (or he) was wrong, and proving it. They had no patience for idiocy in the schools. We used to have this form every year for some government thing involving kids on the nearby reservations, and my mother would write "None of your business" or "None of your d..n business" on it and send it back, un-filled-out. When a homework assignment was to watch the movie Sybil and do a report, my mother told the teacher he was going to have to find something else for me to do because we didn't have a TV. He said I could go to someone else's house. She told him just how ridiculous that was and that I was not going door to door asking to interrupt someone else's TV watching for a homework project. My mother would definitely have told someone where to stick all this "math mountain", "hundreds chart", "show your work" stuff. I'm getting to that point myself, having mercifully skipped most of it with DS and now only just getting rolling with DD.

On the other hand, about taking the kid's side, if my teacher sent home a report that I was messing around or something in class, my mother had no qualms about sticking that to me, either. My elementary school was mostly farm kids whose parents took education very seriously, and if you got in trouble at school, there would be worse trouble at home. But if school was the trouble, that was dealt with, too. That school is still number one in the district, with the next generation of the same families.

Nautigal - I just have to ask - how did your parents get away with this? And the next question - are you homeschooling?

Oh, I know the answer to that. I am just very matter of fact when I refuse to provide information.

"Why do you need to know that?"

"I'm not comfortable providing that information."

"Can you explain to me how this will be used to benefit my child's education?"

If you're both professional and no-nonsense, you find out that, why-- NO-- they DO NOT actually need things like your child's SS# or birth history.