DS5 has been doing addition and subtraction for a while now 1 1/2+. Before he started K he could tell you what 10-7 was immediately. Lately I've been noticing that he will no longer just give an answer but must count everything on his fingers. I've been becoming increasingly frustrated because I know he knows this. I've recently, can't believe it took me this long, realized why he is doing this. In math class they have them count everything on their fingers! They add with their fingers, they subtract with their fingers, they check their answers on their fingers!
I think the school sees it as going "deeper". This lets the kids see the math and manipulate it, at least this is what I am assuming. I can see where they are coming from with kids just learning the concept of addition and subtraction but DS is way past that. How do I stop this? how do I let him know that it is OK to just know the answer? Explain to him that knowing the answer will actually help him do the type of problems that he wants to do? To me it feels like he is going backwards and this is a very bad habit to get into.
Agree with MoN here. It's good to see the same concept/procedural tool from different angles.
One of the things missing from a lot of math instruction at lower levels is the idea of "checking" using an alternative method. While I realize that with arithmetic, automaticity is the eventual goal, the HABIT of using a secondary method to back up your conclusions is actually a good one. He won't keep using it here, and neither will classmates.
I completely agree with checking your answers! DS and I had a talk about why that was important the other night. He would get a problem wrong and be sooo upset, he couldn't understand how it was possible. I'd ask him if he checked his answer and he would say no. We go back and check the answers and then he could see where missed something, usually because he wouldn't show his work in the first place. Oh well, he'll learn eventually.
The counting on his fingers thing though actually seemed like it was creating a barrier to him answering, and understanding, some problems. He'd want to count on his fingers from 30 to 50 instead of using the skill, idea, that 20 is two 10s.
The school has told me many times that they don't care if a kid knows something, the want them to "understand" it. I'm actually not positive that they wouldn't make him go back and count on his fingers to prove that 12+5=17.
I hope you are right. I'm just finding it very frustrating right now. This might just be that it is coming on top of everything else I'm dealing with school about and I'm making too much of it.
I also agree with master of none and HowlerKarma. Also, speed here is not important in my opinion. Let him take his time to experiment so he can get a better understanding and a better foundation for future learning.
In math class they have them count everything on their fingers! They add with their fingers, they subtract with their fingers, they check their answers on their fingers!
I think the school sees it as going "deeper".
The current educational theory about math is that children have to develop "number sense." (I agree with this in principle, although the way it is applied, they tend to assume that this happens around age 5-6 and they don't account for the kids who have it earlier.) This is regarded as foundational; and they are emphasizing manipulatives as a way of reinforcing "number sense." They don't want kids to have algorithms or memorize math facts before they have an intuition about what those facts mean.
I would like to see more differentiated math starting in K, but I don't have a major problem with this concept as an idea about child development...
DeeDee
The counting on his fingers thing though actually seemed like it was creating a barrier to him answering, and understanding, some problems. He'd want to count on his fingers from 30 to 50 instead of using the skill, idea, that 20 is two 10s.
For my DD5, I sometimes just let her do it the slow way until she eventually discover the easier ways. I remember she used to count from 1 to 51 for 1+50. But this requires a lot patience and there is also the risk of the child getting frustrated.
I agree with what other posters have said and I get that kids need to learn the reason why, but I also understand Eibbed's frustration.
Our DD7 who has been adding/subtracting in her head for quite some time now just mentioned yesterday to me that she knows she could do more problems on her timed addition/subtraction test, but the teacher wants her to do some sort of dot counting to get the answer. DD showed me how she counts points on the numbers to get the answer. I asked DD if she knows 5+5=10 then why can't she just put down the answer and go on. The response I got was something like "Mommmmmm, that isn't how I'm supposed to do it".
Yes-- I get it too. The dot-counting well into second grade was not a good experience for my DS either.
DeeDee
I remember she used to count from 1 to 51 for 1+50.
Agh, my kid is doing that! I've tried to explain about "counting up" from the larger number, and she just looks at me like I'm from Mars. She's got this huge verbal working memory, combined with much less impressive visual-spatial skills. She looks like she's leaping ahead in math, but she's not learning the short-cuts she's going to need. (I asked her how many wheels three cars have, and before I could even start sketching groups of four wheels she popped out with "twelve!" She did it entirely by counting in her head.) Glad to hear your kid got over it, I hope mine will too!
To understand that counting on from the larger number works, you have to be completely sure that addition is commutative (1+50 = 50+1). I think it's not surprising if a young child doesn't get this, or even if they behave as though they get it and later don't - I think this kind of thing can happen as understanding deepens. E.g. if you notice for the first time that 50-1 isn't the same as 1-50, you might also doubt yourself in addition for a while! I wouldn't push this.
To understand that counting on from the larger number works, you have to be completely sure that addition is commutative (1+50 = 50+1).
What I meant was, she doesn't get "counting on" even from the first number. So if I give her 9+2, she can
count all the way up to 9 verbally without losing track of the 2 (which would tax most adults' verbal working memory, if we didn't have our addition facts memorized), but if I suggest that she just start by saying "nine," since she already knows that there are nine, it just doesn't make any sense to her.
I'm definitely not pushing it, I just make suggestions now and then to see if the penny will drop. I'm mostly just amazed that this kind of mis-match is possible. And a little worried that being so extremely good at a bad strategy will end up hindering her.
A numberline might be a helpful way for her to "see" this relationship, MegMeg.
I recall a lot of mystifying (well, to me, anyway) little things like this when DD was 3~7 yo. Some of it was unexpectedly more age-appropriate development overlaid with NON-age-appropriate cognitive development. It sounds like the same basic phenomenon. Predicting series was another thing that DD had a horrible time with, as I recall. It was a very peculiar-seeming "blind" spot, because she could do things all AROUND that one particular skill. KWIM?
A numberline might be a helpful way for her to "see" this relationship, MegMeg.
Heh. See, that's the part about not so good with visuo-spatial stuff.
It was a very peculiar-seeming "blind" spot, because she could do things all AROUND that one particular skill. KWIM?
Absolutely!
She's got this huge verbal working memory, combined with much less impressive visual-spatial skills.
(I asked her how many wheels three cars have, and before I could even start sketching groups of four wheels she popped out with "twelve!" She did it entirely by counting in her head)
Maybe this is just my fault as a visual thinker, but these two statements seem contradictory to me. How would she have counted in her head without mentally visualizing the cars?
To understand that counting on from the larger number works, you have to be completely sure that addition is commutative (1+50 = 50+1).
What I meant was, she doesn't get "counting on" even from the first number. So if I give her 9+2, she can
count all the way up to 9 verbally without losing track of the 2 (which would tax most adults' verbal working memory, if we didn't have our addition facts memorized), but if I suggest that she just start by saying "nine," since she already knows that there are nine, it just doesn't make any sense to her.
IOW, she hasn't yet made the transition from "counting all" to "counting on". She doesn't "really" get that when you count, the ordinal number you used to label the last item is always the cardinal number of the set of items you've counted so far. Which is entirely developmentally normal, but I know how weird it can be to catch our children being developmentally normal from time to time :-)
I have a note of my astonishment at finding that the concept of "more" really did develop in stages in DS, then 3y0m. To casual observation he appeared to understand it, but on reading about how it developed and testing him I found that, indeed, although he could correctly answer "which is more?" questions if both numbers were 6 or less, *or* if they were separated by more than about 10, he couldn't answer "which is more, 6 or 7?". It still astonishes me now, actually - I had a real "how can he not understand that, given all the things he does understand?" feeling about it, but I also had it written down that being able to do this but not that was normal...
We used sidewalk chalk to construct a numberline, and then had DD step/count problems (both addition and subtraction) as a way of understanding this process when she was around 4, I think.
So it wasn't necessarily something that only works with visual-spatial learners. It can work on a kinesthetic front, as well.
Bottom line, though, is that she really only "got" this when she was developmentally ready. Until then, one has to just figure out a work-around strategy for the developmentally inappropiate/underdeveloped skill.
We used sidewalk chalk to construct a numberline, and then had DD step/count problems (both addition and subtraction)
Been there, tried that! The chalk number-line is still out there on our sidewalk! She had great fun jumping around on it and counting her way up, but absolutely refused to focus on addition games. (This is the kid who pesters me for addition problems on paper.)
It may just be a developmental readiness thing.
My son unlearned all sorts of things in pre school that he knew concretely and abstractly before then. Including: whole word reading (went for a ball of whatever when they started insisting he do it phonetically), mental maths (slowed right down due to counting to 20 every single day when he could already do double digit addition and subtraction in his head), writing (they insisted on daily colouring to strengthen writing muscles), telling the time -they only did this in Gr00 (age 4 - 5) and only to half hour. so he forgot that he already knew how to tell the time. He forgot his left from right which he had instinctively known since before age 2. It was even on his silly report card! So I am fully of the opinion that if they need to count let them with whatever method they enjoy (numberline, manipulatives, fingers toes whatever) but if they don't need to then don't make them!
I sent my 5 year old to school being able to count on and back about 80% of the time. A month later he couldn't add 3+2 without using both hands and counting from one. It took him the whole year to get back to where he started. And he still makes the same mistake when counting back and gets an answer one high.
Luckily he has been able to learn to read at his own speed.
My kid basically "thought" a lot about math, played with the calculator and can do addition (even 2 digit with carry-over), subtraction, multiplication (he does something with his head and so I know he is not memorizing the facts but actually computing), basic questions like "109 + y = 120. What is y ?" type of questions verbally. He can count to a number/backward from any given number. He is very unchallenged at school with respect to math (and other things). We plan to again ask his teacher, but I see K as a lost year.
I am also not sure what value worksheets such as "put the ending consonant/ending letters and color all objects that end with the letter "t" in one color" have for a person who has been reading for a while now. Is this kind of worksheet supposed to enhance their spelling abilities ? He does those types of worksheets, though he is occasionally baffled by the tiny pictures they have on there (he used to openly protest before, but I told him it is disrespectful not to do worksheets or show the work). However, that said, is there a "better" way to show the work ?
Maybe this is just my fault as a visual thinker, but these two statements seem contradictory to me. How would she have counted in her head without mentally visualizing the cars?
I can't visualise the cars, doing so would likely "overflow my buffer" and loose the question... I think in words not pictures, I "self talk" through the problem (in whatever method I am currently up to using).
I remember my great excitement talking about a visual spatial style spelling technique to a friend, and I how I thought it would help my daughter. She and her husband both responded "Well how would that help, everyone can do that!" Er no. I couldn't do it, it would have been of no use to me what so ever. It was on the other hand of great help to my DD...