Difficulty estimating quantity linked to math learning disability

[Kristiina]

I find this article very interesting. It is showing that problems in identifying quantities correctly is often found from students with math learning disability. For me this sounds like a one more article faintly supporting learning math concepts early in life (although more info would be needed to make this assumption    ).

http://www.nih.gov/news/health/jun2011/nichd-17.htm

In the second series, nine to 15 dots of one color appeared, and the students were asked to say how many dots they saw.

Images similar to those used in the test procedure. To measure children's ability to estimate and compare quantities, the researchers administered two series of tests. In the first, the children viewed groups of dots and were asked to say whether there were more blue or yellow dots. In the second, nine to 15 dots of one color appeared, and the children were asked to say how many dots they saw. Each screen was visible for only one fifth of a second, so the children wouldn't have time to count the dots.
Each screen flashed before their eyes for one fifth of a second, so the students did not have time to count the dots before answering. Each series of tests consisted of dozens of screens; the researchers considered the most accurate answers across the two series to indicate a more highly developed approximate number system.

The researchers found that students with math learning disability (math scores at or below the 10th percentile) had the poorest ANS scores. Dr. Mazzocco said that this finding suggests that problems with the ANS underlie math difficulties for children in this group.

However, children in the 11th to 25th percentile, on average, were no more likely to have poor ANS scores than were children in higher percentiles, who had no mathematical difficulties. It seems likely, Dr. Mazzocco said, that math difficulties in this group stem from a cause or causes distinct from the ANS.

[velvetkatze]

THat's very interesting. I wonder - at what age could that be discovered? I have a concern that my 3,5 y.o daughter cannot learn math. I have started her on Doman Math (dots) from 18 months, she never was interested. I used all the tricks in the books to show them, showed them in presentations - to no avail. Right now - when asked how many of something she sees - she insists on counting things first with her finger - even if there's only 3, 4 or 5 or 6 of something, not even when they are in a pattern. She can only subitize up to 2. Everything else she insists on pointing and counting - sometimes wrongly. Completely refuses to count on (starting from number other than one) - every time we do sums she insists on counting everything. I am wondering weather this is something that they are referring in this article or I am doing something wrong - because I cannot move on from sums and subtractions like that.
Has anyone had similar problem?

[Kristiina]

Hi,

My 24mo old son is similar. He can say numbers to 16 with help but doesn't recognize quantities after one. He seems to lack something called "one on one correspondence". Because I have read that some children can see the quantities before age of 12 months, I'm thinking that maybe some children just need more time to connect their brains correctly to understand the concept of a quantity.

Matematics have always been very easy for me. Naturally my mom didn't do any early learning with me, so it's very hard to compare . I try to think that this is just a phase for my son and he might grasp the fun of math in few years but I'm afraid he might not love the math the way I do  .

IXL has great list of other math skills you could learn:  http://eu.ixl.com/math/preschool

Butterworth has studied this topic and listed milestones for early arithmetic learning. Naturally these ages are not absolutes but more like averages, to give an idea when the learning might happen. I also remember reading a study where it was said that counting with fingers is a normal step in learning to count and understand numbers.
http://www.mathematicalbrain.com/pdf/BUTTJCPP05.PDF

Table 1 Milestones in the early development of arithmetic

Age	Milestones (Typical study)
0 months	Can discriminate on the basis of small numerosities (Antell & Keating, 1983)
4 months	Can add and subtract one (Wynn, 1992)
11 months	Discriminates increasing from decreasing sequences of numerosities (Brannon, 2002)
2 years	Begins to learn sequence of counting words (Fuson, 1992); can do one-to-one correspondence in a sharing task (Potter & Levy, 1968)
2 years 6 months	Recognises that number words mean more than one (‘grabber’) (Wynn, 1990)
3 years	Counts out small numbers of objects (Wynn, 1990)
3 years 6 months	Can add and subtract one with objects and number words (Starkey & Gelman, 1982); Can use cardinal principle to establish numerosity of set (Gelman & Gallistel, 1978)
4 years	Can use fingers to aid adding (Fuson & Kwon, 1992)
5 years	Can add small numbers without being able to count out sum (Starkey & Gelman, 1982)
5 years 6 months	Understands commutativity of addition and counts on from larger (Carpenter & Moser, 1982); can count correctly to 40 (Fuson, 1988)
6 years	‘Conserves’ number (Piaget, 1952)
6 years 6 months	Understands complementarity of addition and subtraction(Bryant et al, 1999); can count correctly to 80 (Fuson, 1988)
7 years	Retrieves some arithmetical facts from memory

[sonya_post]

@ Velvet,

I don't really have time to address all the things you brought up right now, but there are a ton of hurdles kids must overcome before they can do math. Some kids are bright and early, and some kids are not. Some kids think counting means touching things and saying numbers. They don't get what you mean when you ask them to count. One to one correspondence usually shows up between ages 2- 4 1/2. You can't make it happen. It is something that you have to wait for. You can do things to facilitate it but other than that, it is a waiting game. She will not get counting on until she gets what you are asking her to do. Most kids can recognizes quantities up to 3, beyond that it is very difficult unless it shows up in consistent pattern. Doman math doesn't work for everyone. Just as the reading doesn't either. Reading has worked for us to different degrees with each child. Math has never worked, but that may be because I haven't stuck with it.  She is not outside the bounds of normal development yet. So don't worry. 

There are some old threads on here that discuss these issues in detail.  Do a search for Marshmallow math and Kitchen Table Math and you will find the threads. But  if we bump this thread there are some experienced parents that I'm sure would love to assist you. And I will try to get back to this by the end of the week.

[velvetkatze]

@Sonya_post
thanks for your reply. I guess I just have to wait and see. I did read that article and some others I could find on this forum. Some people praise Life of Fred math books. I'll compare everything and choose what to do next.
For now - we had a leaflet through the door for trial of Reading Eggs program, they have Maths bit as well - we're doing this, and it gives me some ideas as well. Problem is - I am not very good at maths myself and everything about Maths is terrifying to me, but I keep soldiering on for my kids sake :-) (I don't want them to be like me, because Maths are really important in life, and it kind of cripples me in that area).  I am not showing to her my relations with maths and make it sound exciting every time we do something - but maybe she's picking up on this - I don't know...
Anyways - all the posts and advice would be very much appreciated.

[sonya_post]

Instead of waiting and doing this in one fell swoop, I will do it in parts as I have time.

1. If you are having difficulty with math and are frightened the BEST place I can send you is to Crewton Ramone's House of Math. I posted some stuff about him under the current Mortensen Math thread. It is not organized. That is fine. Just start clicking around.  I attached a math blocks template you can print out and follow along if you don't have blocks. Which I assume you don't.

2. If math really does make you upset, start there. Your daughter will sense your fear and assume it as her own. So, first get over that hurdle. I promise you, a few hours watching video over  at crewtonramoneshouseofmath.com and you will come away with all of the following reactions and maybe all at once: relief, joy, confidence, and anger. The anger comes in when you realize that it doesn't have to be that hard. None of it is very hard. Really. None of it.  Trig, calc, fractions, multiplication - it is all very easy once you know what it is you are doing.

3. Don't worry about counting so much as you want to make sure that she understands that numbers mean quantity.  I made this file to help my kidlets do just that. It doesn't have words with it, but you can tell her what she is looking at. Like 5 birds, 5 cows, 5 on the tally sticks, 5 on a dice, the word five. etc. http://library.brillkids.com/download.php?cid=1&tid=&lid=&fid=9121

If I were starting over with a baby, which I am I now have a 6 week old in my care, I would do things differently than I did before. But that is great thing about EL. It isn't going to hurt them and you learn a lot.  I have spent hours and hours and hours thinking about this. I am fairly comfortable with all areas of teaching now, but math has always been a stickler for us. You will find pockets of people doing a good job, but it doesn't work well with every child. There are real reasons for that . It has to do with how we think and when we are able to grasp certain ideas. So, after tons and tons of reading and research I have a much better idea of what needs to happen to get a child to grasp math. And honestly , it is not all that different that what we are doing for reading. Really. We just haven't done a good job of applying the principles across the board. I will continue to post here as I have time. But please go check out Crewton Ramone. You won't be sorry.

[sonya_post]

One of the best books I read early on when teaching math as an EL subject was Kitchen Table Math. The reason the book was so good is not so much that it prepared me to make my child a math wiz, but helped me understand the hurdles children have to overcome in order to grasp what is going on. It is way more than you realize and on top of that, the places where a child can get confused is likely infinite. Maybe that's an exaggeration. but probably not by much. So in the early years - 2-3.5, every child is going to be different and you have to wait for stuff to " just click".

When I made the subitizing LR file, the impetus for that was reading about Moshi Kai. He remembers that the concept of a number finally clicked for him when his mother showed him 1 lion and then 2 lions and then 3 lions. She did not count items consecutively, she showed him groups of things and gave those things numerical meaning.  This idea shows up in the Manual of Methods which is the Teachers Manual for the 19th century set of school books in the Eclectic Education Series. The Ray's Arithemetic recommends that you:

1. Never show a child the numerical symbols until they are very comfortable with the concept of what the number means. For example: the number 7 is taught using manipulatives. The child should recognize 7 as  7 beans, 1 bean and 6 beans, 2 beans and 5 beans, and 3 beans and 4 beans or whatever manipulatives you are working with.  1- 10 are taught this way.

2.  All math is oral until 2nd or 3rd grade. So the use of symbolic representation doesn't show up for some time as the symbols themselves can cause further confusion.

3. Children who are learning to write should also not be forced to do sums. It takes up too much mental power. Therefore there is no written work until a child is comfortable with both writing and mental math.

Now this set of books, which is really skimpy compared to what you are used to, is small. Math is only done for 15-20 minutes a day. And when kids dropped out of school at the end of 8th grade they were capable of running a business, calculate and understand interest, manage the amount of seed needed to plant fields. In other words far more capable than most of us are even after college math.

One of the other problems with counting and touching things as you count is that the child gets the idea that the last item counted is the number instead of all the items in the group. So let's say I have 5 raisins and we count them one at a time and slide the raisin across the placemat as we do so. When the child gets to the 5th one he will think that is 5.  He assumes that you mean that raisin right there is 5. And there is nothing to distinguish a 3 from a 5 in that context.  So the counting hasn't helped any but rather added confusion.

These are just some of the ways a child can get confused and each child may have areas of confusion that are unique to that child. But since there are some that are very common like the child assuming that counting means touching stuff and saying numbers, we want to make it as easy for the child to succeed. And so we take out as many variables as we can. So if I were starting out with a 2-4 year old, I would make sure that the counting occurred in groups. So I would have a group of 1, and then 2, and then 3 and then 4 and then 5 raisins. Etc. And then line them up in rows with each row one longer than the previous one. And then count the groups. So you would touch the group of one and say "one" and then touch the group of two and say "two" and so on.

And an easy way to work on one to one correspondence is just have your daughter help you set the table. Do you have 4 in your family? Tell her you need 4 plates and 4 glasses. Etc. Then have her put one of each at in the right place. She will need help with this the first few times. But she will get it.

One last thing to encourage you. On one of Crewton Ramone's teaching videos he says that if you can speak English you can do math. English is much harder. He's probably right - but I didn't always believe that.  I take care of a little girl with Down Syndrome. She turns 6 tomorrow. She is working on some fairly advanced math for her age. She is multiplying, adding and subtracting, and doing algebra and squares and square roots. She is not struggling and she is having a lot of fun. Her biggest issue, which is her issue with all the things we do, is the fine motor skills. That is going to take way longer to address than math.  She knows what squares and the roots mean. When I told her that when we play with squares some people think that is very hard. I told her that when she finds the number of one side, that is called a square root. And finding square roots is really hard for some people. Her response was terrific: "You kidding me."

[sonya_post]

This will be the last post  and then I will post a video to explain some things.  If you have the ability to read these posts and understand them,  congratulations. I don't go back and fix typos or grammar, I tend to put periods and commas in when my fingers stop typing and I usually have at least one child climbing on me.

When it comes to early learning, much depends on the teacher. If the teacher is a poor teacher the student will not be a success. Babies/toddlers haven't developed the kind of language skills that are necessary for even basic explanations.  Some parents are intuitive at how to reach their little ones and some are not. One thing I learned well from John Mighton of Jump Math is that if there is a problem assume it is  the teacher. We aren't doing our job. That is well and good and all, but most people aren't teaching math to toddlers so there aren't and books on how to go about this. We are laying a new foundation. On top of that, most of us come with our own math baggage. When I was in school things came fairly easily to me. I didn't have to work hard. So, I it is difficult for me to break concepts down to smaller and smaller bites. I am guilty of giving too much at a time. 

If math language could be confusing for 6 and 7 year olds 120 years ago, when math education was significantly better, how much more so for 3 and 4 year olds. On top of that we have the added burden of parents who sit down with their little sweetums carrying their own math baggage. This will take patience.

I read recently that we shouldn't use manipulatives because math is an abstraction and kids need to learn to think in abstractions. The problem is that until a child is somewhere around 10-11 s/he is unable to deal with absolute abstractions. Until then a child is just learning to think symbolically but still requires concrete examples for understanding. Are there some kids where this is not true? Sure. And are there things you can do  to hurry these stages along? Maybe. But I am not sure you need to. Obviously kids can learn abstractions. We teach children to read and that is a compete abstraction. The difference is that written words have a reference point in the spoken word. And they use the spoken word to navigate the world around them everyday. And even LR doesn't start out with words like:  was, not, busy, fast. It starts out with words that refer to concrete things in a childs life that are also important to the child. Kick, ball, dog.  We show an image of the word and then picture and then a video in some cases, so the child has a reference point to things that he knows. There are few such reference points in math at the age of 3. One and two are easy. They get that. Beyond one and two things a get a little harder to understand.

By the age of 4 most kids, EL kids or not, can start to handle some math work. One to one correspondence shouldn't be an issue for most kids by then. And they have likely discovered money which seems to be a point of no return. The big issue is getting littler kids to do math and even whether you want to push it. And if we answer yes we want our toddlers to do math, the next question is what do you want out of it. Are you interested in just teaching rote memorization or are you looking for your children to really understand numbers and what they mean. There are some parents on these boards who have take the memorization route and some who have gone the "number sense/understanding" route.  I'm a both/and. It isn't necessary to chose between the two.

I am going to post a video next that will examine some of the problems I presented and how I have addressed them. And how we are moving ahead. For us, moving ahead is the exciting part. Math went from being THE most stressful subject for both EL and homeschooling to one of my favorites. Literature is still at the top, but it is getting harder and harder to choose as we have become a literature/math/music/history/nature study family.

[sonya_post]

So I haven't posted that video yet, but it is still on my list.  However, just to prove the point of all previous posts........

This morning I was working with a just turned 3 year old on math.  When we finished her 10 minute play time she kept playing with the Mortensen blocks. We were using the numberal ID tray, and she had been building 10's. Anyway, out of no where she asks me where her six block would fit. She was trying to place it in the tray, but there was already a six block in the tray. So I told her to put it in 7 slot. She started to cry and said then there would be space left over. So I told her to remove her six and place the six she had in her hand into the tray. She didn't want to do that. And then she blurts out, "Are you saying that all the sixes are the same? They can never be a seven?" I told her that if the six wants to go to the seven party she has to take a one along. Then her light bulb switches on and she says, "So, all the threes are the same, and all the nines are the same and all the fives are the same?" Yes, I say. She spent the next 20 minutes lining up the blocks just to see if they were the same. She then runs into the kitchen and shouts, it's true. It really is true.

Now, if you would have asked me this morning before we did math if she understood quantity and same I would have told you yes. She gets one to one correspondence. She has been adding numbers to ten and we have been putting the blocks together and lining them up to make squares. Which means the numbers must be same. It would never have occurred to me there was anything she didn't understand. I knew we needed to keep playing with numeral identification but I thought we were just doing it to make it second nature, not because there was something completely off in her understanding. This is why Ray's has you working on numbers as they do for several years.  Point was driven home again.

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