November 12, 2007 |

How do children learn to count? You could imagine that numbers are words, and children learn them like any other word. (Actually, this wouldn’t help much, since we still don’t really understand how children learn words, but it would neatly deflect the question.) However, it turns out that children learn to count in a bizarre fashion quite unlike how they learn about other words.

If you have a baby and a few years to spend, you can try this experiment at home. Every day, show you baby a bowl of marbles and ask her to give you one. Wait until your baby can do this. This actually takes some time, during which you’ll either get nothing or maybe a handful of marbles.

Then, one day, between 24 and 30 months of age, your toddler will hand you a single marble. But ask for 2 marbles or 3 marbles, etc., your toddler will give you a handful. The number of marbles won’t be systematically larger if you ask for 10 than if you ask for 2. This is particularly odd, because because by this age the child typically can recite the count list (“one, two, three, four…”).

Keep trying this, and within 6-9 months, the child will start giving you 2 marbles when asked for, but still give a random handful when asked for 3 or 4 or 5, etc. Wait a bit longer, and the child will manage to give you 1, 2 or 3 when asked, but still fail for numbers greater than 3.

This doesn’t continue forever, though. At around 3 years old, children suddenly are able to succeed when asked for any set of numbers. They can truly count. (This is work done by Karen Wynn some years ago, who is now a professor of psychology at Yale University.)

Of course, this is just a description of what children do. What causes this strange pattern of behavior? We seem to be, as a field, homing in on the answer, and in my next post I’ll describe some new research that sheds light onto the question.

Hey, I wouldn’t use marbels with babies or toddlers, I have known even 5 year olds to put marbels in their mouth.

My daughter is 13 months and can count to 5. Of course she probably doesn’t know what the numbers mean but she’s learning quickly. Thanks for the ideas on how to bring meaning to the “word” numbers. I won’t be using marbles but instead some Cheerios! Very rewarding snacks

Marbles??? What a silly medium to use with babies or any toddler under 3. Who would give marbles to a baby? This must have been written by your typical neuroscientist engrossed in a world of academia and with little real world experience with children. i know one neuroscientist who had no idea whether a 6 month old could walk :)

nice information.

My daughter is 23 months old, and for around the past 6 months she has been able to count out cotton buds if my wife or I ask for a specific number (up to 4, tends to be all we need). When I ask her for a specific number of marbles, she hands the right amount to me. As an example, the other day I asked for two marbles – she gave me two, and when I asked for a further two, she put them next to the other two and said four, then added another and said five. It is not pot luck, I have done this successfully a number of times – though she does occasionally get bored or a bit confused. She has been able to count how many fingers I hold in front of her for months. She has also been able to say her entire alphabet unaided for months and recognise all the letters for about 6 months – count to 20 with no help – and recognise certain written words. She knew her left from right at around 14 months (with mixed success – but overwhelmingly gets it correct).

I don’t ‘hot-house’ my child, she is a happy, confident child growing up in a deprived part of London, England with two parents that simply love her lots and invest the time and energy in making sure she’s the best she can be. She has had no extra tuition or professional assistance and we have never read any of the 1001 book on ‘How to make your child brainy’. I have no plans to hive her off to private school – she will go to state school so she can learn the social skills needed to get on with and truly respect the majority of people on this earth, and I can guarantee she will continue to grow and learn at this same pace. She is a normal child fulfilling her potential.

I respect research and information which will help parents, however sometimes i think it can be more limiting than enlightening. It’s generally all about a parent’s expectations for a child and an intelligent approach to raising them and making learning fun.

That sounds more like basic classical conditioning to me. He simply knows what his reqard should be for X action.

Several of the comments so far have brought up hypotheses not very unlike ones that have been brought up in the literature over the years. I’m going to post some more data today, and you can see what you think.

Please try my web-based experiments

I suspect that the concept of grasping, intrinsic interaction, and brain development, in infant physical and brain development, are important factors relevant to this discussion. Infants will often grasps objects that are put in their reach. I suspect that they initially grasp multiple marbles because of a lack of refined physical and mental ability. With the refinement in physical and mental development, they naturally grasp one. With “practice”, they learn to associate one marble with the word one. Given this conditioning, if you ask for two, the infant does not recognize or understand this word, and will select a random quantity, other than one. When the infant is asked, over a periods months, for two marbles, it eventually picks two, perhaps because of further physical and mental refinement, or because the researcher responds in a way, when the infant selects two, that confirms to the child that they have selected the correct number of marbles. This same process possible continues up to three marbles. Clearly, there seem to be some kind of threshold at this stage of development. As well, I know nothing about the specific interactions and responses of the researchers. Certainly, this knowledge must figure in a more complete understanding of this issue.

I believe at that age children can keep track of three different objects. That’s not necessarily counting, though. The issue is that the number 3 is too small. Even in adults, dealing with numbers less than 4 seems to be fundamentally different from dealing with larger numbers.

Also, keeping track of three objects doesn’t seem to necessarily tap the same processes as counting. One of the ways you can tell, is that it is extremely unlikely that if you asked your child to give you 3 of anything (pieces of sugar, balls, etc.), your child would succeed. That is even after your child learns the word “three”.

Also, you can try the following experiment: show your child two cups. Then put one piece of sugar into the first cup, then put 4 pieces (one at a time) into the second cup. Make sure that your child cannot see into the cup — this needs to be a memory test. Then let the child pick the cup. The child should pick at random (you’ll have to do this a number of times, since on any given trial, the child has a 50/50 chance of guessing correctly).

Please try my web-based experiments

Well, I am amazed how or why it is necessary to mix language skills and other kinds of skills. It is obvious that counting only gets done once you have figured out that there is something about the “how many” and then spent some time thinking of ways to make sense about these matters. If it “just so happens” that usually this will be tone and connected with number marking words in the age of three, then fine.

The experiment you told about was all fine – it did as little as possible to give any hints what exactly it is that was was wanted from the child. If unuversally better understandable sign language (lift three fingers and point to the stuff saying) was used too, I bet the results would have been remarkably different.

Our 25-month old regularly gets a treat of three piece of crystaline sugar, the kind sold in Asian supermarkets and used to sweeten tea, it comes in little lumps about the size of a green pea. At first, at about the age of 20 months, he would get only one piece, but that slowly escalated to three. So far so good.

now, try giving him only one. he takes it, and stays there, looking at the bag. Ok, mr smarty, you give him one more and put the bag away. he takes it and stays there, looking at the cupboard, visibly annoyed at your behaviour. take the bag out of the cupboard and give him number three and he happily goes on his way, quite satisfied. We have repeated this experiment many times, always consistent results, once he has three, he’s fine with it, and our obstinate non-compliance with his desires completely forgiven ;) One is no good, two is no good, three is quite satisfactory thankyouverymuch.

How is that not counting?