My five-year-old has been able to rattle off the numbers in order into the teens for a while, but when you ask her to count a set of objects, she can only get up to three consistently. “One, two, three–um–five?”

I have an idea of what might be going on in her head. It is pretty clear that she knows that four comes after three. I suspect that she has also figured out that when counting objects you are announcing at each step how many you have pointed to so far. When she points to the first object she knows that she has pointed to one object and announces “one.” Upon pointing to the second object she knows that she has pointed to two objects and announces “two.” When she points to the third things go similarly, but when she gets to the fourth she runs into trouble, because she doesn’t have any good idea how many have been pointed to.

I hear you saying “Whoa, if she knows that four comes after three then of course she knows that after pointing to one more than three things she has pointed to four things.” Not so, because she hasn’t learned that yet. Sure, you know what counting is all about, but kids don’t until they’ve been taught. What my daughter is doing when pointing to the first three objects is subitizing the number of objects pointed to so far. Subitizing is the act of being aware immediately of how many objects are in a collection without counting them. We humans can easily subitize collections of one, two, or three objects.

Up to this point my suspicion is merely that: a suspicion. My hypothesis has to be tested. We need to isolate the pieces of counting. The elements of counting are: 1) reciting the names of the numbers in order; 2) pointing to objects one-by-one; 3) doing 1 and 2 simultaneously; and 4) coordinating actions 1 and 2, saying exactly one number for each object pointed to. We isolate these elements in the case of my daughter by asking ourselves a series of questions:

First, can she recite the numbers aloud, in order consistently? Yes. She has no problem with this up to at least ten.

Second, can she point to objects one-by-one, in sequence? Yes. No problems there.

Third, can she point to objects one-by-one, in sequence while reciting the numbers aloud? Initially we aren’t sure, and we decide that we need to distance this skill from counting itself, so we ask ourselves:

a. Can she recite aloud a sequence of words other than the counting numbers? Sure, she knows the alphabet, as well as many songs.

b. Can she point to objects one-by-one, in sequence while reciting aloud a predefined sequence of words in order? We don’t know initially, but my wife tries it with her and she is successful (for instance, with the alphabet).

Fourth, can she coordinate the two actions above? That is, as she points to objects in sequence and recites words, can she match them up, pointing to exactly one object for each word she says? Again, we aren’t sure initially, but my wife tries it with her and she is in fact able to do it.

This last one is the complete skill of counting. Once she can do that she can count, right? So what’s tripping her up? Well, counting is two separate things: it’s a process as just described, and it’s a way to ascertain the number of objects in a collection. These are distinct facets of counting, but they are intimately connected. You do the process and the last number that you say is the number of objects in the collection. These two facets of counting are usually learned by children separately. It is my understanding that most children first learn the process of counting and only later learn that this process gives you information about how many things are in a collection. A young child who has “learned to count” may count the cookies on a plate “one, two three, four, five, six, seven,” but then when asked “how many are there?” reply with “I don’t know.”

I think that my five-year-old learned things opposite the usual order. I’m pretty sure that she has figured out that counting is all about determining the size of a collection, but initially she is unclear on how the process works. Only by divorcing the counting process from numbers were we able to make any progress. In the last several months she has progressed well, and is on her way to being a proficient counter.

See also: Wikipedia article on counting

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3 Responses to Counting

  1. Charles Hepburn II says:

    Very interesting analysis and investigation. I would also like to contribute to this line of reasoning. I would propose that the more social pressure that is upon the child who is trying to count, the more they will feel that pressure to “get it right.” Sometimes kids can test to see if they still feel approval/love from a parent, even when the “get it wrong.”

    Sometimes backing off a bit on the child can relieve this social pressure for correctness. This may in turn relax the child, and then it may flow naturally out. The bottom line point here is that the child needs to feel like they are unconditionally loved and valuable no matter if they can perform in a specific task/subject or not. When the child feels that their self-worth is NOT on the line, they tend to put their toe into the water of learning again.

    Also, fish aren’t good a flying… eagles aren’t good at swimming. Sometimes a particular skill set just takes a bit more time for certain kids. Kids grow in spurts, and not all kids will progress at the same rate, or in the same way. It’s important that the pressures of being a good parent don’t compel us to overlay our expectation of their progression on top of their natural areas of interest.

    Also, from an adrenal stress arousal standpoint… the pressure to perform with a “test” situation (mommy and daddy are seeing if I’m smart enough), that can give the kid some “test anxiety” and thus trigger an adrenal condition (fight or flight), and thus the kid usually picks either flight (purposely getting it wrong, ignoring your question) or defiance (fight — a kind of “hey dad, forget about that, look over here instead”).

    When adrenalized, the Human brain can only really recall from intellectual memory about 3 or 4 things, max. For example, the next time you are in a heated argument (not typical for us Mormons), or you become adrenalized, try to name all the 7 dwarfs from Snow White… or recall the process for solving a particular linear algebra problem.

    Your cognitive abilities shut down (partially, depending on your phobic scale response level) and your brain’s limbic system (r-complex) kicks in… you have an animal/primal brain now, and accessing the higher neo-cortex functions is limited.

    Just something to consider. I have no idea if this is really the case or not, I’m just speculating. Only you wife and you are fully qualified to know what’s best for your children.

    Thanks for the situating conversation… we need more of that in the world!

    • toomai says:

      Thanks for the thoughts. I’m pretty sure that it wasn’t an adrenal response, nor that we were putting too much pressure on her. But I do think your “fish aren’t good at flying…eagles aren’t good at swimming” comment is right on. My daughter is dyslexic, as am I. We dyslexics have a hard time learning processes, though we do pretty well with understanding concepts, big-picture ideas, interconnections, etc. So I was able to see pretty clearly what was going on in her head: it’s basically the same thing that goes on in my head! This sort of learning just requires a different approach for her than the standard one. Fortunately, since I learn in much the same way that my daughter does, I’m able to help her through this sort of thing pretty well. (My wife on the other hand–despite her more extensive training in teaching and natural skill at it–was pretty baffled initially.) We’re also fortunate that there are a lot of resources out there now for helping dyslexics learn.

      • Charles Hepburn II says:

        As I said, you know best what your child needs. I’m glad it is not what I suggested. It could be that I am interpreting your situation through my own lens.

        Maybe I am mistaking observation for introspection (self-reflection). I know that my own kids often exhibit these issues, so I must be sure I take my own advice.

        Thank you for sharing information on dyslexia, whereas I didn’t realize this was a criterion in the situation. This is a good example of someone with the best intentions rushing in with their own solutions to another’s situation. I didn’t take time to fully diagnose before I prescribe.

        The fact that you are even aware and working on this with your daughter is an amazing example of fatherly dedication to the well-being and development of your child. Many fathers don’t even bother to show up for parenting each day, which is unfortunate.

        You are doing an amazing job!!! Endure to the end. 🙂

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