## Counting game and subitizing

[22 Jan 2013]

When we count objects, there are several things going on. First, our brains need to distinguish between "object" and "non-object" (this can include having to differentiate size, color, texture and so on).

Next, a curious thing happens depending on the number of things we are trying to count.

If we count a small number of objects, say 5 or less, we don’t tend to count them individually. We just "see and know" that there are 3 boxes, or 3 cats or 3 circles in front of us. This process of "knowing" the number of objects is called **subitizing**. We share this ability with many animals who appear to "know" how many objects there are with just a glance.

But if the number of objects climbs beyond 5, we need to use more of our brain since we need to count items individually. We need to vocalize (at least in our head) how many we are up to, and we need to remember which items we have already counted and which ones there are to do. We may also use some strategies like counting in 2s or 3s to make it easier, but which also add to the cognitive load.

All this extra brainwork for counting higher numbers takes more time. But how much?

### BBC’s Subitizing Game

The BBC’s article, Can you count faster than a chimp?, is accompanied by a "Count the Dots" Flash game, which instructs users…

"See how fast you can count. … As soon as you have counted the [dots], press the space bar to move on".

I felt there were problems with the way this game was designed. I could press the space bar at any time (pretending that I had already finished counting), which seemed a bit odd. Also, what if my count was incorrect? I may think I’m counting at a certain speed, but incorrect attempts were also included (and the game didn’t even "know" they were wrong).

The BBC was obviously not trying to be scientific, but their game didn’t hit the target for me.

### My subitizing game

So I set about writing a counting game where you would actually need to count and it would keep track of your correct answers and times.

Try it out here: Counting Game

### Related article

I wrote a related piece earlier called Number Sense, which starts with a video of Maggie the dog illustrating her counting ability.

### Observations

Some interesting observations so far (with an admittedly small data set to date):

- There are slight increases in counting times as you go from 1 up to 5 objects.
- There is a noticeable increase in the time taken to count 6 objects and above. This is not the same finding as Dehaene’s in his book
*The Number Sense – How The Mind Creates Mathematics*(his research indicated the time increase was almost linear for 3 or more objects. You can see his chart in the Number Sense article mentioned above.) - Counting 9 objects takes a bit less than 8 (perhaps we see "a lot" of objects and just assume it must be 9).
- Your keyboard skills, including your knowledge of where the number keys are on your keyboard makes a difference. Also, if you have a number pad, it’s a lot easier and quicker (most laptop keyboards have a pseudo-number pad arrangement. Check your user manual).
- It’s very hard to beat 10 correct in the allotted 10 seconds!

### For the geeks (technical bit)

The game looks simple but has quite a bit going on behind the scenes. I don’t develop in Flash any more (since it doesn’t work on most mobile devices.)

The game uses:

- jQuery for the "game" controls
- JSXGraph for the dots (I wanted to use HTML5′s canvas, but the game wouldn’t work in IE8 or less)
- Ajax, PHP and MySQL for sending the data to the server and for retrieving the average times for attempts

### Conclusion

Our "number sense" is crucial for our success in math. One of the simplest manifestations of this lies in our ability to count.

I’m interested to see how people from different language groups perform on this task (and how it would be affected if different number symbols were used). See Math tests and rice paddies for some background on the cultural influences of number.

For convenience, here’s the link to the game again: Counting Game

22 Jan 2013 at 11:50 pm [Comment permalink]

Whoa this is pretty interested!

I played around for about 15 min, and the highest I got was 8, without the numberpad – which I’m guessing would make it easier.

I’ve never come across subitizing before, but from when I first started playing I was able to enumerate 9 faster than 8 because I am faster at subitizing 3 vs 4.

After a few minutes, however, I was actually able to subitize 6 and 8. For 7 and 9 I guessed…either it looks more than 8 (which I can at this point subitize) or it ISN’T 6. Because I can subitize 1-5, now 6, and 8 then I can with a fair amount of accuracy guess the remaining two.

Unless I’m unconsciously enumerating two groups (3 + 3, 4 + 4), I think subitizing is something you can actually “learn”. At least I felt that after 15 minutes of playing straight, I was able to inch closer to breaking 10 correct!

23 Jan 2013 at 9:28 am [Comment permalink]

@Oz – Thanks for the interesting feedback.

Maybe when we do 8, even if we are counting pairs, it’s a bit harder to keep track of what we’ve counted already. Interesting that you feel you’ve “learned” how to subitize 6 and 8!

27 Jan 2013 at 6:00 pm [Comment permalink]

Regarding the 9s – I figured out that it’s the highest number (as I counted incorrectly once as 10 and… I failed two tests in a row that way).

The absence of 10s and higher increased my time for me to count the 9s a lot! Sometimes I was able to figure out that it’s 9 without even counting all dots – I just look at the dots, divide them in two parts visually, I count the visually smaller part (with 4 dots) and I directly hit 9, because I see that the other part have more dots.

12 Feb 2013 at 9:32 pm [Comment permalink]

I love this game. After a while you begin to “know” larger numbers too.