# The Boundary of Subitizing (The Rewind Version)

Before I proceed with this series on subitizing, I must raise these questions: Is there a subitizing boundary? Is there a number of objects which are simply too many to subitize? If so, what might that number be?

2. The Boundary of Subitizing, “The Rewind Version”

3. **How to Make Quick Subitizing Images + 3 Free Resources**

5. **These Dots Will Grow on You**

6. Seeing Multiple Perspectives Through Your Eyes and Through the Eyes of Others

**NOTE: The Rewind Version Below has been slowed down and will be much more useful in your classroom.**

Let’s think about a ten-frame with a dot in each square. I think we would instantly recognize that as ten dots without having to count or calculate, Or ten dots arranged like ten bowling pins. If the seven-pin is missing, would we recognize that as nine without counting? I think the arrangement is critical and if we define subitizing as recognition regardless of arrangement, then I think the maximum is very small, three or four.

Here is a question that I don’t know the answer to. Is it really subitizing if you have to calculate? When I see the five groups of five, even though they are arranged in a very familiar way, I think I still did a five times five mental calculation. Does subitizing simply mean not having to count?

Timothy, I share your question: “Is it subitizing if you have to calculate?” I’m planning to address this concept some more in the 4th post in this series, which will be entitled “Beyond Subitizing.” I’ll also mention it in the third post which is about how to make quick images in the classroom. It’s a great question, and I think we need to pay close attention to it. I really like how you are thinking carefully about your own thinking.

It’s a fair question: “Is it subitizing if you are calculating?” I guess the only answer I can give is “Maybe I’m not subitizing then.” Because when I determine the number of dots I CAN’T do it without some calculation. For the 5 dots my mind processes “2 groups of 2, and 1 group of 1”. I am doing the calculation in my head, but I’m not counting the individual dots. Then I expanded that to 5 groups of 5 dots and used the same concept.

I guess my question would be “If subitizing doesn’t include ANY sort of calculation then how exactly does your brain determine how many dots there are?”

Yes, these are great questions. What exactly is happening? Also, is it all one thing, or can it be a combination? Does a definition of subitizing mean no calculations, and if so is there a concept somewhere in the middle that is really a combination of both processes that we haven’t named or identified yet?

Here’s a thought I had…

https://youtu.be/M7mcfWswubo

Tim, this is a great use of technology to share your thinking. You have tapped into an important idea about how we can grasp familiar groupings quickly, like those found on a die. It’s almost as if we can “subitize groups” of familiar items. For example, if I roll 5 dice, and I see 3 fours and 2 fives, I can quickly determine the total without looking at every single pip on the dice, or even necessarily paying very close attention to the patterns themselves. I simply group the fours, groups the fives, and then find the total, even though there may be many, many ways to do this.

I seems to depend on how the dots are arranged. I was able to recognize 6 and 1 as 7 much easier when the 6 dots were arranged as they are on a die. It was much more difficult to recognize 3 and 4 as 7 when the 3 and 4 were not arranged as they are on a die.

In response to the question of maximum number we can subitize, I have always assumed it was 4, and anything past that is only recognized when arranged as on a standard die, playing card. Looking forward to the rest of the series!

Thanks, Timothy. Your points are very important, and they really frame very nicely where I am about to go with this series. I’m eager to explore what happens when we see a larger number of dots, and the number appears to be too large to subitize and the formation appears to be outside of pattern recognition. Thank you for this insightful feedback.