Saturday, April 21, 2012
Subitizing - Making Sense of Numbers
With subitizing. Rhymes with oobitizing. (I always thought it rhymed with rub-itizing.)
Know what it is? If you're teaching, it's a great tool to add to your toolbox!
Ever since I read about it in Teaching Children Mathematics, I've been on a mission to learn more. Basically, it's the ability to instantly recognize a quantity. An example that frequently comes up: dice. Most adults see a number on a die and immediately recognize the number, without counting. We define two different types of subitizing:
Perceptual Subitizing - a number is instantly recognized, usually with quantities of 5 or less.
Conceptual Subitizing - recognizing small quantities within a number and combining to find a total. For example, you might see 7 dots as a combination of 3 dots and 4 dots.
You can see how the ability to subitize leads to all kinds of math skills. If you can instantly recognize a quantity, you can count faster, add/subtract/multiply/divide more easily and efficiently...the list goes on. It's a no-brainer that we want our kids to master this.
So I've been trying.
I started by placing objects on a peg board, showing a quick glance, and having the child replicate it on his own board. I also tried flashing quantities on a DIY counting rope.
More recently, I've been flashing quantities on a five frame. We used ducks after our lesson with Little Quack's Hide and Seek.
I've only done subitizing a handful of times (probably less than 5) this year. My little student showed a good grasp of numbers up to 5, but anything beyond that was pushing it. I thought. Shows how much I know.
Yesterday, I printed off some subitizing cards. (Went to a TON of effort. Smirk.) Googled "subitizing cards" and printed out cards from the first Google link. (Apparently, they go to a private school site, but I found the same ones linked here titled "subitizingcards.pdf.") They are FANTASTIC. Mostly because I didn't have to make them. But also because they fit neatly into a cardboard flap. I literally grabbed a piece of cardboard out of the recycling box and had a flap made in seconds. You'll see how it allows you to flash the dot pattern and then reveal the number after the child states an answer.
I apologize that the child's volume isn't more clear. I need to invest in an external mic. Listen carefully, however, and you'll hear the reasoning that went into his answers. You might think about when he used conceptual subitizing...or when he was able to instantly see smaller quantities within the number and add them together to get a total.
Although you certainly don't need to ask a child how he arrived at an answer, I found it very helpful to help assess my student's abilities. I was surprised that he knew so many number combinations. Formal addition is going to be an easy next step.
Now...go subitize! Here are some more links/resources to assist you:
A terrific blog entry, Why Learning to Subitize is Important. (Thanks, to Tricia for the suggestion!)
Staff development with 1st grade teachers
In this YouTube Video, the facilitator guides teachers through steps that children might take in gaining number sense. It's 20 minutes but really gives you an education.
Math Coach's Corner
Donna has several posts about subitizing. She writes that subitizing is "foundational to the development of number sense." She links blacklines from John VanDeWalle's book with lots of subitizing cards. I'm printing these next. Also read her post describing different ways that kindergarten students saw a dot pattern.
Dr. Nicki's Guided Math Blog
Love Dr. Nicki's resources. She has several posts on using subitizing in the guided math setting.
Freebie! - Number Rack
Read about Math Learning Center's new free app, Number Rack. It could be easily used for subitizing, both online and on an iPad/iTouch. The entry also links you to a free activity/lesson book.
PDFs - Use with Subitizing
This site has a whole list of pdfs to print for subitizing with kids.