Subitizing – two years ago, I had no idea what it was.
In September 2010, I was asked to do my first demo lesson as Numeracy Helping Teacher. In a Kindergarten classroom. I taught Math 8 to 12. I was terrified a little nervous. Thankfully, Sandra Ball was there to hold my hand provide moral support. In these last two years, I have become much more comfortable in primary classrooms. And I can pronounce subitizing and tell you what it is – it’s recognizing, without counting, one to five objects (“1, 2, 3, What do you see?”).
This year, it has been very rewarding to support Surrey Kindergarten/Grade 1 teachers with an assessment package developed by Carole Fullerton and Sandra Ball. “What Do They Know?” focuses on three areas: subitizing, partitioning/decomposing, and patterning. In addition to fall and spring assessment tools (instructions, blackline masters, materials, rubrics), an instructional resource with suggestions for subitizing, partitioning/decomposing, and patterning lessons is also included. Carole and Sandra wrote about WDTK in a special elementary mathematics issue of BCAMT’s journal, Vector. Please read the article here.
With all-day-K in effect this year, the timing is perfect. There is time (It is time?) to focus on early numeracy. The number of Kindergarten teachers in Surrey has almost doubled this year, many of them teaching Kindergarten for the first time.
WDTK provided me with opportunities this year to work with K/1 teachers. When teachers invited me into their classrooms, I asked them to choose three kids. Then, I modeled each of the three assessment tasks with these three students. After, the teachers and I discussed the results. It was common for these teachers to be surprised by their students. Often students who were identified as struggling demonstrated capacity in at least one of the three areas. Sometimes these students even outperformed their high-achieving classmates. Later, these teachers were able to complete the assessment tasks on their own with the remaining kids.
I look forward to spending more time in Kindergarten classrooms – every secondary math teacher should get the opportunity at some point in his or her career.
Chris Hunter 
I just forwarded Carole and Sandra’s article to our Kindergarten teachers and Superintendent (he and I exchange math articles like they were candy). I’m more and more interested in what/how math is taught in lower grades because I get the kids in grade 6, and I feel badly that I don’t know why they don’t know what they should know, and I feel worse not being able to help them. The ability gap starts to widen in middle grades, and this is very scary!
I like subitizing, you taught me a new word today! Is there a word for recognizing more than 5? It’s not called “six”… 🙂 Thanks, Chris!
Fawn, you can’t recognize more than 5 without counting, decomposing, grouping or patterning. Psychology researchers have identified a time gap between the time to identify a group of 5 as 5 and the time to identify a group of 6 as 6. (I think 5/6 is the split-may be 4/5 for some). Five we recognize instantly-without cognitive processing. Six we process, and that takes a fraction of a second longer.
Fawn, check this out.
When I flash this picture at kids, some will instantly tell me it’s six. When I ask “How do you know it’s six?” they’ll say 3 and 3 or 4 and 1 and 1 make 6. As Christopher said, this is subitizing and decomposing. It’s cool to see with larger quantities, but 6 was all I could find to take a picture of while at my desk.
Oh, this is so good! I didn’t know that. Thank you, Christopher and Chris, for draining a bit of my ignorance pool. (I’ve never used/heard of that analogy, but it’s rather sad that I think my ignorance fills an Olympic-sized pool.)
Fawn, your K/1 teachers might be interested in Carole’s book Number Sense – A Combined Grades Resource for K, K/1 and Grade 1 Math Classrooms which we include with the WDTK assessment package. Also, we’re excited about Carole’s newest books, Mastering the Basics – Addition and Mastering the Basics – Multiplication, and have plans to support teachers with this series next year. Maybe your superintendent is looking to provide elementary math teachers with resources? No kickbacks at this end. Honest.
http://mindfull.wordpress.com/2012/02/20/mastering-the-basic-facts-resources-from-campbell-river/
http://mindfull.wordpress.com/2012/04/04/missing-part-cards-laying-the-foundation-for-subtraction/
Thanks! I’ll forward to the teachers and superintendent.
Also, the book The Number Sense by Dehaene is a useful resource if you’re at all interested in the brain processes underlying subitizing (and number more generally). Totally readable.
Just ordered the book, Christopher, arriving Tuesday, can’t wait! Thank you so much!