It's about this time of year that I start getting nervous and wonder if I am doing the right thing by spending so much time developing number sense and place value with my students. Why, you ask? Well, my fellow second grade teachers, who I admire and respect very much, are far ahead of me in the math textbook. While we count objects and practice strategies for using mental math in my classroom, my colleagues are teaching their students how to add and subtract with regrouping! Yikes! I feel so behind!
And here's another little secret about me. I don't always use the math textbook and often don't follow the lessons or chapters in order. I skip around. And I don't do all the pages in the book! I know! I am such a rebel. But, as I said before, I always get a bit worried or nervous or guilty around January or February because I am not keeping up with my colleagues.
But here's what I tell myself during these times of doubt.
Place value can be such a difficult concept to understand and I believe one way to build that understanding is to provide lots of opportunities counting objects.
Observing students as they group and count objects helps me identify their understanding and misunderstandings about place value and number sense. I think many of our math textbooks and worksheets mislead us into thinking our students understand place value because they can identify the tens and hundreds place, tell you what a digit is worth or even build a number with place value blocks. But ask these same students to organize and count large numbers of objects and you quickly see that they can't count transfer their knowledge of place value blocks to objects that aren't already grouped for them.
When I give my students time to organize and count larger quantities I see first hand how they begin to internalize our place value system and see the patterns. I can tell them there are 10 ones in a ten or 10 tens in a hundred until the cows come home, but when they notice it themselves and share it with a peer or their teacher it sticks! Watching a student who preferred to count her objects by ones begin to group objects by tens, and then to move on to grouping those tens into hundreds shows me how that student is building a strong understanding of place value.
On the days we count collections it's a bit loud and messy. Groups of students are laying or sitting on the floor, cups and bowls for organizing are out and there's always lots of excitement. My job is to facilitate. I move around the room observing and asking questions like, "How are you counting." "What are you noticing when you count?" In the beginning I sometimes have to help students communicate with each other. Working cooperatively is very new to most of them. I also stop and share with the class when I notice a group using an efficient counting strategy or when a group has what I call their "Ah Ha!" moment. Since our collections are large with more than 200 objects to count it forces students to become more efficient with their counting methods. When one group becomes overwhelmed while counting by ones I can ask, "Is there another way to count so you don't get confused." Or I can share what another group is doing. "Look at what Katie's group is doing? They are organizing in groups of ten. Do you think that might be helpful?"
I love the math conversations I hear while we are counting collections. All students are engaged and motivated. Everyone, whether they struggle with math or excel are challenged and successful during this time.
I will continue to doubt myself and my methods periodically but that is probably good because it forces me to reflect on my practice and fine tune my lessons and activities.
You can visit my class blog to see counting collections in action.
Do you use Counting Collections in your classroom?
What are your thoughts regarding how students develop place value?