We throw the term around but rarely define it. I had two experiences this week that help bring the concept into sharper focus.
I was fortunate enough to work with second graders on Oahu, in a Hawai’ian language school. I had beansticks and bundles and leftovers with me. After the keiki (children) became familiar with beansticks, I posed this question to them; “Build the number that is 1 beanstick and 15 beans.”
All children were able to figure out it equaled 25. But some children built it with two beansticks and 5 loose beans and some did exactly what I’d asked. Then we had to discuss if both answers were correct and equal. It led to a lively discussion and some very strong opinions!
It was developmentally interesting to see the children struggle when we moved to bundles and leftovers. Since they couldn’t see the 10s as clearly, building one bundle with 20 ones was much more problematic. The children spent a great deal of time taking the bundles apart, counting 10s, and putting them back together. Obviously, they didn't trust my bundling skills!!
My second experience was sitting in a workshop with Dr. Yeap Ban Har, our favorite expert from Singapore. He talked about number sense as a complete understanding of number bonds. Our children need to understand 25 is 20 + 5, but also 10 + 15. Without this understanding, they won’t be prepared for regrouping. As they get older, that understanding needs to generalize. 3/5 is 2/5 + 1/5. If one dividing 351 by 3, it doesn’t help much to break the number into 300 + 50 + 1. Number sense means the child understands that 300 + 30 + 21 is a much more logical way to decompose the number. Ban Har will be joining us at our National Conference for Singapore Math on July 9-10. http://sde.com/nationals/2014/
Try posing some number sense questions to your students and then give them some time to struggle with the concepts. Don’t jump in and help too soon!