Thursday, February 27, 2014

Don't Be So Helpful!

I had the joy of spending a day learning from Dr. Yeap Ban Har, from Singapore, again last week.  I've seen him many times and always learn something new.  This time he talked about the importance of social learning for our students--how they can learn from each other with less help from us.

I use these strips for lots of activities, including vocabulary, divisibility rules, rounding and estimating, ordering, etc.  But this was a task for teachers.
Students have built the number 3,246. 

 You've asked them to find the number that is 300 less than this number, but they're struggling.  What questions can you ask the group to help move them?  And can you sequence your questions from the least helpful to the most helpful?  We tend to jump in and tell students what to do and rescue them.  As we work to build more perseverance, we need to be a lot less helpful.

These are the questions a group in TX came up with.  How would you sequence them from least helpful to most helpful?  What other questions would you add?  It's interesting to take the time to think through our questions.  To help our students more, we need to be a lot less helpful!

I've been working with place value strips for a long time. ( I'm very excited about Crystal Spring Book's new student-sized strips.  They come in sets of 10 or 30. .)

Monday, February 17, 2014

What is Number Sense?

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.

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!