By sixth grade, it was a mixed bag, as far as who knew their math facts and who understood the standard multiplication algorithm. I wrote about this previously in my Napier's Bones post, but I didn't share the cool thing that happened when mistakes became part of the learning process.
Morning warmups usually included a three-digit by three-digit multiplication problem to get their math brains working. When I would ask for answers, the usual suspects raised their hands while the others sat silently, hoping I wouldn't notice they were still breathing.
I dutifully wrote down "the answer" and asked for other solutions. "The answer" owner was slightly indignant that I didn't trust it was correct. I persevered. After some coaxing and assurances that no students would be publicly flogged during this process, a few more hands raised.
This was great – a turning point! What started out feeling like I was pulling teeth, eventually became a spirited discussion, as they learned to trust the process.
When time came to share out, hands shot up! We'd look at the list of answers. I'd remind them of my "Rule of 5"(at least 5 people had to have the same answer), and off we'd go.
Usually, some were only a few digits off, while others were not even in the ballpark, but they shared anyway. At first, I would solve the problem using Lattice and explaining (thinking out loud) that I preferred that method because I could easily find out if my mistake was in adding or multiplying. That made it OK for those kids who struggled with the regular algorithm, and used lattice, to share.
Some of the students would take another look at their work and ask to change their answers in the list.
"Terrific! You found an error! Was it in addition or multiplication?"
It took awhile, but eventually I had most everyone contributing, at one time or another. They all wanted their answers on the board (and later, the document camera. How did I ever survive without that handy piece of equipment?!!) But the best part was, if they saw their answer wasn't part of the majority, they'd immediately recheck for mistakes and offer another solution.
Students became more at ease talking about where their mistakes were, recognizing if it was out in left field, it was probably a multiplication error. Otherwise, they didn't add correctly. At that point, I only had to facilitate, while they demonstrated their solutions.
And the best part- it carried over into other math discussions. They weren't afraid to share and ask questions if they disagreed.
Yep, I'm a firm believer in letting students own their mistakes, recognize them, and fix them. That ownership is an important part of the learning process!
"You can only go forward by making mistakes." Alexander McQueen