"Is this right?" Way too often that is the main question students ask in a math class. So much of traditional elementary math curriculum is focussed on computation - it can seem as though getting THE RIGHT ANSWER is the whole point of mathematics.

Of course, that's not the point of mathematics. I don't claim to have the right answer for what mathematics is - some of the Herons are engaged in an ongoing debate about whether math is invented or discovered, but that's another blog. What I do know is that in the best math lessons, the point of the math isn't to come to a single foregone conclusion but rather to push and prod on our understanding of how numbers work, to make and test conjectures about patterns we think we see and to explain the validity of how we are using numbers in a way that can convince others.

Over the years, we have collected and created a large repertoire of lessons and routines that emphasize authentic math explorations and discussions. Illustrative math, the curriculum we adopted more fully this year, has been the source of many of those explorations. A typical lesson has only one or two deeper tasks in which students seek to use math meaningfully and then talk to each other about what they are thinking.

This past week, the fourth graders were engaged in just such a task. They were given three solved problems and told that there were either two truths and a lie or two lies and a truth and their job was to figure out which problems were worked correctly. Each group tackled a different problem. They worked to understand what the situation was and then to figure out if the solution presented was correct. They used diagrams and estimated; some groups solved the problem themselves then compared it to the solution presented. All three groups decided that their problem was not solved correctly. All three were lies. (Here are the problems)

"Wait a second, I thought there were supposed to be two truths and a lie!" one Heron exclaimed. Hmmm...

Each group got up to the board and explained the math they had done to get their answer. After each one we discussed and agreed that the group was right and that the solution as written was a "lie." "Maybe they're trying to get us to think!" I said hopefully. We checked the teacher manual...and made a startling discovery:

"They multiplied by 53 instead of 52!" "They didn't take out the bottom floor that's not 11 feet." "They did the bottom floor twice!" The students were jumping up and down and...dancing (this is a group that likes to dance!) "They're wrong!!"

I calmed them down (just enough...it's important to ride the wave a little in these kinds of situations) and asked them what we should do. "Write them a letter!" was the response. "O.K. when you do it, make sure you explain yourselves really well. After all, you have to convince them that they are wrong so you have to be very persuasive, show them your solution and explain how it's different from theirs."

Here is the result:

This is the goal of math at Prairie Creek - to empower students to understand their world and to be able to explain their understanding effectively.

"Is this right?" You tell me.

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