We were working on Mental Math strategies today, and I had the students attempting to show their thinking on paper. First, we try to think of all the steps we do in each problem we try mentally. Instead of doing this in our heads though, we write down what we see in our heads as we see it (not always an easy task with grade 5/6!). For example;
134 + 143
In my math notebook I would write
134 + 140 = 274
274 + 3 = 277
These are the two steps in which I followed to do this problem in my head. We have been working on writing our thoughts on paper as they come into our heads. During the exercise, I noticed something funny going on, so I called an emergency math congress on the carpet.
Me: Unicorns (I call them unicorns), I want you to look closely at the following two notebooks, and tell me which one you think is better.
Notebook One was immaculate and neat, everything was lined up in a row and written in perfect numerals, however, under the perfect script were remnants of erased numbers, barely visible. Notebook Two was covered in scratch marks and lines and X's and it was sloppy and messy.
Kids: Notebook one! (in unison and immediate).
A: Because it is neat and easy to follow and she got the answer right.
Me: Interesting. What about this one?
B: It is messy and there are lots of black marks on the page.
Me: Did he get the answer right?
A: Well yes, he did, but he made lots of mistakes along the way.
Me: Did Notebook One make mistakes?
A: Yes, but she erased the work and wrote it neatly.
Me: Ok, imagine you are me, and you have to grade this. I need to know what you were thinking when you did this problem. Which notebook is easier to understand what the person WAS thinking at the time?
B: The messy one.
A: Because you can see his mistakes, and you know when he changed his mind.
Me: Good. So, from now on, lets try and be messier when we work out problems, make sure you write down everything, even the mistakes you make.
I love a messy math notebook. I love scribbles and doodles and X's, and big heavy black pencil marks that are smeared, and maybe some paper that is crumpled because of frustration, and random numbers in the margin, and shapes and pictures.
It is like a snapshot of the brain at work. A recording of thinking in action.
Go on kids, be messy.