The question went a little something like this:
Clifford sees 2 big brown dogs at the pound
Emilie sees 4 little black dogs at the pound
Then they had to fill in the drawing of what that represented… Only Clifford and
Emilie were provided on the worksheet and my daughter had drawn with the best of
her 4 year old ability a great representation of the dogs. And even the numbers (mind
you they are backwards)
And then the worksheet asked 2 questions:
1) Who saw more dogs?… To which my daughter had drawn an arrow to Emilie
and written her name.
2) How many dogs were there in total?..….. and in my daughters handwriting there
was almost a perfect #7.
Seven…? She got it wrong… Oh the horror… What should I do? How could this be? Think of what all the teachers will say if she will not be good at math. 2 brown dogs + 4 black dogs is 6 dogs… that is the only answer it could be. The teacher had written Bravo and put stickers on it but maybe she just didn’t want my daughter to feel bad for getting the wrong answer.
All the time I was looking over the worksheet my daughter was staring at me with her big blue eyes and a smile on her face. How could I tell her that she had done it wrong? How could I crush all the joy and pride she was feeling about her assignment? So instead of just jumping in and telling her the mistake I took a breath and asked her to explain her worksheet to me. She was so excited; she read through it and got to the part where she had written seven. I still couldn’t come out and say that she had got it wrong so I figured maybe if I got her to point them out she might see her own mistake. I asked her to point to the dogs and show me them while she counted.
Which she did…
I read: Clifford saw 2 big brown dogs… she pointed and started counting... one, two…
Lisa saw 4 little dogs… she pointed and counted three, four, five, six…..
Oh I couldn’t bear it….. so I asked her why she had written a 7 on the page. She looked at me and calmly said, “well mommy” ,as she pointed to Clifford, “Clifford is number seven” because Clifford is a dog too (A big red one… she had got the colour right).
I found myself reflecting back on this example last month in class when a student got an answer to a problem, but did it in a way completely foreign to me. As he explained it, I could see where his thought processes were going. He logically went through the problem. To me his method seemed wrong, but it was just foreign. I tried to show the student my method for solving the problem because honestly I thought it would save him time because it was more streamlined, and he just got confused. In this instance I agreed that he could do the work his way (because it made sense to him) and after he explained his process to me I could see where he was coming from. He completed the rest of the questions and got prefect.
To many times my students have confided in me that their previous math teachers “didn’t get how they did their math”, or marked them wrong just because it wasn’t written in the format that they teacher desired. I feel sometimes as a math teacher that we are too fast to jump to the solution and not look at how the students get to the answer. If a student does not respond to a question in the way we were expecting them to, we should not tell them that they are wrong and try to teach them the “right way”. Who’s to say our way of thinking isn’t wrong? We should not be penalizing our students for thinking outside the box or coming up with creative solutions. After all, isn’t the ultimate goal that we want from our students, is for them to be good problem solvers. Research has taught us that we need to encourage differentiated instruction because we know that students learn from a variety of ways. So why is it that some teachers still think that there is only one way for a student to solve a problem?
We need to remind ourselves as math teachers that it is this kind of thinking that we want from our students and it should be encouraged, not corralled, or forced into compliance. Whenever I come across students who do not follow the norm, I try now to pause and take a breath. Then I have the student explain how they were able to come up with the answer. This not only helps them verbalize their ideas (there’s your communication mark), but more times than not, it teaches me a new way of tackling an old problem. I can then keep that in my arsenal for teaching future students who have problems “getting” my original methods of explanation.
And the next time I see my daughters JK teacher I need to thank her for, not only seeing that my daughter was correct in her thinking process, but most importantly for showing me that I need to pause and reflect a little more over my own teaching.
by Melissa Krausse