This week we worked with counting and ten frames in my
bilingual Kindergartend classroom. The students were eager to work with the
block manipulatives and eager to show off their skills as “mathematicians.” I
observed the lesson and took pictures for the noticing blog. Here is what
occurred.
Teacher: “Please put 6 blocks on the ten frame.”
Students begin to put
blocks on the ten frame. Student A’s ten frame looked like this:
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Student A and Student
B were sitting next to one another. Student B’s ten frame looked like this:
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As the teacher walked
around, she notices student A’s and Student B’s ten frames.
Teacher: “Student A! What are you doing! That’s wrong.
You’re not listening! Look at Student B’s ten frame, do you see how his go to
the end? If you don’t do that, then, you’re wrong. Student B was listening, why
weren’t you?”
I was kind of taken a back, and I think that comes from
learning about CGI last year. In my head, I would have accepted both answers, I
mean, they were both right, weren’t they? Both students have 6 blocks on their
then frame, and both students counted 6 blocks.
I decided to investigate why my MT had said this. I looked
at the lesson, and it explicitly stated that “blocks should all follow paths,
with numbers over five going to the end of the ten frame and restarting on the
next line.”
And all I could think was, “Does it really even matter?” It
just seems like nit-picking. Both ten frames are representative of 6, so why is
it important that all of the students’ answers look the same. I liked that my
student had a different idea of how to show six. As a class we talk about representing
our numbers of the day in different ways all the time. Using a CGI approach
would allow the teacher to accept both the answers as correct, it would also
save time and the embarrassment of the student.
I think there are at least three important principles here:
ReplyDelete1) As you correctly state, if our objective is to advance students' mathematical thinking, then the thinking they do is what is important, not some arbitrary rule or method or instructions that we give them. Thus, having the students defend their logic for this problem would be more important in getting them to learn and do mathematics than getting them to adhere to these arbitrary instructions for the task.
2) This would be a great opportunity for students to compare answers. As you say, the second student seems to understand, but is not approaching the solution in a given way. By comparing the solution with Student A, Btudent B may easily revise his thinking.
3) Another way you might learn about why your mentor did / said this is to ask her in a non-judgmental way. "Could you explain to me what you were thinking about when you were monitoring the student work?" This is just a good general principle: to ask your MT about what she is thinking as she is teaching. This will illuminate some of her practical knowledge; even if we don't always agree with the decisions, it is useful to know what she is thinking about as she works in the classroom.