## Archive for May, 2012

### Frogs on a Log

I have been so intrigued by how students build numeracy that I’ve really devoted a lot of time to working with K-2 teachers and students. Recently, I’ve spent about an hour a week at one of my schools that has 4 year old kindergarten. I thank this teacher for inviting me in, for welcoming suggestions, and for wanting to improve her math instruction. After interacting with the students and observing the teacher work with small groups, today I was able to teach a lesson to 2 small groups! Let me tell you how much I enjoyed it and how it was like a breath of fresh air! I’m always amazed by how much students know at any age and any grade level when we ask the right questions! These “little” kids know so much more than I think we often give them credit. Not only that, but I think as teachers we don’t give ourselves enough credit for how much we actually expose and teach our students! The teacher wanted to focus on the concept of subtraction and our enduring understanding was that when you subtract, numbers get smaller. Elementary I know, but so important! After discussing current units of study with the teacher, we decided to tell a story about frogs on a log. Here it is:

**One day I went to the pond. At the pond I saw frogs on a log. First there were _____ frogs on a log. Then ______ frog(s) jumped off the log. How many frogs were left on the log?**

In working with the students, I asked them each to think of how many frogs they thought could be on the log. This allowed us to see if students only picked numbers they were comfortable with, as they’d been singing a song about Five Little Frogs. This also was a way for us to see if they would choose numbers that made sense, for example would the students choose a larger number of frogs to jump off the log? It was a celebration when all of the students chose numbers that could be subtracted without getting a negative. How would we explain negatives to 4 year olds?

The students did such a wonderful job talking about the math, and explaining to me how they knew the number was getting smaller. We even had some opportunities to discuss if the number of frogs left on the log was more/less than the number of frogs that jumped off.

Here’s what I challenge you to do with your students, no matter what age/grade level; ask them these probing questions before you just tell them it’s right, wrong, or can’t be done:

How do you know?

Can you prove it to me?

Will that work every time?

Can you explain that another way?

The beauty of teaching math through problem solving is that students really do most all of the work, (once you’ve thought of meaningful problems for them to solve), and their diverse ways of thinking and understanding the world isn’t always like my own. I’m constantly learning new things! What have you learned lately from your students?