Inventive Strategies

In my problem solving interview at Houston Elementary, my student used direct modeling and traditional algorithms for most of the problems I asked her, but some of her strategies seemed particularly unique. For example, I gave her the following problem:

There are 30 kids in the cafeteria and 23 more kids come in for lunch. How many kids are in the cafeteria now?

She began using manipulatives at first, but then decided to use her paper instead. She first wrote out 30 - 23. Then she drew a line between the 3 and the 2 and wrote "50" underneath it, and a line between the 0 and the 3 and wrote "3" underneath it. Then she added the "50" and the "3" to get 53. This really showed how she was able to break the number apart into tens and ones and add them together separately.

When she wrote it out on her paper, it looked something like this:

In this way, she grouped her groups of tens together (3 + 2 to make 5, which she knew represented 50) and her ones together (0 + 3).

Another strategy she could have used would be to use manipulatives to demonstrate the addition by having one color (red) representing tens and another color (blue) representing ones. Then she could add the red manipulatives together and the blue manipulatives together to represent each place value of the answer : 53.

She could also use a counting technique of drawing out ten sticks on her paper and then adding them together. She could then draw out ones on her paper and add those together. Then she could add the two answers together.

Both of these methods are similar to the method she utilized, but are just slightly different ways of approaching it.

Talk Moves!

1. Although I didn't have an official written lesson plan to teach this week ,the teacher gave me a place value chart and a few worksheets to go over with the students. I have only been working with the students for about a week, and this was the first time we weren't testing . I wasn't very comfortable just going over a worksheet, since I'm used to doing more interactive activities to teach math, but I also wanted to be helpful to the teacher. I tried to use some of these talk moves, especially revoicing and asking the students to apply their own reasoning to someone else's reasoning. Wait time was more of a challenge because, although I felt the students did need time to think, the more wait time I gave them, the more off-task they seemed to get. I really had to find a balance between giving them "wait time" and giving them time to just goof around.

I feel that the talk moves I did use were effective, and had the students grasped the concept better, I would have applied some of the more "higher order" talk moves such as asking the student to apply their own reasoning to someone else's reasoning. But when working with students who have trouble explaining their own reasoning (especially ELL students) to begin with, this is often the last talk move I want to use.

2. If I could re-do this lesson, I would probably use the talk moves more deliberately and more effectively. I have to admit, I didn't consciously ask the students the questions with the "talk moves" in mind, but maybe if I had, the lesson would have gone more smoothly. Also, I think that after I practice the skill of identifying the place value of different digits in the numbers (which is the skill I was teaching) more with the students, I will be able to apply talk moves such as "asking students to apply their own reasoning to someone else's reasoning."

Once I was ready to apply this talk move to my teaching however, I feel that it would help my students better understand their own thinking as well as other students' ways of solving the same problem.