Many teachers, as they explained their approaches to teaching particular concepts, mentioned teaching key words, clues, and tricks.

If it says “in all” ….Add.
If it says “left”…Subtract
Start with the bigger number…

This approach comes from teachers instructing and guiding more than designing work and facilitating.

My conclusion from our work was that teachers needed increased time to design (a form of problem solving) and that for many working with colleagues was a necessity. A look at their text materials showed too few good problems for solving.

Here’s just two design ideas that emerged from some very short discussions…

A kindergarten text had this problem:

Harry had 14 hats. He has 9 left. How many did he give away?
14 hats drawn on the page were there for the students to use.

Several problems followed that copied the exact format (Allowing the clues and key words approach).

We redesigned so that students had some problems that read:

Harry has 9 hats. He used to have 14. How many did he give away?

These changes allowed teachers to engage students in more math thinking, talking and uncovering strategies for solving a problem.

Discovery…I can draw the 14 hats that he started with and circle the 9 that are left and count that 5 were given away. Or I can draw the 9 that are left and keep adding hats that were given away until I get to 14. I had to add 5 more. The strategy is using a drawing to help problem solving.

A fourth grade teacher shared that she had given problems to solve to students in cooperative groups of 4 with a higher and lower performing student in each group. Her observation was that the lower level students did little thinking about the problem.

The PLC identified two alternative designs…

One was to group the lower performing students together with a problem with less complexity and the higher performing together with a more complex problem. In this case the teacher may provide more guidance or scaffolding to the lower level students.

Another was to pair a high and low student together as partners and when assigning tasks, identify that the lower level student would be the one responsible for presenting the explanation of the pair’s solution. This design requires the lower performing student to seek understanding and places the higher student into a coaching role.

In order for teachers to build strong learning designs, they must first be able to identify the learning behaviors that will most likely create the student achievement. Then, design to get those behaviors. This is often much more complex and demanding work/thinking on the teacher’s part than is preparing a “teaching” lesson plan.

School leaders and coaches may need to initially facilitate these conversations and then create the time and expectations that teachers collaborate on learning designs.