Fractions as numbers vs. fractions as ratios
A grade 4 team was recently considering the following task for a lesson in which they hoped to have students make a connection between fractions and decimals: What would you say about this? I wrote them two emails about it. First email: What would be the purpose of...
Learning goals should describe cognitive change
A surprisingly difficult but critically important part of designing a lesson is establishing the learning goals. Many teachers write learning goals in the form of behavioral outcomes: “Students will be able to…” Frequently this is what their administrators want, and...
It’s not the teacher’s job to teach the students!
What?? you might be thinking. What else could the teacher's job be but to teach? The teacher's job is to ensure that students learn – all of them, we hope, though we know we will usually fall short. In Japan, most (elementary) math lessons are designed as "teaching...
The choice of numbers matters!
I am looking at a lesson research proposal for grade 5 on division of decimal values by a whole number. The problem the team plans to use is 4.26 ÷ 3, and their goal is for students to discover that the same processes they use to model division with whole numbers...
Read the documentary on Lesson Study
For anyone who found it difficult to find time to listen to the terrific radio documentary by American RadioWorks, you can read the segment about Lesson Study here. Some of my favorite quotes: "We need to shift from thinking about how to improve teachers to thinking...