## Representing vs. solving; and missing-addend problems

I have seen many lessons in which the distinction between how to model or represent a story problem and how to solve the story problem get confused. This happens especially with story problems in which either the starting value or the change is unknown, a type of...

## Letting students in on the secret in a TTP lesson

The core of a Teaching Through Problem-solving (TTP) lesson involves presenting students with a problem that requires that they learn some new mathematics. For students to focus their energy productively, it helps them to know what that new mathematics is – at least...

## Making sure the problem context supports student learning

I had a delightful opportunity to join a planning meeting with a group of teachers from one of the schools we work with in Chicago. The team was working on a lesson for their 8-year old students about interpreting remainders in problem contexts. Here is how the...

## Great article on division with remainders

One of Chicago's Lesson Study Leaders, Joshua Lerner, wrote a terrific article in NCTM's journal Mathematics Teacher: Learning and Teaching in PK-12. It is titled, "Recommendations for Teaching Division with Remainders." From the introduction: Recently our team of...

## 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...

## Facilitating a post-lesson discussion

In response to multiple requests, I have finally written up this guide for facilitating a post-lesson discussion, which you can also find on our resources page. I will say that cultivating a good post-lesson discussion tends to be easiest if the planning team has a...

## Guide for facilitating post-lesson discussion

We offer this guide for facilitating a post-lesson discussion. Please take a look, and if you use it, please give us your feedback!

## 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...