*how did I do*?). But when teachers look at student work to figure out what and how students are thinking, they can give comments that are more descriptive (“Here’s what you seem to be thinking and understanding now”) and forward-looking (when a teacher says, “here’s something else you might think about in this work” a learner generally thinks,

*maybe I’ll try this next*).

**An Orientation Toward Understanding **

*together*by reflecting on samples of their students’ work in professional learning groups.

**Putting It Out There: Worth the Risk**

- Better understanding of what students are thinking about the concepts and skills they are learning.
- More effective feedback that is more descriptive and more likely to involve students.
- More targeted next instructional moves to address students’ current thinking.
- Satisfying and productive professional development.

#### Looking at student work for evidence of student thinking more than correctness is a powerful method for changing the school culture to one in which educators and students alike focus on student understanding.

*students*had needed more feedback on the quality and depth of what they wrote in their logs during their observation work. By sharing these results, this teacher learned some things about feedback that will likely “stick” and change her practice more deeply than most other professional learning she could have undertaken.

## Looking Together Is Powerful

*inductive*reasoning: teachers look at student work, interpret it in terms of student thinking, ask questions, and reflect. This sets it apart from professional learning that begins with a didactic presentation, then has teachers apply the principles taught to their practice—reflecting

*deductive*reasoning. With PLC-type teacher learning, there’s a way into the learning conversation for everyone (everyone has samples of student work). And because every teacher’s student work is different, differentiation is built into this learning. Thinking out loud with colleagues models for everyone the process of analyzing student thinking.

**Feedback that Strengthens Teachers’ Practice**

*paraphrased from the textbook. The group brainstormed possible solutions to this problem that they all could try. They could:*

- Change the phrasing of the prompts to make it clearer that more was required than a textbook sentence (e.g., Describe at least one thing about the migration routes of the first Americans (see the map on p. x of your textbook) that makes the migration seem like an amazing feat to us today).
- Model good responses and give students feedback on the quality of their responses, so students could understand how to provide more thoughtful answers.

*why*these were quadrilaterals. One typically high-performing student wrote: “They both have 4 sides. They both are polygons. The diamond all the sides are the same.” In the sorting task, he simply wrote the number of sides inside each figure, implying but not actually sorting. Their explanations lacked the depth she was looking for in their mathematical thinking—perhaps simply because they didn’t take the time to explain what they may have thought was obvious.

**Feedback that Changes **

- Is based on criteria that have been shared with students ahead of time.
- Notices and names at least one thing the student did well and makes at least one suggestion for improvement.
- Includes an opportunity for the learner to use the information to improve this or future work.

Tara sent 14 friends either a letter or a postcard. She spent $3.84 on postage. If it costs $0.20 to mail a postcard and $0.33 to mail a letter, how many letters did Tara send? Show what you did to get your answer.

*systems*of equations, as an efficient strategy to this problem would involve. If Darcy could successfully model even one of the two equations needed to solve this problem using systems of equations, it could be the next step in her journey toward being able to use linear equations to solve problems.

**Shifting the Classroom Culture**

### Uncovering Student Thinking

In their latest book, Susan M. Brookhart and Alice Oakley unpack how to more effectively analyze student work.