**Vignette 1: Language Arts, Upper Elementary **

An upper elementary language arts teacher began the lesson by asking a series of planned questions about a story students had just finished reading:

- The teacher first reminded the students about their reading learning goals for this week which focused on identifying the main idea and supporting details within a story.
- Her questions required careful analysis by the students, so the teacher structured her approach by asking students first to think about their answers as individuals and, then discuss their answers in small groups.
- Each group was to reach consensus on a single answer and that group answer was then shared with the rest of the class using Whiteboards which designated students held up. With this questioning and group work approach, the teacher was able to identify several groups of students who were having difficulty understanding the concept.
- Summaries of the main idea of the story varied widely in accuracy and clarity. As the lesson was nearing the end, she asked the students to look at the various groups’ answers about the main idea, to select the one that they thought was the best answer, and to write down why they made the choice they did.
- She had students answer using an Exit Ticket – index cards on which students wrote their individual answers and then handed to her as they left the classroom. This approach provided her with a quick way to review student thinking at the individual level, thus providing information that she could use to shape the next day's lesson.

**Transcript of Podcast: **(pdf, 8kb)

**Vignette 2: Mathematics, Upper Elementary **

A 5th grade mathematics teacher had been working with his students in the area of data analysis, and had recently introduced the class to the concept of using measures of central tendency to summarize data. He was aware of several of the typical misconceptions that students had about the concept of “median.” In particular, he knew that students often did not think that ordering the numbers in a data set was a necessary first step, and that students often did not understand how to handle data sets with an even number of elements. He wrote two multiple-choice questions to address these common misconceptions.

At the start of the lesson the teacher reviewed what they had covered thus far in regards to measures of central tendency. He also wrote the learning goal on the board: “Today we will learn how to select appropriate measures of central tendency.”

Students had been using electronic clickers for the opening questions in math class each morning. As a quick review of previous lessons, the teacher presented both multiple choice questions to the students. Almost all students answered the two questions correctly. He was about to begin to address the goal for that day’s lesson, when a student asked, “But there could be two answers, couldn’t there?”

He asked the student to explain his reasoning to the class. The student explained that the problem could be solved in two ways – either select the middle number in the set, or put the numbers in order and then select the appropriate number. The teacher decided to poll the class and asked how many agreed with the student’s explanation of two possible answers. Just over half the class agreed that the problem could have two different answers.

The teacher then took the following steps:

- On-the-fly, he wrote up two identical data sets on the board, each with five terms, except one set was ordered and the other was not.
- He asked students to think on their own and then discuss with a partner to decide whether the two sets had the same median value or not.
- As students discussed this with a partner, the teacher circulated around the groups, making some notes of what he heard in the conversations.
- After about 10 minutes, he polled the class a second time, and now much fewer than half the students thought that the two sets had different medians.
- From the notes that the teacher took as he listened to students, he was able to identify several students who had very clear explanations for why the two sets had the same median value.
- He called on those students first to share their thinking with the class, and then asked students who disagreed to give their explanations.
- One student who had not previously been convinced by her partner shared her new understanding with the class.
- The teacher decided that the class was now ready to move on to the planned part of the lesson, but made a note to return to this problem for the class warm-up in a couple of days.

**Transcript of Podcast: **(pdf, 8kb)