Guide for using “Do I Have a Window Seat or an Aisle Seat?”

From APEC HRDWG Wiki

As part of the APEC Education Network (EDNET) project Classroom Innovations through Lesson Study, a Guide for Planning and Analyzing Mathematics Lessons in Lesson Study was created to help educators learn about Lesson Study so as to improve mathematics education. This page provides an example of using the Guide to review a 5th grade lesson from Japan titled, "Do I Have a Window Seat or an Aisle Seat?", and analyze it using the guidelines presented.

Learning Objectives

According to the instruction plan, the goals of the lesson are (p. 5),

• Students can think about how to categorize whole numbers from their own point of view.
• Students can understand the merit of paying attention to the reminder that results when a whole number is divided by a certain number.
  

During the summary section of the lesson, students were given 2 additional numbers to check their locations. From the video, we can tell that the majority of students used division to determine the seat locations. In addition, when teacher asked why they used the division strategy, a number of students indicated that the strategy was easy and quick. Thus, this lesson seems to have achieved its learning objectives.

Learning Tasks

In addition to these mathematical goals, the research team is working on helping students become autonomous problem solvers (p. 1). In particular, they are exploring how to draw out students' own questions that can guide their learning more effectively. The planning team felt an interesting (to students) learning task is important. Moreover, the team decided to pose a question with insufficient information so that students will ask for additional information.

Watching the introductory stage of the lesson, it is clear that students were genuinely interested in determining whether or not their seats are by windows. Furthermore, the initial question posed with insufficient amount of information prompted students to request a number of additional information. These ideas contributed to students making the learning task their own task.

Teacher Support

Although students understood what the problem is asking, there were some students who were struggling to get started. The teacher called those students to the front of the classroom to provide additional support. He first told those students that at any point if they knew what they needed to do, they could go back to their seats. The teacher asked students to determine a particular seat number by pointing to the seating chart. Students were able to tell the seat numbers immediately. So, the teacher asked how they knew and made a few suggestions what they could possibly do to further extend their ideas to solve the problem. As we can see from the video, this brief session seemed to provide just right amount of support, not too little nor too much.

During the remainder of the independent problem solving time, the teacher circulates around the classroom. He asks some clarifying questions and make some suggestions to extend students' thinking. He also records the methods students are using in the seating chart.

Incorporating Assessment

During the whole class discussion, the teacher calls on Ichikawa-kun first, who recognized that the numbers were increasing by 4. The teacher then had him arrange the number cards (1, 5, 9, 13, ...) on the board. The next child noted that the number cards represented the window seats on the left side of the train, and the right side window seats will be 1 less than these numbers. The number cards for the right window seats (4, 8, 12, 16, ...) were posted.

Yoshikawa-kun then used the four's multiplication facts. Since his number was 47, he noticed that it was 1 seat away from a multiple of 4, 48, therefore, his seat was not a window seat.

Then the boy in red shirt proposed the idea of using division. His number was 55, so when he divided it by 4, he obtained the quotient of 13 and the remainder of 3. He noted that the seat numbers that are divisible by 4 or those with the remainder of 1 will be window seats.

The discussion followed very closely to the lesson plan. This was made possible by the teacher carefully noting which students were using which strategies. Thus, even though he might appeared to be calling on volunteers to share their ideas, he was carefully orchestrating the whole class discussion, using the data he collected as he circulated among students during the independent problem solving time.

As discussed earlier, during the summary segment of the lesson, the teacher asked students to determine whether or not two additional seat numbers were window seats. The video shows that most students were indeed using the division method. Not only were students using the division method, they were doing so intentionally because they felt that was the most efficient method.

Revising the lesson

There are a couple of points from this lesson that may be worth further reflections. First, the students were given an empty seating chart they could use. Although the teacher told the class that they did not have to use it, the availability of the chart may encourage more students to use the chart. The question is whether or not that will actually limit students from using more mathematically sophisticated method. If students' focus is solely on answering the question, that might be possible. On the other hand, if students are interested in finding out patterns that might be useful in answering the question, having actual seat numbers may be helpful.

Another point to consider is that the orientations of the seating chart as presented originally (and also on the chart handed out to the students) and the way the number cards were posted on the blackboard were different. When students began discussing right/left window seats, translating from one chart to the other might have been confusing to some children.