Home      Organizing Induction      Improving Practice   

Sample sketch: Bar graphs (fifth grade)

Two interesting features of this discussion: The matter to be learned is a tool, and the teacher treats it as such. The teacher's careful sequence of questions makes the students do the work.

The information in this sample may be more general than you will want to produce in your own work.

Discussion Sketch

Discussion sketch, Side 1

On this side, quickly mark a few key characteristics of the discussion. On the other side, compactly record a discussion by noting the teacher’s questions, student’s comments, and teacher’s responses to those comments.

Curriculum expectation or benchmark:


Objective (what students should know or be able to do): Students will relate a concrete case to the idea of relative magnitudes, their representation in numbers, and their representation in bar graphs.

Object to be discussed (text, data, image, video, map, chart, representation of a phenomenon, students' personal experience, etc.): A set of containers with different volumes.


Grouping pattern

__X_ Whole class:            

__X__ Small groups: For the measurements

____ Pairs:

Uses of language

__X__ Students learn language: Of graphs

____ Students learn about language

__X_ Students learn through language:

Type of discussion

__ Recitation: Teacher asks what students know and builds upon what students know so students share a small body of knowledge.

_X_ Guided discussion: Teacher invites and helps students to comprehend, explore, analyze or evaluate a phenomenon, concept, problem or issue

__ Open-ended discussion: Teacher invites students to synthesize and evaluate, and participates with restraint.

Map the classroom and enter student names



Discussion sketch, Side 2*


Teacher's question or statement

Student's statement or question

Teacher's response


The teacher walks in carrying a large paper bag full of clinking glass.  Entering the classroom with a large paper bag is highly unusual [in this Japanese elementary school].

By the time she has placed the bag on her desk the [fifth-grade] students [appear to be] regarding her with rapt attention. What’s in the bag?


She begins to pull items out of the bag, placing them, one-by-one, on her desk. She removes a pitcher and a vase. She soon has six containers lined up on her desk.

A beer bottle evokes laughter and surprise. [The observer thinks that] the children continue to watch intently, glancing back and forth at each other as they seek to understand the purpose of this display.


The teacher, looking thoughtfully at the containers, poses a question: “I wonder which one would hold the most?”

[With the containers and this object-based question, the teacher has given students a problem to solve].

Hands go up, and the teacher calls on different students to give their guesses: “the pitcher,” “the beer bottle,” “the teapot.”

The teacher stands aside and ponders: “Some of you said one thing, others said something different. You don’t agree with each other. There must be some way we can find out who is correct. How can we know who is correct?”

[The teacher uses a response-based question to keep the ball in the students' court.]



Interest is high [it seems to the observer], and the discussion continues. The students soon agree that to find out how much each container holds they will need to fill the containers with something. How about water?

The teacher finds some buckets and sends several children out to fill them with water. When they return, the teacher says:  “Now what do we do?”

[Again the ball in student's court; seems likely that the teacher has taught the kids to handle water before this.]

  [It seems significant that this column is blank for several moves; the teacher is keeping things going by her leading responses to what the students say.]

Again there is a discussion, and after several minutes the children decide that they will need to use a smaller container to measure how much water fits into each of the larger containers. They decide on a drinking cup, and one of the students warns that they all have to fill each cup to the same level—otherwise the measure won’t be the same for all of the groups.

At this point the teacher divides the class into their groups and gives each group one of the containers and a drinking cup.


Each group fills its container, counts how many cups of water it holds and writes the result in a notebook.

[In this measuring, the students have the opportunity to form clear and concrete referents for the magnitudes "1," "2,", etc.]

When all of the groups have completed the task, the teacher calls on the leader of each group to report on the group’s findings and notes the results on the blackboard.  She has written the names of the containers in a column on the left and a scale from 1 to 6 along the bottom. Pitcher, 4.5 cups; vase, 3 cups; beer bottle, 1.5 cups; and so on. As each group makes its report, the teacher draws a bar representing the amount, in cups, the container holds.


Finally, the teacher returns to the question she posed at the beginning of the lesson:  Which container holds the most water?  She reviews how they were able to solve the problem and points out that the answer is contained in the bar graph on the board. She then arranges the containers on the table in order according to how much they hold and writes a rank order on each container, from 1 to 6.

[Here the teacher takes over to recall the path of the discussion. She emphasizes the connection between the relative volumes of the containers and the numerical and graphical representations of those magnitudes. The bar graph is represented as a tool of the work.]  

She ends the class with a brief review of what they have done. At this time, she mentions that the terms for the horizontal and vertical axes of the graph are "ordinate" and "abscissa."


*Excerpted from Stigler, J, & Stevenson, H. (1991). How Asian Teachers Polish Their Lessons to Perfection. American Educator, Spring edition. Edited lightly to minimize claims and maximize description.

Back to list of sample sketches