Piper's Lesson Study Notes

Lesson Study Notes (9/29/09)

Lesson Action

Introduction

Most of my notes in this section catalog the exchange between the class and the teacher. Note: not all of the exchanges of the lesson were recorded on here, hence some of the gaps later on in the lesson when the teacher seems to “suddenly jump” to the journal. There was conversation before this and more conversation about the math journal, but I did not have the chance to record it.

T: “What does area mean to you?”

• “Space”
• “area….like”
• “like this is my area, space”
• “It’s like squares”

T: “What does perimeter mean to you?”

• “measure the outside of an object”
• “the outline of the notebook”
• “perimeter is the outline of an object”

T: “Where else have you seen area and perimeter in the real world?”

• “if you’re getting enough aluminum foil to cover food before you put it in the oven”
• Tile a floor, need to know how big tiles are
• “perimeter is by the edge of the desk. Area is inside it”
• “on a construction site”

T: (Noted the importance of knowing area and perimeter of irregular shapes)

T: “How would we measure perimeter (of the rectangle on the ELMO) with pencils?”

• “With a ruler?”

T: “We can’t because we don’t have one.”

• “We can put pencils on the shape”

T: (puts one pencil on the top of the rectangle line) “What’s wrong with this picture?”

• “The pencil’s too long.”

T: “What do we do?”

• “Cut it.”

T: “How about estimating?”

• (Voiced assent)

T: “What about area, how could we find it, with these hexagons?”

• (incoherent student response)

T: “So we’re going to fill the shape.”

• “You’re not filling all the spaces!”

T: “What are the problems?”

• “Spaces”

T: “What do we have to do?”

• “Estimate”

T: “How many do we know for sure?”

• 5

T: “How many can we estimate?”

• 2 and ½

T: “So the answer is 7 and ½ what? Pencils?”

• No! Hexagons!

T: (instructs class to open their math journals and set them up for the activity)

**Students are AMAZED by the ELMO**

T: “Was it (the measurements with pencils and hexagons) accurate?”

• No, because we had to estimate.

T: “Why did we estimate area?”

• Because there were hexagons that went over the shape and open spaces

T: (Gets ready for the transition into work time) “Should we hear any talking at this time?”

• “Yeah, about math.”

T: “Right.”

During

For this section, I first looked around the room and focused on which manipulatives were picked first. Then, I keyed in on five students in particular, whom I assigned either a number or letter to, within my notes.

Initial reaction: First manipulatives chosen: tape measure, ruler, paperclips.

Student Q

• Used paperclips to get the leaf’s perimeter, and added up the number of half paperclips.
• Said this was not accurate, because “I had to estimate them because they’re either too big or too small.”
• Then, he used triangles for area measurement.
• “I’m measuring the inside with the triangles.”
• “There’s not enough triangles, I’m gunna use squares.”

Student 4

• (a fourth grader)
• “The ruler is too hard to use”
• Then, he went onto using the triangles. He first traced the triangles and then he counted them.
• Student did uncover a problem with measuring the stem “because you can’t trace the triangle on the stem, it doesn’t work.”
• The student then went onto explain his tracing and counting method to another student.

Student 3

• “It (the ruler) is too hard to use.”
• This student was very frustrated with the activity. She was also very unmotivated and off-task constantly.
• Student 3 is a fourth grader

Student 5

• She was done with the first two measures of area and perimeter very quickly, and she moved onto measuring area and perimeter with a third method.
• As she used the circles to measure area, she overlapped many of them.
• She noted that the circles were “not accurate, they’re too big, because their fatter than the stem.”
• She then went onto measure the perimeter by using the lengths of the felt squares.
• Additionally, she used the triangles and squares to measure both perimeter and area.

Student 7

• Unbent the paperclips to wrap them around the lead and measure perimeter.

Post-Activity Class Discussion

In this section, I made sure to note, what I felt were the most important exchanges between students and teacher in the discussion. Again, this is not the whole discussion, just pieces of it.

T: We’re going to share how some people got their area and perimeter measures. “If you think something happened that you don’t agree with, then feel free to speak up, respectfully.”

• Quiet student commented on her method to wrap the string around the leaf (mostly incoherent from where I was sitting)

T: “Did anyone find a good way to find area?”

• “I traced the leaf on grid paper and I counted the squares.”

T: “Squares to find perimeter? How did you do that? Was it accurate?”

• “I lined the squares on the perimeter. No, because they were overlapping.”

T: (student name)?

• “ I hooked the paperclips together and measured around the perimeter”

T: “Was that accurate?”

• (incoherent response)

T: “Anyone else use paperclips to find area, or perimeter? Were they accurate?”

• I did, and it wasn’t accurate.

Post-Lesson Debriefing Session

I took notes on our initial ideas of improvements that can be made to the lesson, which we discussed in the staff lounge.

• More description of using units that are non-standard
• More scaffolding needed for the meaning of “accurate”
• More time should be allowed
• Maybe the lesson could be broken down into two days, the first focusing on perimeter, and the second area allowing them access to the same manipulatives on both days.
• Maybe add preassessment before the lesson so we can see the growth of knowledge as a result of their exploration.