case 1

Day 1 clip 1: Introducing Clown's Walk

Ms. Coombs begins this lesson sequence in her regular Algebra I class with an activity involving a computer tool that displays the back and forth motion of a character named Clown.

 


Day 1 clip 2: Exploring Clown's Walk

This portion of the class occurs immediately after Ms. Coombs asks the class to work in pairs on the activity described in the previous clip.

 


Day 1 clip 3: Exploring Clown's Walk Using the Finger Tool

This segment shows Ms. Coombs working with another pair of students as they try to create the graph of Clown’s walk as described on the activity sheet introduced previously.

 


Day 1 clip 4: Exploring Clown's Walk Using the Finger Tool, Part II

As a result of her interactions with the students (see Clip 2 and 3), Ms. Coombs realized that the students were engaging in the task without using the finger tool.

 


Day 2 clip 1: Exploring Speed From A Graph of Clown's Walk

In day two of the lesson sequence, Ms. Coombs re-visits Clown by focusing on a graph of Clown’s walk showing his distance from start as a function of time.

 


Day 3 clip 1: Exploring Rubin's Walk

On day two of the lesson sequence Ms. Coombs assigned a homework activity in which students were asked to explore Rubin’s walk by examining the function that represented his walk.

 


Day 4 clip 1: Clown’s Walk as Total Distance Traveled versus Net Distance

In this clip, at the beginning of day four, Mrs. Coombs discusses an assignment from the previous day in which the students were first asked to watch a video of Clown.

 


Day 5 clip 1: Introducing the Bungee Jumper

After the lesson on day four, Ms. Coombs and Dr. Thompson discussed the importance of making sure that the ways of thinking entailed in using finger tool were a part of all conversations.

 


Day 5 clip 2: Graphing Distance from Ground Relative to Time

In this segment, students work in pairs to graph the bungee jumper's distance from the ground relative to the number of seconds since she jumped..

 


Day 5 clip 3: Graphing Jumper's Speed Relative to Number of Seconds since She Jumped

This segment shows Ms. Coombs working with another pair of students as they continue their worksheets.

 


Day 6 clip 1: How to Talk about Covariation

Prior to day six, Ms. Coombs and Dr. Thompson discussed the need for classroom rules to guide discussions about moving objects.

 


Day 6 clip 2: Exploring the Bungee Jumper Video Frame By Frame

In this segment, also from day six, the class continues discussing the video of a bungee jumper.

 


Day 6 clip 3: Ms. Coombs Discusses Students' Graphs

In this third video clip from day six, Ms. Coombs asks the students to watch a replay of the bungee jumping video while referring to three student-generated graphs of the relationship of changes in time and changes in vertical distance from the ground.

 


Day 6 clip 4: How Graphs Show Speed

In this fourth segment from day six, Ms. Coombs asks students to refer to the frame-by-frame version of the bungee jumping video in order to discuss how the student-generated graphs show speed.

 


Day 6 clip 5: Discussion of Students' Thinking and How It Arose

After discussing Day Six with Dr. Thompson, Ms. Coombs agrees that the students appear to be graphing the path of the jump instead of thinking about co-varying quantities.

 


Day 7 clip 1: Exploring Distance From Bridge as a Function of Time

Dr. Thompson then agrees to teach the lesson on Day 7 in which he revisits the bungee jumping task, but changes the quantity on the vertical axis from distance from the ground to distance from the bridge.

 


Day 7 clip 2: Exploring Distance From Bridge as a Function of Time

In the clip shown here, Ms. Coombs works one-on-one with a student who is trying to use the finger tool to show the relationship of the bungee jumper's distance from the bridge as a function of time.