Video analysis - graphing

The purpose of the activities in this video is for students to represent graphs in a variety of ways and to extract meaning from the graphs. The students first create a story about the graph, which helps them learn that the graphs depict a relationship between two quantities. Next they create tables as another representation of the graph, and finally they develop an equation to show a fourth representation. The content of the graph is therefore shown as a graph, a table, a story, and an equation – four representations!
Lesson Analysis 1: Describe the primary task in this lesson and identify the mathematical skills and concepts that this task is designed to develop.
The primary task in this lesson is for students to create a sequence for their classmates and teachers to figure out missing numbers. In order to meet that goal, students will develop the skill of representing a concept in several different ways and problem solving to find a generalized equation for that sequence.
Reflective Task 1: Describe how appropriate you think the primary task in this lesson is for developing an understanding of the mathematics being taught.
I think the primary task in this lesson was very appropriate because the students had to use various representations to display the meaning of the graph, communicate mathematically in groups, and problem solve to figure out a sequence that would be a challenge even for their teacher. Not only were the process skills used, but the students developed a better understanding of the relationship between two variables in a graph because they attached personal meaning to their graphs through stories.
Lesson Analysis 2: Describe what the teacher does to support learning while students are working in groups.
The teacher supports learning by asking guiding questions to assist the students’ thought processes. She did not simply tell them the answers or tell them how to think, she guided their learning through questions. She also encouraged the students to communicate mathematically with each other, telling them to “talk about it in your groups.” As she rotated between groups, she listened to their thinking patterns to understand where they were misinterpreting or forgetting some important aspect of their problem.

Once again, I benefited from watching the videos because I could actually see the teacher leading the children to understanding. It is helpful to witness someone carrying out the strategies we learn in school. Observing her decisions motivated me to one day guide students to learning through the process standards rather than teach them the way I was taught.