Video - Lesson on Graphs

1. What are the mathematical ideas in this lesson and how significant are they?

While watching this particular video, I noticed that the teacher was incorporating many different ideas into her lesson. She began the lesson by showing her students the problem on the overhead projector and reading it aloud to them. Then she posed the question about why the problem had an 'x' and what that 'x' meant. By the teacher asking her students these questions the students are able to think about what it meant here and why it would be in the problem. Many of the students had answers about what they thought it was and what they believed was meant by the 'x'. This is significant because the teacher is explaining to the students why it is important and how the students can develop an understanding for what they are trying to find. The 'x' represents a number, any number, that can be determined by completing the math problem. Graphing the problem is also an idea that the teacher was trying to represent. By having the students graph the problem, they are able to visually see what number or numbers can be represented by the 'x'. By graphing, the students can eliminate numbers that the 'x' cannot be, which will help them formulate a number that can be represented.

2. What evidence is there that students have learned the mathematics being taught?

The evidence that is present in the videos, is that the students are able to explain in great detail how they came up with their answers and how they created the graphs. The one student who was explaining the graph and how the ski company's profits changed over the course of five plus years, was able to show the rest of the class how she came up with her numbers and how her graph represented the numbers that she had come up with. The students were able to create their own problems, which shows that they understood and learned what was important and needed to be present in the problem.

3. How effectively are student mistakes addressed and misconceptions dealt with?

From the clips of video that I watched, the teacher seemed to address the students mistakes and misconceptions every time. This way the teacher was able to see where the students were getting the mistakes or misconceptions. If the teacher had let the mistakes or misconceptions continue not only would it hurt the students because they would be learning the wrong information, but it would also hurt the teacher because she might have to reteach something over again. This would hurt the teacher because she could have stopped the students from continuing these mistakes in the beginning. Also be addressing the mistakes and misconceptions the teacher is showing the students that others in the class are making the same mistakes and that it is alright as long as they are addressed in an orderly way.