Video #7 Lesson on Graphs

Purpose for the Activity
In this activity the teacher wanted the students to understand the relationship between a word problem or story problem, a data table that numerically shows the data and the information graphed on a coordinate plane. The students practiced generating ordered pairs. They also worked on identifying and assigning the x and y axes. Next, the students generated the algebraic equation. All in all, the teacher wanted the students to be able to show each problem as a graph, a table and an algebraic expression.
The teacher had the students talk about the graphs as a story. I liked the example she gave, comparing the relationship of the graph to an oven baking cookies. The oven’s temperature slowly climbs at a steady rate until its reached temperature. Once it has reached the temperature it has been set to it fluctuates around that number for the amount of time that it is used. Then as the oven is turned off it slowly looses heat until it has reached room temperature. Good pedagogy suggests that students understand mathematic relationships better when they can apply it to a story or in another context. The students took time to create a story that fix a graph which helped them to understand the foundation which the rest of the assignment built on. As the lesson progressed the students worked with generating tables, graphs and the algebraic equations.

Questions:

#1 Describe how appropriate you think the primary task in this lesson is for developing an understanding of the mathematics being taught.

I feel that the teacher did a thorough job with this topic. She set up a context for the students to explore the concept on their own and attack the problems from different angles; some of the groups started with the tables and progressed onto the graphs and algebraic equations, some of the groups started by making the graph and then generated the table. However, I do feel that the teacher’s initial instructions were a little vague. She spent a lot of time reiterating the directions; I feel that her initial instructions, given to the whole class, should have been more thorough. Furthermore, considering the time constraints, a ninety minute block period every-other day, I think that the teacher balanced the amount of time spend in whole class discussion and group work well.

#2 Describe how the teacher’s questioning, and the manner in which student responses are handled, contribute or do not contribute to a positive classroom learning environment?

The teacher discussed her questioning style at length in the interview section of the video. I was very pleased to see the degree to which she used errors to teach concepts and emphasize ideas and relationships. Furthermore, the teacher acknowledged that the students feel comfortable sharing mistakes and asking questions because of the positive classroom learning environment that she created. Clearly, she was sensitive to the student’s mistakes and very tactfully dealt with errors. Her sensitivity to the student’s mistakes was possible because she clearly understood the types of errors that the students made and why they made the mistakes they did. She quickly addressed misconceptions and mistakes in a very non-threatening manner. However, she never just gave students the answers, she always lead them to the answer through her line of questioning.

#3 Describe what the teacher does to support learning while students are working in groups.
The interview section of this video addressed the strategies that the teacher used to support the individual groups and help them reach the next level of understanding. She knew her students well enough that she knew when a simple question would be enough to redirect their thinking and lead them to the correct answer. However, she knew that some group needed more personal attention and stopped to discuss the problems with them at length. The teacher said that in this lesson they tried a different grouping arrangement, she allowed them to select their own groups. Personally, I would not do this; I feel that having done it once that the students would frequently ask to choose their own group and that it might become a point of contention. Perhaps, had she grouped the students more purposely they would have avoided some of the confusion that may have been caused by the students distraction caused by grouping situation.


Overall Use of the Video
Unlike the last video I felt that this video was less effective because it was broken into so many pieces. The former lesson was shorter, with less parts and the general flow of the lesson was more apparent. In this video series, I was very confused as to the sequence of events and the general progression of the lesson. The video quality was very poor and that detracts slightly from what I, as an observer, get from the lesson. However, the interview section of the video was more valuable in my opinion. Sand Allen provided very specific examples of techniques she used, errors that they students made, the objectives that she had for the lesson and what she believed the students got from the experience. Overall, she spoke about the lesson using specific examples and was less theoretical than Rosemary Klein, the teacher from the previous lesson.
There are some aspects of the video that are frustrating. I wish that I could see the overhead properly. Some of the audio is difficult to understand and the subtitles do not consistently make up for lost on inaudible speech. Being able to see the student work as the video progressed would have been helpful as well. However, overall I feel that the video is very useful. It has certainly given me some ideas about how to best teach this information in my own classroom.