Fourth Grade Video

The fourth grade video addresses variables - a difficult topic for young children to understand. They have not worked extensively with variables up to this point, so the newness of the topic might intimidate them and inhibit learning. To help the students build understanding of variables - a mathematical concept - the teacher incorporated a lesson devoted to creating a variable machine. The variable machine was simply two strips of paper - one with the alphabet written vertically on the lined paper, the other with the numbers 0 - 25. Placed side-by-side and attached to eachother, each number was paired with a letter, or variable.

Reflective Task 1 says, describe how appropriate you think the primary task in this lesson is for developing an understanding of the mathematics being taught. I thought this primary task was valuable because it focused on the concept of variables before delving into the function of variables. One math curriculum that I have had to use is Saxon (in tutoring). Saxon math spends far too little time on developing concepts, while drilling problem after problem of various algorithms. The students become confused as to when to subtract from what side, where and when to place the decimals, and so often, I have found myself helping the students survive the class rather than helping them understand. I certainly can see the value of spending ample time on the concept of variables prior to using variables on paper.

Reflective Task 1 under discourse says, 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. First of all, I noticed that the teacher encouraged thinking by telling the class to "Talk to me about what you were thinking." Apparently, her students were comfortable with this manner of academic speaking and explaining, because immediately one of the students responded, explaining her group's thought process much more adeptly than many adults could do. I noticed that some of the teacher's questions were lower level thinking questions, but many of them required evaluation, synthesis, or analysis. For example, "How could you make your table's names have a higher value?" challenged the students to analyze what they had already done, and synthesize that information to create a new pattern.

Lesson Analysis 2 says, Give two examples of evidence that students are having difficulty understanding the mathematics being taught. One of the tables included a little girl who could not explain why her group changed the numbers so that the low numbers were at the beginning of the alphabet. This indicates that she does not understand the concept of variables - that the letters are simply representations of the numbers, and by assigning numbers to certain letters, the value of the letters will change. Another group decided to increase their scores by changing the length of their names. They thought that if they would include their middle name, the values would increase. This indicates that they were not comprehending the main objective of the lesson. Their goal was to get a higher score in any way possible. They did not realize that the only way the scores could change without lengthening their names would be to assign different numbers to different letters (variables).

Overall, I benefited from watching an experienced teacher teach mathematics in a constructivist environment. I have wondered many times how the principles of mathematics could really be applied in the classroom, but seeing it on the video gave me a glimmer of hope that it can be done. I learned that if I am to be an effective teacher, I will have to branch off of the textbook and worksheets. I will need to facilitate mathematical discussion and explanations, and I will need to provide a student centered environment in which understanding is discovered - not spoonfed.