Classroom Management

While watching the video, I first noticed the huge differences between classrooms in 1947 and classrooms today. All the desks were facing front, in neat rows and columns. I find in most current classrooms have desks clustered and facing in all directions, or arranged in concentric arcs like in an auditorium. When the students answered questions, they stood up and spoke without permission while modern classroom teachers require their students to raise their hands and wait to be called on. If I were the teacher, I wouldn’t have done the math myself when explaining the conversion problem. I would have focused on bigger concepts, or asked the students how to do the math.

I found it familiar that while the teacher was gone, the students talked and goofed around. This was common in many of my high school classes. One of the things I found unfamiliar was the fact that the teacher was working on the board while the silent class watched and took notes. As a high school student most of my teachers would take a more active role and engage the class.

In the first scenario, the teacher expected the students to be well behaved and silent. He expected them to know how to study and raise their grades without knowing how. In the second scenario, the teacher asked more questions and expected the students to participate. He was still expecting good behavior but was more lenient when punishing bad behavior. With this friendlier attitude, the students respected him more and were less likely to act out.

Reflecting on this video in class, we talked about the six NCTM principles.

• Equity was the most apparent issue. The class was probably 100% white. The teacher was using examples that were sexist. Girls were supposed to be good at cooking and boys were supposed to be good at building.
• Regarding Learning, the students were all expected to learn the way the teacher taught. There was no accountability for differences in learning styles.
• The Teaching was not student-centered and very lecture oriented. In a modern classroom, the teaching is supposed to be more interactive.
• In the second scenario, the teacher was more critical of the Curriculum. When demonstrating a problem, the teacher left no “wait time”, or student interaction. The focus was on the conversion from yards into feet.
• Using the Assessment, the teacher could figure out which topics the students had most trouble with.
• The only available Technology in 1947 was the textbooks, chalkboard, and pencil and paper (used traditionally).

References

• How to maintain classroom discipline: Good and bad methods training educational video [video file]. (2007). Retrieved from http://www.youtube.com/watch?v=gHzTUYAOkPM.

Teachers' Conceptions of Equity

The motivation for the article stems from the assumption that the majority of secondary math teachers have largely unexamined, varying conceptions of what NCTM's Equity Principle means in the classroom. The research question asks what equity means and how we will recognize it when we see it.

Teachers participating in the study met monthly over a year, for about 2.5 hours each meeting. They discussed their initial conceptions about equity, findings from reading research about equity, and their final conceptions about equity after the sessions. This reminded me of my Senior Seminar class, when we would reflect on articles that focused on a particular mathematical content or process (e.g. Trig functions, Representation, etc.), and then would discuss our conclusions and reactions. One of the things we were taught to do was to assume everybody in the class has read the assigned article, so that we wouldn't waste time summarizing.

I am trying to simulate that same practice in this blog (Mathematics Education Research). Even though it would be easy to summarize the research that I find interesting for those who haven't read it, I have to remind myself that anyone interested in reading those articles can obtain the resources to do so. Else, the article's abstract provides a summary. Rather, this blog is more about my reactions and thoughts about the readings—or viewings—so that I can expand on it and provide insight for myself and others.

Anyway, the results of the first part of the study showed that the teachers' conceptions of equity fell into four major categories, and that although these categories were remarkably different from one another, the participants agreed that the responsibility of working toward equity falls on the teacher. During the second half of the study, teachers were asked to pick one student in their class, who was struggling mathematically, to get to know on a more personal level. The teachers that succeeded found that those students raised their level of engagement and achievement in the classroom.

Bartell and Meyer (2008) conclude that the first step for teachers to support and maintain equity is to explore and identify their own conceptions of equity. Further, becoming more personal with an under-proficient student can boost morale and achievement, and not to mention, help the teacher form bonds with his or her students. The authors then pose a few open-ended questions at the end, perhaps as motivation for future research.

References

• Bartell, T. G., & Meyer, M. R. (2008). Addressing the equity principle in the mathematics classroom. Mathematics Teacher, 101(8), 604–608.

Graphing Calculator Use: Activity and Affect

The thesis of this article provides an effective method that captures data on how and why individual students choose to use graphing calculators—henceforth, HGT—outside of whole class situations. I believe McCulloch's purpose is clear and valid. Most recent research on HGT focuses on its effect on student achievement, or else focuses on the teaching and learning of a specific topic in content. This past research drives her interests in this paper:

1. When students work independently rather than in a large group, what are they actually doing with HGT?
2. What aspects of HGT do they attend to?
3. How do emotions, values, beliefs affect their HGT activity decisions?

McCulloch mentions several difficulties and drawbacks about traditional methods of data collection, so offering a new method and determining its effectiveness has well-founded intentions.

To address the problem solving strategies and decision making in detail, a task-based interview is typically implemented. Basically, this means the problem solver—the subject—will think out loud in front of the interviewer. However this design is unsuitable if it is used to collect data about emotions and values. McCulloch's study combines the task-based interview with a video-SR (video stimulated response, a procedure in which videotaped behavior is played back to the subject in hopes that he/she will recall his/her activity). With this combination of designs, the subject will recall both cognitive and affective activity. In addition to capturing the subject's activity, a video capture card was used to capture the screen activity on the HGT. When these three components are put together, the event is recreated.

I think this method should be used for an intensive examination of a subject, but would not be appropriate as an extensive study for a large group or class. The resources of time, money, and equipment are simply not available. The article also mentions other limitations.

McCulloch makes several conclusions from her study:

1. The methodology used is very effective regarding capturing data from individual students, and opens many doors to future research.
2. The methodology captures information that was unattainable in the past.
3. The methodology allows students to reflect and recap their activities with the HGT, providing a learning experience.

I'd like to make one more point about the outcomes of this study. In the article, one of the limitations identified was that the subject's emotions played an important role when reviewing the video-SR interview. therefore… the student will associate [them] with that event in the future (p. 80). I do not see this as a drawback though. In my experience, the concepts with which I associated certain emotions were the ones that I remembered the most in school. Teachers should always promote positive emotions in students and never negative ones, but I cannot ignore the fact that I achieved well when I was tested on the concepts for which I had negative feelings.

References

• McCulloch, A. W. (2008). Insights into graphing calculator use: Methods for capturing activity and affect. International Journal for Technology in Mathematics Education, 16(2), 75–81.