A Student Teacher's Curriculum

Gwen Lloyd, Ph.D., is a former faculty member at my alma mater, Virginia Tech. She was my advisor when I initially transferred into the Mathematics Education program here. Her article explores one student teacher's interaction with materials used in a kindergarten mathematics curriculum. Anne, the student teacher participant, had used two different approaches to her use of curriculum, but in both cases, each use was adaptive (p. 63).

I had used this article as one of my resources for my Curriculum Principle Project. The most relevant sections of the article were not those of Lloyd's methods and results, but of the background research. Lloyd talks about the history of views of teachers' curriculum use. Over time, researchers have had a great contrast of views, ranging from the view that teachers see the textbook as a fixed source of any and all information that is to be delivered to the students in a linear manner; to the polar opposite view that teachers are interpreters of information, changing the curriculum to suit their own classes' needs. Further, two specific, independent studies had analogous findings: they each demonstrated that these contrasting views are extremes of a linear spectrum, with any kind of teacher interaction with curriculum falling on any point on the spectrum.

The motive for Lloyd's study was reasonable. As I've stated in my Curriculum project, I think it's important to learn more about how teachers interact with their curriculum because we can use that information, cross-referenced with data about students' responses, to see what works and what doesn't. Knowing this, we can change and develop, and know how to change and develop, a curriculum that fits students' needs.

After reading the research questions, I found out that Anne was using two different sets of materials (abbreviated EM and MTW (p. 71)) in her kindergarten mathematics instruction. What I wanted to know was whether she used these different sets in the same class, or across different class. If the latter is true, I wonder how big of an effect differential Anne will have on her students' lives at such a young age. If she is using different methods on different classes would there be a butterfly effect? This question applies all the time, when we consider different teachers of the same course. I found out later in the Data Collection section that she, and another teacher, were using both of these materials on the same class, with alternate chunks of time (2 to 4 consecutive days) devoted to each set. It turns out that Anne's class is receiving instruction from both material sets.

Another data collection discussion I found interesting was that among the four kindergarten teachers in this class, each teacher saw one-fourth of students each day, and rotated stations. That way each teacher would have to teach the same lesson each day for 4 days in a row, to a different group of students. Lloyd also pointed out that in this system, the students got to participate with each of the teachers, but none of the teachers were able to observe each other.

I think the Findings section was very in-depth and complete. Lloyd covered Anne's use of each set of materials and the Curriculum Design and Curriculum Construction in each set.

The Discussion talked about how Anne fell on the spectrum from the two studies. She initially lay on the middle of the spectrum but her alterations were leaning her to the right (towards the more deviant extreme). The rest of the Discussion was about what factors could have been an influence in Anne's curriculum use. I think this is a major subject to talk about for any kind of data collection. There are so many variables that we must account for when collecting data, and we need to consider how much and what kind of an effect they have on the data. This also helps contribute to suggestions for future research: to conduct a wider, less in-depth, study and to minimize the variables.

Lloyd suggests that future research examine teachers at different levels of experience and us[e] different types of mathematics curriculum materials and textbooks (p. 91). Basically, she suggests that future researchers broaden the scope to get a better understanding of how Anne's case can be generalized. After all, the findings from Anne's class are particular and specific to her class only. Teachers who are reading this study must be careful when interpreting its results.

References

• Lloyd, G. M. (2008). Curriculum use while learning to teach: One student teacher's appropriation of mathematics curriculum materials. Journal for Research in Mathematics Education, 39(1), 63–94.
• Vennebush, G. P., Marquez, E., & Larsen, J. (2005). Embedding algebraic thinking throughout the mathematics curriculum. Mathematics Teaching in the Middle School, 11(2), 86–93.

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.