See more in Publications and Presentations, Education Publications and Presentations

Kumar, S., Correa, C. & Sims, L.M. (2003, April 21). First and Foremost: Examining lesson introductions by Chinese and American elementary school mathematics teachers. In K. F. Miller (Chair), Making Teaching Public: Studying Teacher Thinking Using Video Techniques. Paper presented at the annual meeting of the American Educational Research Association, Chicago.

Background

Cross cultural comparisons of US and Asian elementary Math classrooms (such as Stigler and Perry, 1989) have highlighted many useful differences in lesson structure and teaching across cultures. We have learned, for example, how Japanese and Chinese lessons involve much more time on mathematical tasks, and have more coherent structures, while US lessons are highly procedural and rarely involve reflections or verbalizations by the students.

In this study, we take a deeper look at some of the events that occur when lessons are introduced in US and Chinese classrooms. On the face of it, lesson introductions look very similar in both cultures, typically beginning with a review of previous material, followed by an introduction of the new material (a new problem, or procedure, or concept) for the day. However, teachers end up achieving very different objectives in the two countries. We examined these introductions in greater detail, looking beyond their structural similarities in order to get to the essence of their differences and the different goals they achieve.

We are studying lesson introductions specifically because they
1. Set up interaction expectations and the role of teachers and students
2. Engage and motivate children
3. Allow us to look at several important pedagogical aspects of a lesson that frequently occur at the start (links to prior knowledge, links to everyday life)

Methods

Data
Videotapes of 10 US and 10 Chinese elementary math lessons (grades 4 and 5) were studied. The data are not meant to be representative of the countries, but provided valuable insights into some consistent differences.

Defining a Lesson Introduction
Rather than a time based delineation (first 10 minutes, or first 25% of the period, etc.), lesson introductions were defined as the initial part of the lesson consisting of explicit review material (if any), followed by at least one complete instance or example of the new material for the day.

Coding
The first step was to identify the two sections – a) review, and b) presentation of new material - for each lesson (a few lessons launched directly into the new material without a review of any kind). Among the many coding schemes possible for looking at different aspects of teaching, we restricted ourselves to a simple one that seemed to pick apart the key differences between the introductions in the two cultures. Our coding system looks at two main types of events - references to prior knowledge, and complex teacher-student interactions.

All codes are prefixed with T- or S- to indicate whether the event (utterance) originates from a Teacher or a Student. Within the review section, review material is coded as directly related to the theme of the lesson (RL) or other review material (RO). For the new material section, references to prior knowledge or previously learned material are coded either as those covered in the review part of the same lesson (PL) or those covered on previous days (PP). In both sections, we look at the level of teacher attention to student comprehension by assigning the code W whenever a student response is followed up by the teacher asking a deeper conceptual question (such as “How do you know that?� or “Why is that so?�). In addition, we also assigned the code “Teacher Explains Procedure First� (T-PROC-FIRST) if the teacher explicitly states the algorithm, procedure or rule before the students do so.

Results

Although the classrooms we studied were not representative samples of the two countries, some consistent differences cropped up in the deeper analysis of these videos (even with our very simple coding scheme).

Differences and their implications
1. Review sections in the US have significantly fewer references to distinct conceptual ideas that are directly related to the current lesson topic than their Chinese counterparts. The US lessons seem to be missing out on an opportunity to build new content and knowledge on students’ prior knowledge.
2. US teachers touch on review topics and recapitulate them in superficial ways whereas the Chinese teachers constantly question their students about the conceptual basis of the reviewed rules and ideas. The Chinese teachers seem to emphasize the importance of the students’ own knowledge and set up the expectation that the students need to understand the older material before they go on to the new material. In contrast, US teachers seem to reinforce the idea that students do not need to master the old material as they will be told the rule for the new material anyway.
3. While presenting new material, Chinese teachers constantly refer to previous material that was covered in the same lesson and in previous lessons. The US teachers rarely refer to any previous material, and, when they do so, the reference is often to material covered in previous unrelated lessons, rather than the topic at hand. This result confirms the importance of building on prior knowledge in Chinese lessons.
4. None of the Chinese teachers ever presented a procedure or rule for that day’s lesson before letting the students work on it first. The US teachers, on the other hand, often set forth the rule, and then spent the rest of the class applying it and practicing it. The teacher is very clearly seen as the source of knowledge in US classrooms.

Conclusions/Discussion

What we’ve learned
On the face of it, both US and Chinese classrooms have very similar lesson introductions. If we simply break up the lessons into chunks defined by type of activity, and assign labels to them, we see something that looks like a) review of prior knowledge, followed by b) presentation of new material.

Our research has shown that while a broad panoramic look at the two countries results in similar views, a closer investigation reveals some simple but startling differences. References to students’ prior knowledge are essential in building new knowledge, and the Chinese teachers explicitly make these references and make sure their students know them. In addition, they also ensure high levels of student comprehension and conceptual understanding by asking deeper non-procedural questions even when the students respond correctly.

Where we’re headed
While this research on looking at the deeper structures of classroom is interesting in its own right, we also plan to use the results and the simplified coding scheme with teachers who will be using the videos as learning tools to examine their own practice.

Video records of classrooms from different cultures are becoming popular in professional development programs (Jacobs and Morita, 2002), and have provided us with contrasts that make our own implicit teaching styles and objectives explicit. However, other research at the Cognitive Development Lab has shown that unlike educational researchers who spend many hours looking at the same 10 minute clip, teachers who watch these clips tend not to focus much on the mathematical content and pedagogical issues at hand. Instead, they pay more attention to the teacher’s personality, classroom management and layout, student behavior, and other “quirks� such as the teacher using a straight edge to draw the line between the numerator and the denominator in a fraction. If we want teachers to learn from such video examples, we need ways of looking at classroom videos that efficiently and clearly set forth the mathematical content of the lessons. Highlighting key differences in different parts of lessons, especially the start of a lesson, is one possible framework that teachers can use to understand some of the pedagogical issues at play.

[Highlights for the presentation]
After a brief introduction to the study and its goals, we will present video clips of a “good� lesson beginning in a US classroom (i.e., one where the teacher reviews previous material and presents the new material systematically) and a lesson beginning in a Chinese classroom. These examples will be discussed using our coding system and their implications will be proposed. We will also present some general results based on our preliminary analysis. We will conclude by talking about how these results are going to be used to inform future studies.

References

Jacobs, J. K., & Morita, E. (2002) Japanese and American teachers’ evaluations of videotaped mathematics lessons. Journal for research in mathematics education, 33(3).
Stigler, J. W., & Perry, M. (1988). Mathematics learning in Japanese, Chinese and American classrooms. In G. B. Saxe and M. Gearhardt (eds.), Children’s mathematics. San Francisco: Jossey-Bass.