by Akihiko Takahashi, Tad Watanabe, and Makoto Yoshida with Patsy Wang-Iverson and Wendy Coffman
There are many ways lesson study can be improved. This paper focuses on making lesson study more effective through kyozaikenkyu (pronounced "kyo-zy-'ken-kyuu"), a process in which teachers investigate all aspects of the content and instructional materials. kyozaikenkyu can contribute to the improved content and pedagogical knowledge of teachers. Lesson study provides a context in which teachers can collaboratively engage in an intensive kyozaikenkyu while planning a research lesson.
As lesson study becomes more popular in the United States, the focus of lesson study practitioners has shifted from simply learning how to conduct lesson study to how to conduct it more effectively in meaningful ways. In the early stages of adapting lesson study to U.S. practice, lesson study researchers and professional developers created a template for novice practitioners to use while planning research lessons. While templates are helpful, the process of kyozaikenkyu has not always been visible in these templates. Teachers and administrators engaging in lesson study have come to realize that in order to have a positive impact on teaching and learning, lesson study must be conducted thoughtfully and skillfully. Just going through the motions of lesson study is not enough. On the surface, lesson study may appear simple, but once teachers are exposed to what lesson study really is, it becomes apparent that conducting effective lesson study is not simple at all. Sonal Chokshi of the Lesson Study Research Group stated it succinctly: "Lesson study is easy to learn but difficult to master."
There are many ways lesson study can be improved. This paper focuses on making lesson study more effective through kyozaikenkyu, a process in which teachers investigate all aspects of the content and instructional materials in the context of how students think about and understand the concepts they are going to learn. kyozaikenkyu helps teachers anticipate how students are thinking and understanding the concepts they are learning during the lesson because of the depth of content and pedagogical knowledge teachers gain from the process. Lesson study provides a context in which teachers can collaboratively engage in an intensive kyozaikenkyu while planning a research lesson.
The literal translation of the word kyozaikenkyu is "investigation of instructional materials." We in the U.S. might be inclined to think of instructional materials as a textbook, teacher manual, and perhaps some mathematics manipulatives, but in Japan, kyozai (or "instructional materials") encompasses a wider range of materials: the course of study, the educational content, learning goals, textbooks, teacher manuals, manipulatives, equipment, research and case study publications, lesson plans and reports from lesson study open houses, and ideas gained from research lesson observations. In addition, kyozaikenkyu includes investigation of students' prior knowledge, learning experiences, state of learning, and understanding, which makes it possible for teachers to be able to anticipate students' reactions and solutions to the problems students study during lessons.
Ideally kyozaikenkyu should take place during the planning of any unit/lesson, but it should take place particularly during the planning of the research lesson. To understand the full process, it may help to define kyozaikenkyu in two phases: (1) strengthening subject matter content knowledge, and (2) studying instructional materials and tools (Iwaasa, 1981, as referenced in Yokosuka, 1990). These two phases lead to the intended outcome of kyozaikenkyu: "planning a lesson that matches the current state of the students' understanding, culminating in the development of an instructional plan" (Yokosuka, 1990, p. 73).
Strengthening teacher content knowledge is one of the goals of lesson study, and kyozaikenkyu helps to dig deeply into content matter. There are three chief areas that this phase includes: (1) subject matter and its scope and sequence, (2) current state of student understanding, and (3) goals and desired outcomes.
To help guide readers through the kyozaikenkyu process, this paper uses examples in mathematics but only because the authors are most familiar with the practice of kyozaikenkyu in mathematics. kyozaikenkyu is important in any subject matter, and the questions asked during the kyozaikenkyu practice in mathematics apply to other disciplines as well.
Understanding the specific subject matter as well as where it fits into the scope and sequence is the first step of kyozaikenkyu. Most teachers have experience with reviewing scope and sequence, but with kyozaikenkyu, it is important to note that the scope and sequence goes beyond a list of related topics. Study groups should spend time trying to understand the subject matter, the characteristics of the particular topic they have chosen, and why they teach this topic in a particular way at a certain point in the curriculum.
One obvious place to begin kyozaikenkyu is with the standards, textbooks, and teachers' manuals used to plan lessons. Textbooks are a collection of instructional materials as well as an interpretation of standards set by various organizations (e.g., National Council of Teachers of Mathematics [2000] or state academic standards). Teachers need to examine and understand how a textbook interprets the standards and how it intends to help the students build their knowledge and skills.
To begin looking at scope and sequence, it may help to have study groups composed of teachers from different grades so that they can closely examine vertical alignment across grade levels. Study groups may want to focus on the following questions:
A typical scope and sequence found in U.S. textbooks is a grid with mathematics topics and grade levels listed along the axes. On this grid, dots indicate the grade levels in which the particular topic is discussed. One purpose of kyozaikenkyu is to transform this scope and sequence into a flow chart that shows the connections among various topics and highlights their relationship. Such a flow chart is a common feature of Japanese textbook series (see Figure 1, below). Of course, developing a flow chart is not an end in itself. Rather, the study group should try to articulate the relationships among various topics as carefully as possible, sometimes challenging and questioning a particular order of topics.
One author of this paper, Tad Watanabe, said at the 2003 conference: "Helping teachers understand content relationships across the grade levels is a big responsibility. These vertical articulations are very important, but often times, teachers are not given the opportunity or time to do this." kyozaikenkyu begins with a careful analysis of content relationships within and across grade levels. Teachers who understand the scope and sequence of the curriculum are more likely to be clear about the mathematics concepts they are teaching. Thus, they are able to better articulate what students need to learn as well as what kind of mathematics they need to experience.
Example of Investigating Scope and Sequence: Addition of Two Two-Digit Numbers. As an example of investigating scope and sequence, consider the concept of adding two two-digit numbers, which usually appears in second grade. Clearly this topic is based on students' understanding of the meaning of addition and their procedural fluency with single-digit addition. But what is the purpose of teaching this idea? One possible answer is "so students will have the foundation of adding larger numbers." But in what way does learning to add two two-digit numbers provide the foundation for adding larger numbers? What concept is it that students need to understand, as opposed to an algorithm they must master?
One essential concept is that numbers can be added only if they are referring to the same place value. This understanding is deeper than simply being able to carry out the algorithm, "add tens together and ones together." If students understand this concept, the procedure for adding three-digit numbers is a relatively straightforward expansion of the procedure for adding two-digit numbers. Moreover, if students understand this concept, then addition of like numbers with decimals will not pose an insurmountable challenge (Ma, 1999). However, if teachers see the reason for teaching double-digit addition as simply mastering the algorithm, then students must feel that they need to learn another procedure or algorithm for adding two three-digit numbers, and yet another rule for adding decimals. Analyzing the subject matter and its scope and sequence in this manner helps teachers to begin planning lessons that are more coherent and forward-thinking within the context of the entire unit, subject area, and curriculum.
Understanding students' actual state of learning regarding the research lesson's topic is the next step in kyozaikenkyu. Questions to consider might include:
A deep understanding of students' knowledge is critical in order for teachers to take advantage of their own improved content knowledge. Teachers' improved content knowledge alone might give rise to more ideas about what students might learn, but when it is combined with the knowledge of students' understanding, teachers now make conjectures about different learning paths students might follow. Understanding of these learning paths helps teachers improve their ability to observe and understand how students think, learn, and understand concepts they are learning during the research lesson.
At this point in the process, while teacher knowledge may be growing, and discussions of ideas may flourish, it is important to begin to narrow the focus of the research lesson so that teachers can identify concrete goals and desired outcomes. There is a Japanese saying that "to teach one, you have to learn ten." An important corollary to this saying could be that "once you've learned ten, you need to select and focus on one." With teachers' increased learning of content matter, it is important to focus on only the most important concepts for students, so that they do not lose sight of the lesson's specific goal.
After studying the subject matter and its scope and sequence and identifying the students' state of understanding, the next step of kyozaikenkyu is to establish a clear understanding of the goals and intended outcome of the research lesson as well as that of the entire unit. The goal can be identified by locating students' current understanding in the scope and sequence of the specific subject matter. Teachers might ask, "What are we going to teach?" and "What is the desired outcome of this teaching?" By identifying a clear and explicit goal that is aligned with the students' state of understanding, the study group can later use it for evaluation purposes. Assessing student understanding and learning is much more accurate if the group states clear goals from the beginning.
Once the study group has articulated a firm understanding of the subject content, sequence, and students' state of understanding, the second phase of kyozaikenkyu is to consider the tools with which this content can be most effectively presented to students. This phase culminates in creating a plan for instruction.
Investigating instructional tools begins the second phase of kyozaikenkyu. This step may involve analyzing, selecting, and modifying potential tasks or activities, or even developing new ones. In addition, the group should carefully consider concrete materials and other manipulatives to be used with the potential activities.
Looking at tasks and activities found in textbooks only as "raw materials" challenges teachers to investigate whether the textbook's activities, viewed through students' eyes, naturally lead to student understanding, or whether they need to be supplemented, or even replaced, in order to reach the specified goal. This process challenges teachers to look for the connections among concepts and to help students make these connections by seeking outside resources if the textbooks are not sufficient. Investigating textbooks in this manner represents a very significant and time-consuming responsibility for teachers and content specialists as they plan research lessons as well as daily lessons. But without this scrutiny, lesson study will not be a deep professional development process and will not lead to positive learning outcomes for teachers or students. Furthermore, this process of scrutiny is a concrete product of lesson study that can be shared among study groups.
The scrutiny of the instructional materials, especially with the input of a knowledgeable other, can lead to very specific questions, such as:
While talking about specific numbers, manipulatives, and blackboard organization may sound like overanalyzing the learning activity, it is this kind of deep understanding of the instructional materials that can help teachers achieve intended student learning goals.
Example of Studying an Instructional Tool. The research work of Makoto Yoshida (1999) illustrates how Japanese teachers meticulously discussed a lesson on simple subtraction involving regrouping. Teachers discussed what numbers they were going to use in a subtraction story problem. They thought that the numbers used for the problem affected the way students would solve the problem. One of the teachers noted that most of the textbooks used 12 minus 9 and 13 minus 9. What those textbooks said was that they started out by introducing the subtraction-addition method (genkaho). In the case of 13 minus 9, first subtract the 9 from 10 (10-9=1), then add what is left in the ones position (which is 3) to that number (1+3=4). The teachers thought that 13 minus 9 was too limited in terms of eliciting a variety of student solutions. They thought that something like 12 minus 7 (or 11 minus 6) might produce more interesting solutions such as the subtraction-subtraction method (gengenho), which breaks down 7 into 2 and 5, subtracts 2 from 2 in the one place, and then subtracts 5 from 10.
In addition, these teachers talked about suitable manipulatives to use for the lesson. They brought out all available manipulatives that can be used for this lesson and talked about pros and cons of each manipulative. They were particularly interested in using a manipulative that provided a record of students' thinking and solution processes. Through the discussion they expressed that the manipulatives available to them were not suited to understanding students' thought or solution processes, so they decided to develop their own manipulatives.
These detailed intellectual decision-making processes for planning a research lesson help teachers to structure their classroom practice for students' understanding of mathematics concepts.
The final stage of the investigation process is formalizing the actual lesson plan for the research lesson. This is the point in kyozaikenkyu in which the authors recommend using a lesson plan template to spell out the goal, rationale, learning process, anticipated student responses, assessment measures, and expected outcomes that have been discussed during kyozaikenkyu. Writing lesson plans is an important activity because it records what the writing team has learned through kyozaikenkyu and it documents clearly the writing team's proposed ideas. Lesson plans written for research lessons are comparable to a research paper based on kyozaikenkyu and classroom practice.
An example of a research lesson plan template can be found with the 2002 conference paper Planning and Writing a Research Lesson and is available in PDF format.
After undergoing this rigorous kyozaikenkyu process, teachers will find that debriefing sessions can be richer, making the process of developing a research lesson more meaningful than just creating a "perfect lesson plan." In addition, this process helps to connect what teachers learn in lesson study with their daily teaching. Ultimately, teachers can transfer the investigative process to their daily lesson planning, albeit on a less rigorous level, by asking themselves questions about the content, sequence, connections, goals, state of student understanding, and instructional materials. This kind of thinking, on the part of every teacher, is a sign that lesson study is being conducted effectively.
Effective kyozaikenkyu, in the context of lesson study, helps teachers develop content and pedagogical knowledge and helps teachers to:
Learning to conduct kyozaikenkyu will help U.S. practitioners implement lesson study in a deeper, more sustainable way that impacts both teaching and learning. A commitment to a rigorous investigation can also help create a much larger impact on the education community. Hiebert, Gallimore, and Stigler (2002) write about the need for an easily accessible knowledge base for teaching and suggest that lesson study may be a means to establish such a knowledge base. Furthermore, a knowledge base should not be limited merely to a collection of exemplary lessons developed through lesson study. Rather, the knowledge base generated by lesson study needs to include ideas that help teachers understand why to teach a particular idea and how it relates to other ideas. Lesson study should not yield a collection of rules and formulas for teaching, but instead it should be a beginning for a deeper kyozaikenkyu by other teachers.
Because this process is new to lesson study practitioners in the U.S., the participation of knowledgeable others is a critical component. Finding a knowledgeable other who is versed in the subject matter across all grade levels and has many lesson study experiences may be helpful for conducting good effective kyozaikenkyu. (For a discussion of knowledgeable others, see the 2002 Conference paper The Role of Knowledgeable Others.) Knowledgeable others may have access to more materials than are available in the school building. For example, they may be able to provide other textbooks for comparison, effective practices that have been used in other schools or districts, the latest research on certain types of instructional tools, or simply new ideas that a study group had not yet considered. Knowledgeable others may also help by serving as a supportive coach who encourages the study group members to stretch their thinking about which instructional materials may be most effective.
One author of this paper, Akihiko Takahashi, was a teacher and lesson study practitioner at a national elementary school in Japan for about 20 years. The following metaphor illustrates his observations of lesson study conducted by novices who are not practicing kyozaikenkyu, as compared with more experienced practitioners who are practicing this process of investigation:
When novice teachers engage in lesson study to plan a research lesson, they tend to focus on writing precise, step-by-step directions, akin to giving travel directions: where to turn and how many miles to go to reach the destination. Experienced Japanese lesson study practitioners, by contrast, give directions by drawing a map. A map offers different ways of getting to the destination, as well as providing the general idea of the direction in which you need to go (e.g., toward northwest about 30 miles). In addition, the map can include other reference points, such as markers for a flower shop or a pastry shop, so the person can choose a different route to get to the destination, depending on his purpose. Drawing a map helps people gain an overview of the direction as well as details of the surroundings, optional routes, and merits for taking one route over another to get to the destination. This process of drawing a map is analogous to kyozaikenkyu, which currently is lacking among novice lesson study practitioners.
This metaphor summarizes the notion that through kyozaikenkyu, curriculum is no longer dictated by textbooks. kyozaikenkyu is not just learning about the content presented in one textbook or creating the best research lesson. Rather it encompasses understanding mathematical content in the context of its scope and sequence across the grades, establishing a clear understanding of the goals of the unit, preparing necessary instructional materials for the learning activities, and thinking about and preparing instruction that helps students achieve targeted learning goals.
This paper was first published online in July 2004.
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