Watch one of the Japan videos from the Trends in International Mathematics and Science Study (TIMSS)—more specifically, mathematics video 3 on solving inequalities1—and you'll see that after giving his students a word problem to solve, the 8th grade math teacher strolls among the students' desks for almost 15 minutes, leaning over to see what each student is doing, making brief comments to each one, and noting on a chart how different students are solving the problem. Some are counting, some are making tables or charts, and some are writing equations.

The teacher clarifies instructions for one student: "Yes, write your explanation on the paper next to the problem." He clarifies terms for another: "This *180 − 10x* you wrote—whose money is this?" He nudges others forward: "So you counted all the way? Is there an easier method to find the answer?" And he supports and acknowledges more complex approaches: "If you try combining this and that, you can make a mathematical expression." "So you wrote a simultaneous equation—OK!"

This process of roving among desks to monitor and assist students' independent or collaborative work is known as *kikan-shidō* (between-desks instruction). We encountered this practice firsthand while teaching and coordinating professional development at a K–12 school in Saitama, Japan (Ermeling & Graff-Ermeling, 2014).

## From Japan …

We first learned of *kikan-shidō* while participating in lesson study (*jugyō kenkyū*) in Japan with a district-level research group for English teachers. The central feature of lesson study is observing and analyzing live classroom research lessons that a group of teachers has collaboratively planned (Ermeling & Graff-Ermeling, 2014; Lewis, 2002).

During one lesson study project hosted at our school, the English department prepared a lesson for a 9th grade oral communication course and asked one of us to teach the lesson for the scheduled observation. The lesson included teacher modeling and several pair exercises that challenged students to practice speaking English with their peers.

During the post-lesson reflection meeting, one observer suggested a more systematic use of *kikan-shidō*, pointing out that most of the instruction the teacher delivered when moving around the classroom focused on a few pairs of students who struggled with the exercise, whereas intermediate and advanced students received little guidance or support.

The observer suggested spending less time with each pair of students and giving briefer, more concise feedback so the teacher would have time to interact with everyone in the room. He proposed that as the teacher circulated among students, he should note the progress of each one, including any patterns that might warrant whole-class attention. As a result of these observations, the team discussed ways to more intentionally differentiate support for all students during *kikan-shidō* without neglecting those who struggled with the content.

This experience and subsequent observations of Japanese colleagues opened our eyes to the importance of *kikan-shidō* as part of regular lesson preparation, as did our analysis of videos from our own classroom lessons. We saw that the unplanned, cursory exchanges we had with students when they were working on an assignment in class mostly reiterated previous instruction and seldom advanced student learning. We came to understand that the teacher's role during student work time in class—what we chose to focus on, how long we spent with each team or individual, what we chose to say or not say—had crucial instructional value. Improving the use of this time required careful planning.

For decades, Japanese educators have used this practice to engage students in deeper learning around challenging problems and tasks (Sakoda, 1991). In his commentary on the solving inequalities lesson we describe at the beginning of this article, the national research coordinator points out specific video segments in which the Japanese teacher used *kikan-shidō* to engage and support students' independent work:

The teacher purposely speaks loudly when giving advice to a student so that other students can hear … the teacher could exploit the advantages of a whole-class instruction method … by doing

kikan-shidō. The teacher instructs students while strolling among the students' desks, thinking about the upcoming order of presentations for successful whole-class instruction … The teacher carries a lesson plan sheet and writes down the students' understandings of—or difficulties with—a solution, while instructing individual students. (UCLA & the Carnegie Foundation for the Advancement of Teaching, n.d., 05:10)

## To the United States

The practice of *kikan-shidō* can prove valuable to U.S. teachers as they work to address new and more rigorous standards in math, science, and English language arts. The intentional use of *kikan-shidō* can elicit, prod, and facilitate deeper learning in all students.

Using data from six cities across the world and more than 180 videotaped lessons from the Learners Perspective Study, which examined patterns of participation in well-taught 8th grade mathematics classrooms, O'Keefe, Xu, and Clarke (2006) outline four principal functions of *kikan-shidō*: (1) monitoring student activity, (2) guiding student activity, (3) organizing materials and the physical setup, and (4) engaging students in social talk. The examples we provide below come from our direct observations of more than 20 U.S. teachers working to improve between-desks instruction and facilitate deeper learning.

## Function 1. Monitoring Student Activity

After studying the Japanese TIMSS video on solving inequalities, a high school algebra teacher we observed prepared a lesson that placed students in small groups to solve a challenging multistep problem using systems of linear equations. The problem read as follows:

Your friend has interviewed for two different sales positions in competing companies. The Stellar Company pays $500 per week plus 10 percent commission on the total dollars from sales per week. The Lunar Company pays $200 per week but offers a 20 percent commission on the total dollars from sales per week. Sales at both companies are seasonal. Your friend wants some help determining which job option is best.

The teacher circulated during group work; recorded the approach that each group selected to solve the problem (table, graph, or system of equations); and asked questions to elicit and understand students' thinking. For students who were using a table to solve the problem, the teacher anticipated that they might struggle to find how the total amount earned would change for each job. She asked questions such as, "How are the variables changing?" and "How fast are the two jobs moving together?" For students who selected a graph, she wanted to see whether they understood the solution conceptually. She asked those students questions like, "What data do you have?" "What are you going to put on each axis?" and "What is the graph going to tell you?" For students using the system of linear equations to solve the problem algebraically, she paid close attention to how they set up the problem. She asked, "What variables did you choose, and what does each represent?"

It's important to clarify that each method the students chose revealed underlying patterns of their thinking. Students who chose a table to solve the problem were typically less comfortable determining appropriate scale and intervals for a graph. They were also less likely to recognize when a problem involved a system of equations. The table represented a concrete and trusted format for organizing data, calculating values, and thinking through the solution.

Students who chose to solve the problem graphically typically recognized the need for two linear equations and saw the graph as a useful way to identify the point of intersection. They felt confident working with a more abstract representation and less computation.

Students who chose to solve the problem algebraically were comfortable visualizing the problem without all the detailed computation or graphical representation. They viewed the system of equations as the quickest, most reliable method and perhaps recognized that graphing could be imprecise when plotting values that involve decimals.

In the course of her observations, the teacher identified several groups to present their solutions at the end of the period. She ensured that each of the three main approaches—table, graph, and system of equations—was represented.

Much like in the Japanese TIMSS video the teacher studied, the goal of this lesson was to help students better understand the continuum of problem-solving approaches, starting with more concrete methods (creating a table) and moving toward more sophisticated and abstract ones (using a system of equations). By strategically selecting students to present each method, the teacher highlighted the validity and benefits of all three methods but also pointed out the value and necessity of the algebraic approach for tackling mathematical problems with increased scale and complexity.

## Function 2. Guiding Student Activity

It was the first experiment of the year in a 5th grade science lesson we observed. The teacher's goal was to introduce students to the investigative process and teach them to anchor data in descriptive observations. The students would start by exploring simple interactions between liquids and solids; in subsequent lessons, they would use the data to note differences among various physical and chemical changes, discuss patterns that emerged across the data, and draw conclusions on the basis of this evidence.

Using six white powders and six clear liquids—the powders included Epsom salt, flour, and powdered lemonade, whereas the liquids included water, vinegar, and cooking oil—the teacher designed a whole-class experiment with 36 different mixtures and gave pairs of students at least two mystery combinations to analyze. After receiving the mystery liquid from the teacher, students carefully added two spoonfuls of powder to their bags, which listed the number assigned to the white powder and the letter assigned to the clear liquid they were investigating. The teacher asked the students to record each aspect of the experiment in their science notebooks: materials, procedures, observations, and ideas for future investigation.

Once the experiment was underway, the teacher rotated among the desks to support student pairs in developing their observational skills. He listened to student observations, noting when the students offered only vague descriptions, and prompted them to elaborate by asking such questions as, "What do you mean by the mixture 'making noise'?" and "What happened when you first added the powder?"

The teacher had to continually remind students to keep their observations rooted in sensory evidence—what they could see, hear, smell, and touch—while refraining from telling them what he could readily see and describe. Also, by asking such questions as, "Why do we have notebooks?" and "How will you remember your observations?" he continually impressed on students the importance of recording their observations.

In the early stages of the lesson, most students' observations were brief and simplistic: "They mix." "It's hard." "It's white." Only a few student pairs recorded information in their notebooks. The teacher noted that one group was having trouble describing the physical and chemical changes; the students weren't sure what to write. As the teacher encouraged them to be more detailed in their observations, the students began to note more specific characteristics, such as, "the mixture changed color," "it bubbled at first and then stopped," and "it was clear at first and then got foggy." Students across the class responded well to these individualized prompts and showed improvement in both describing and recording observations, an important first step in developing investigative skills.

Following the experiment, the teacher asked each pair of students to share their data. He then summarized all student responses in a large matrix on the board. One student shared two descriptive words from his science notebook—that the reaction "moved fast"—which the teacher highlighted as particularly interesting because it raised a point about the *pace* of a chemical reaction, an important scientific observation.

## Function 3. Organizing Materials and the Physical Setup

In a 1st grade science lesson we observed, students were investigating the basic properties of magnets. The teacher designed an exploratory lesson, placing students in groups and giving each team a carefully organized tray that included different combinations of magnets: horseshoe, rectangle bar, paddle, and ball. The trays also contained a variety of objects that magnets could and couldn't move: steel wool, cotton balls, paper clips, plastic coins, erasers, and a compass. By intentionally including items that could and couldn't be picked up by a magnet, the teacher created a sense of mystery as well as a puzzling situation in which students would need to look for patterns.

Each student chose different items to investigate, enabling them to both individually and collectively explore, compare, and discover magnetic properties. One student discovered how the bar magnets' red and blue ends would pull together, whereas the two blue ends would push away (polarity). Another student created a chain of paper clips hanging from a magnet and observed that if she added more than three, one paper clip would drop off (magnetic strength). The teacher's careful preparation of the diverse trays helped facilitate active inquiry, effectively setting the stage for a rich culminating discussion during which students learned about the unique discoveries from each group.

Students were excited as they described what they learned: "The magnets rolled like magic!" "The two blue ends didn't stick to each other." Because of her intentional organization of materials, the teacher was able to build on these discoveries from her 1st grade scientists, and she finished the lesson by bridging students' observations to the key scientific concepts of attraction, repulsion, and magnetic fields.

We observed a similar focus on organizing materials and attending to classroom logistics in a high school English lesson. The teacher prepared a small-group exercise aimed at helping students shift their revision focus from mechanics and punctuation to quality of content and clarity of arguments. She carefully selected sample papers in advance that had various degrees of weakness in clarity of arguments (for example, lack of a clear main idea or thesis, use of quotes without sufficient explanation, and so on) and removed all student names before making copies for the lesson.

After leading the class through a modeling exercise during which they analyzed different levels of revision, the teacher placed students in groups and provided each team with three papers from a different class period to ensure anonymity and facilitate objective analysis. She also assigned students roles (reader, recorder, commentator) and explained that commentators should pause the group whenever they noticed specific errors with clarity or content.

Instead of briefly reviewing the paper for superficial errors or being preoccupied with whose paper they were commenting on—problems the teacher had noted in previous peer-editing sessions—the students showed increased focus on the substance of the writing and greater willingness to provide specific suggestions for improvement.

## Function 4. Engaging in Social Talk

A 5th grade teacher we observed asked students to work in small groups to complete an exploratory exercise about the earth's water cycle. As she circulated and listened to group discussions, she saw one student carefully explaining to his team members the processes of evaporation, condensation, and precipitation.

During a brief lull in the conversation, she took a moment to affirm the student's skillful explanation. Using language familiar to their inner-city community, she said, "That's your new hustle. Instead of working the street corners, you study hard, get an *A* in class—and that's your proof that you can tutor other students. *That*'s your new hustle!" The teacher later explained that she often looks for opportunities to offer students alternative choices to counter the more negative influences of their environment.

We also noted the intentional use of this practice in a high school chemistry class. The teacher rotated around the classroom as students cleaned up their stations from a lab experiment and engaged in brief conversation with individual students to build rapport. He asked one student about the opponent for an upcoming volleyball match. He asked another about a sister who was in the hospital for surgery. He assisted the students with clean-up duties as they conversed and gradually switched from social talk to questions about what they learned from the lesson activity.

## Preparing for Kikan-Shidō

Teachers can prepare for *kikan-shidō* by thinking through a series of questions and constructing a clear mental image of the lesson activity: What are my goals as I circulate? How will I distribute my time with various groups and differentiate support? What key understandings or misconceptions will I be looking for? What probing questions will I use to check for understanding or advance student thinking? What will I be careful not to say or do that might decrease the rigor of the task? What materials will I need to distribute? When should I engage in brief social conversation with students to provide encouragement and build relationships?

Using a format to plan and reflect on a few key lessons is one way to develop the discipline of regularly thinking through these questions. For example, in the 9th grade oral communication course we described, in which Japanese students practiced English dialogue, our planning template listed common student reactions to the assignment that we should look for, such as reading the conversation without trying to commit it to memory, trying to memorize the dialogue without reading it out loud, and reading or speaking lines mechanically without attempting to convey meaning. The template also listed helpful teacher responses and support during *kikan-shidō*, such as providing feedback on pronunciation and intonation, encouraging students to work on memorization, and providing additional instruction to students who were reciting lines without a communicative purpose.

Carrying a copy of the lesson plan on a tablet or mobile device during *kikan-shidō* is also useful; teachers can review the plan on the spot and take notes as they observe. This kind of planning and reflection will help them develop increasingly nuanced understandings of the choices presented in each *kikan-shidō* episode and the effect these choices have on student learning.

## Persisting with Kikan-Shidō

Much like in Japan, teachers and administrators will need sustained, collaborative learning opportunities to persist with the slow, steady process of "learning to teach between desks." One study suggests it takes, on average, 20 separate instances of practice for teachers to master a new skill, and the number could be significantly higher for more complex skills (Joyce & Showers, 2002).

Findings from a case study we conducted on teacher change showed that it took at least three semesters for teachers to adopt and effectively implement a new instructional approach in their high school science classrooms, which involved significant adjustments to teachers' "between-desks" instructional routines (Ermeling, 2010). One teacher shared the benefits of this approach, which helped her not only guide student activity but also challenge students with an appropriate level of struggle:

I just got my scores back: 18/20 passes = 90 percent. Seven students received a 5, six received a 4, which is so much higher than any class ever before. I'm so happy for my students, I just sat down, closed the door … and cried and cried and gave thanks. I have to believe I changed the way I taught, that making them struggle really bridged the gap. This was my most enjoyable year of teaching in my 28 years. (p. 386)

## From Insights to Change

Adopting "instruction that sticks" means sticking with the relentless pursuit of incremental improvement. It means learning to understand and predict how specific aspects of an instructional practice, such as *kikan-shidō*, will influence learning and how student responses, in turn, might influence teacher actions. It means persevering long enough to understand the nuances of effective implementation—and translating these into practical teacher knowledge and tangible student results.