The Teaching Gap (review)
by James W. Stigler and James Hiebert
It’s no secret that, with respect to K-12 education, the United States isn’t exactly an internationally renowned leader. But what do other countries do that the US doesn’t, and vice versa? One way to find out is to watch a ton of videos taken in various classrooms — this is exactly what James W. Stigler and James Hiebert did in the 1990s.
In particular, they analyzed videos of eighth-grade mathematics in 100 classrooms in Germany, 50 classrooms in Japan, and 81 classrooms in the United States, and they documented their findings in The Teaching Gap, a book published in 1999. Japan was chosen because it had always scored near the top in math, and Germany was chosen because it, like Japan, was “a major economic competitor of the United States.” The authors also included a plan to improve classroom teaching in the US. In this post, I’ll summarize the book and give some thoughts.
1. “Teaching, Not Teachers, Is the Critical Factor”
Kids sometimes blame teachers when they don’t do well in school, and adults also sometimes blame teachers for the same reason. But the authors believe that this blame is misguided: “Although variability in competence is certainly visible in the videos we collected, such differences are dwarfed by the differences in teaching methods that we see across cultures.” They summarized these differences in the form of a motto for each country: Germany got “developing advanced procedures,” Japan got “structured problem solving,” and the US got “learning terms and practicing procedures.” Here’s how a typical lesson went in each country.
Germany: “Developing advanced procedures.”
The authors start by noting that the German school system has three tiers based on the students’ academic achievements and aspirations. The classroom the authors highlight was part of a Realschule, i.e., the middle tier. According to them, most students in this tier “will not go on to university, but many expect to enroll in a technical or vocational college.” The classrooms in Japan and the US did not have this system of tiers; they contained “students of mixed achievement levels.”
A typical lesson in Germany went as follows:
The teacher checked and reviewed homework problems for about 10-15 minutes.
The teacher presented the topic and problems for the day; these were meant to be rather challenging for students.
The teacher walked the students step-by-step through a problem-solving procedure, or a mathematical proof, and asked them to answer questions along the way.
Students worked in class and had homework, which contained a mix of problems based on that day’s lesson and previous topics.
Some lessons in Germany focused more on practice; these often involved two students working on the chalkboard as the teacher asked questions and corrected their errors. Other lessons included more student exploration. Both variations of lessons complement the motto of “developing advanced procedures,” either through the practice or development of those procedures.
Japan: “Structured problem solving.”
To an American, the Japanese lesson begins in a “rather striking way”: “At the signal from the student monitor, all the students stand and bow, in unison, to the teacher. The teacher bows in return, and the lesson is officially under way.” The students also bowed at the end of the lesson.
A typical lesson in Japan went as follows:
The teacher reviewed the prior lesson by briefly lecturing, leading a discussion, or having the students recite the key points.
The teacher presented the main problem for the day. It often built on previously learned material, and like the problems from the German lessons, it was meant to be challenging.
Students worked individually, then in groups, as the teacher monitored their progress and gave hints.
The teacher selected students to share their solutions with the class, or the teacher presented a method themselves, and everyone would discuss.
At the end of most lessons, the teacher gave a brief lecture that summarized the key points of the day. Typically, there was no homework.
Interestingly, other lessons in Japan seemed quite different from the one described above. For example, in some lessons, the teacher directly told students how to solve a problem. In other lessons, students had to memorize facts by repeatedly reciting them aloud. But these lessons make sense when viewed as scaffolding for the primary goal of the math classrooms in Japan: equip students with whatever they need to solve challenging problems.
United States: “Learning terms and practicing procedures.”
The typical lesson in the US was similar to that of Germany, but “the mathematics [was] quite simple compared with that found in the previous two lessons”:
The teacher often started with a “warm-up” activity and reviewed the homework.
The teacher illustrated a problem-solving procedure to students in a step-by-step demonstration and asked short-answer questions along the way.
Students worked on problems similar to the ones solved by the teacher. This was usually done independently, but sometimes students formed small groups.
The teacher went over the classwork and assigned more practice problems for homework, which students usually started before the end of the lesson.
In summary, lessons in all three countries followed the same general format: (1) review, (2) teacher presentation, and (3) student work. But the core activity in the lessons of each country was different:
In Germany, the teacher guided the students through the development of a relatively sophisticated mathematical procedure or proof.
In Japan, the students worked on developing their own solutions, individually and in groups, to a challenging problem.
In the US, the teacher demonstrated a procedure, and students spent most of their time practicing it on similar, relatively simpler problems.
In the rest of the book, the authors primarily focus on differences between the US and Japan. Given that Japan “has always scored near the top in international comparisons of mathematics achievement,” it’s tempting to conclude that classrooms in the US should emulate those in Japan. But the authors emphasize that teaching is a system, “not a loose mixture of individual features thrown together by the teacher,” so it’s important to consider “how the features fit together to form a whole.” For example, many teachers in the United States used an overhead projector, while nearly every teacher in Japan used a chalkboard instead. The authors claim that this is not a superficial difference in visual aid preferences, but rather, it reflects deeper cultural attitudes about education.
2. “Teaching Is a Cultural Activity”
This brings us to the authors’ most profound claim (in my opinion): “We contend, as do other educational researchers, that although teachers learn some things about teaching from their formal training, mostly they learn from simple cultural participation. After all, teachers spend at least thirteen years in classrooms, as students, before they even enter a teacher-preparation program.”
The authors cite family dinner as an example of a cultural activity. We learn the “script” of family dinner (e.g., people sit at a table, eat at the same time, don’t pay a check, etc.) through participation, not deliberate study. In contrast, most people who can write a computer program didn’t learn the skill implicitly — learning to program requires deliberate study. (Their example of a non-cultural activity is learning to “use a computer,” but in 2023, I think programming is a clearer example.)
The authors’ claim is that teaching is also a cultural activity — it is more like family dinner than programming. As a consequence, various cultural beliefs about teaching get passed from generation to generation. For example, generally speaking, teachers in the US act as if mathematics is a set of boring procedures, while teachers in Japan act as if mathematics is an exciting set of relationships. More concretely, American teachers try to minimize confusion and frustration since “they are signs that earlier material was not mastered.” On the other hand, in Japan, teachers “believe students learn best by first struggling,” and confusion and frustration “are taken to be a natural part of the process.”
These differing cultural beliefs could help explain why teachers in the US used overhead projectors in the videos — American teachers believe it is critical to keep students engaged so that they fully learn the procedure of the day. In contrast, Japanese teachers used chalkboards to illuminate the relationships between different parts of mathematics within the lesson. They, unlike US teachers, do not prioritize ensuring that the students constantly pay attention to whatever the teacher is presenting.
Differing cultural beliefs could also explain why teachers in the US often attempt to increase students’ interest by appealing to a “real-life or intriguing context” like sports (e.g., “measuring the circumference of a basketball”), while Japanese teachers “act as if mathematics is inherently interesting” and “seem less concerned about motivating the topics in nonmathematical ways.”
The authors give more classroom differences that could arise from differing cultural beliefs, and here’s one I found particularly remarkable: among the lessons in the United States, 31% were interrupted by things like announcements over the loudspeaker and visitors asking for the lunch count. (I don’t know the latest data, but if I recall correctly, this matches my experience as a student.) In contrast, interruptions occurred in only 13% of the German lessons and none of the Japanese lessons. As the authors observe, “In Japan, classroom lessons hold a privileged place in the activities of the school. It would be exaggerating only a little to say they are sacred.”
3. “A Gap in Methods for Improving Teaching”
If teaching is a cultural activity, then unfortunately, education reform is difficult because it’s hard for any individual change (e.g., classroom layout, equipment, the textbook) to significantly affect the system and its underlying web of cultural beliefs. For example, one American teacher tried a problem-solving approach like the one found in the videos taken in Japan, but the results were disappointing:
Although the teacher changed his behavior to correspond with the actions of the teacher in the videotape, the students, not having seen the video or reflected upon their own participation, failed to respond as the students on the tape did. They played their traditional roles. They waited to be shown how to solve the problem. The lesson did not succeed. The students are part of the system.
Even worse, changes can backfire by reducing student learning and teachers’ belief in improvement. As the authors put it, “Always changing, and yet staying the same, is a discouraging state of affairs. It can lead to a defeatist kind of cynicism.”
To find a solution, the authors turn to the educational reform system in Japan. In summary, that system, known as kounaikenshuu, “includes clear learning goals for students, a shared curriculum, the support of administrators, and the hard work of teachers striving to make gradual improvements in their practice.” Its primary component is lesson study, which has teachers regularly meet to design and improve “research lessons.” More specifically, lesson study generally contains the following steps:
Define the problem: This could be general (e.g., increase students’ interest in math) or specific (e.g., improve students’ understanding of adding fractions).
Plan the lesson: The teachers plan a lesson that addresses the problem. The lesson should have a hypothesis that can be texted in the context of a classroom. They revise the lesson based on feedback from a schoolwide faculty meeting; the process could take up to several months.
Teach the lesson: One teacher teaches the lesson to students while the other teachers observe and take notes. (Interestingly, the other classes are left without adult supervision — two students are appointed class monitors.)
Evaluate and reflect: The group critiques the lesson, often after school, and often rather critically. But they view it as a group effort; “the lesson, after all, is a group product, and all members of the group feel responsible for the outcome of their plan.”
Revise: The group revises the lesson based on students’ misunderstandings.
Repeat step 3: This time, all faculty members are invited.
Repeat step 4: Again, all faculty members might be involved this time.
Share the results: Lesson-study groups often write a report, and/or teachers from other schools visit to observe the final version of the lesson in a “festive occasion” that “is considered an important part of teachers’ professional development.”
Clearly, this is quite a thorough process for just a single lesson. But the authors are big fans of lesson study and hope that the US adopts a similar system. As they put it, “The core of our proposal is to establish something like Japan’s lesson-study system here in the United States.” Most of the rest of the book gives the details of their proposal — if that sounds interesting, I recommend checking it out.
My Thoughts
As mentioned earlier, the idea I found most profound is that teaching is a cultural activity. Sure, educators can read papers and attend workshops, but it seems impossible for anyone to ignore their years of experience as a student. Unfortunately, this makes substantial reform difficult, but as the authors argue, hopefully not impossible.
I feel less certain about the authors’ implicit preference for inquiry-based learning (IBL) over direct instruction (DI).1 One message of the book is that the IBL-based classrooms in Japan are more successful than the DI-based classrooms in the US. This rubs against the evidence for direct instruction and full guidance, but I don’t want to get into that debate here.
However, I like the author’s proposal of lesson study in the US because it addresses a recurring concern of mine: since teaching involves countless small decisions (e.g., which examples to show, how to assess students, the attendance policy), I often think to myself, “Surely people have already developed the ‘right answers’ for these things.” But as far as I can tell, for better or worse, there’s no established set of best practices; perhaps a system like kounaikenshuu would be beneficial.
On that note, here’s an inspirational passage from the end of the book:
The star teachers of the twentieth century have been those who broke away from the crowd and created different and unusual methods of teaching… The star teachers of the twenty-first century will be those who work together to infuse the best ideas into standard practice... In a true profession, the wisdom of the profession’s members finds its way into the most common methods. The best that we know becomes the standard way of doing something. The star teachers of the twenty-first century will be teachers who work every day to improve teaching — not only their own but that of the whole profession.
To be clear, the authors don’t explicitly endorse IBL; instead, they write, “In a book on teaching, it might be surprising that we have not recommended a particular way to teach. Instead, we have proposed the establishment of a… system for the improvement of classroom teaching.” But in my opinion, given the stark contrast they illustrated between classrooms in Japan and those in the US, it’s all too natural to infer that they prefer IBL over DI. Additionally, in a 2009 article, the authors wrote (emphasis mine), “In order to improve the teaching of math in the United States, we need to engage students in exploring mathematical relationships and wrestling with key mathematical ideas,” and one of the authors co-wrote a 2015 article titled “Beyond Growth Mindset: Creating Classroom Opportunities for Meaningful Struggle.” Exploring, wrestling, and struggling are key elements of IBL but not DI.