In an exchange on Twitter that is typical of that platform, someone pointed to how math is taught in Japan. This form of argument is often used as the ultimate proof that we don’t know what we’re doing in the U.S. because Japan. For example:
This tweet was in response to someone saying that drill and memorization is practiced in other countries that seem to do better than the U.S. on international tests. The tweeter responds by exhorting us to look at how math is taught in a Japanese classroom as shown in a series of videos taken of math lessons in classrooms around the world (including the U.S.). The video study was part of a TIMSS project undertaken in the 90’s and written about in a book called “The Teaching Gap” by Stigler and Hiebert.
Against my better judgment about getting involved in a dispute on Twitter, I replied, pointing to an article by Alan Siegel, who is a retired professor of computer science, who taught at the Courant College at NYU. In it, Siegel analyzed the video of the Japanese classroom and stated “"Education analyses and policy reports seem to be based on incomplete portrayals of the actual teaching as documented on videotape."
Siegel’s analysis does demonstrate that Japanese classrooms do rely on memorization and explicit instruction. Furthermore, it shows that contrary to what is believed by many in the math reform community, the students in the Japanese classroom did not invent their own strategies, nor discover solutions on their own. The tweeter responded:
Missing the point is part and parcel of Twitter and I won’t go too far into that, except to say that the person further responded that he didn’t have time to read a 30+ page paper written by a computer science professor who knew little of math education trends of the 80’s and 90’s.
A few weeks after this “conversation”, another person in the reform camp unearthed an article from 2015 on the Japanese classroom video written by none other than Emily Hanford.
The article was somewhat of a coup for this person because of Emily’s notoriety for her “Sold a Story” series. The series exposed how the teaching of reading in the U.S. has been compromised by unfounded theories and ineffective practices. The series had a significant reach, response and effect. In fact, the series caused math reformers to gather their wagons in a circle for fear that a comparable “Sold a Story” article about math education might emerge. Reformers were now suddenly saying things like “Of course explicit instruction is important, we never said it wasn’t, we use it when we teach”…etc.
So I can imagine that this person was cackling with glee at this find of the 2015 piece by Hanford, waving it like a flag for all to see, saying: “Yeah, let her write an article about math education; and by the way, be careful what you ask for.”
In her article, like others who viewed the video, she acknowledges that Japanese students did in fact memorize terms and formulas and teachers did in fact show them the procedure for solving problems. But in the end, Japan was doing things differently than the U.S. and she then resorts to the “In Japan they…” type of appeal that wins the hearts and minds of math reformers everywhere. She states:
“[T]here was significantly more time devoted to having the students apply this knowledge, on their own, to new and challenging problems. The students learn there are multiple ways to solve a math problem; it’s not just about memorizing a procedure the teacher taught you.
“At one point in the American lesson [shown in a video that is linked to in her article], the teacher tells students he is going to give them a “couple of minutes” to do some problems on their own. They have a worksheet with 40 problems on it. The students start working, and the teacher walks around the room to check on their progress.
“But it takes just 40 seconds for the teacher to interrupt the class to say, ‘OK, you want some prompting on this one?’ He goes to the board to demonstrate a procedure, and in the process gives the class the answers to three of the problems.”
With such evidence in hand, (written by none other than the celebrated Hanford herself) reformers could now reclaim their ground. They could point to this as evidence of the superiority of the Japanese methods, and the inferiority of U.S. methods, even if, as Hanford says, both rely on memorization and explicit instruction. The difference is the challenging problems students are given to solve in Japan as opposed to the U.S. And yes, there are more opportunities for students to work on challenging problems in Japan, according to what is shown in the videos.
Yet, in reading Dr. Siegel’s paper, I was struck by how much the teacher did in fact help students through the problem. And given the amount of help the teacher provided, Hanford’s criticism of the U.S. teacher in the quote above seemed susceptible to further scrutiny. So I contacted Dr. Siegel to ask him his opinion of her analysis of the videos in question.
He states:
“The Japanese method does ask the students to struggle with more complex problems, but not alone. They will already have familiarity with the one fundamental concept needed to solve the current problem, but will not yet understand how to use it to solve the latest problem.
“They get three to six minutes to work on the challenge problem of the day. During that time, one or two teachers circulate among the students and offer suggestions. The six minutes are broken into two 3-minute sessions. In the first, the students work individually, whereas they are allowed to work in groups in the second.
“At the end of the second 3 minutes, the tutored students will present what they learned. Then the teacher gives a professional presentation, and shows everyone how the idea is used to solve the problem. Then another problem of the EXACT SAME type and solved by the EXACT SAME approach is given. At this point, at least half of the class can solve it.
“My take: The three to six minutes they typically get to try to solve a challenge problem will not be enough time for anyone in a class of 30 to solve the problem. There are consequences.
“1) It shows them that there is a technique that they are missing, and need to understand. That is good.
“2) It supports the students' beliefs that they are not talented enough to become an expert in STEM subjects. That is bad.”
Dr. Siegel concludes that Japanese teaching is indeed different than ours but comes at a price. What the reformers and others notice and admire is immersing the students into a new type of problem, causing them to “struggle”. What the reformers ignore is how much help the Japanese teachers had to provide. What they also ignore is how the process tends to undermine the self-confidence of the class. Siegel suggests that there is probably a way to “split the difference” between the traditional approaches used in the U.S. and those used in Japan. But given the trend in math education to let students struggle by not giving the instruction they need until afterward, changes in math teaching are likely to be face resistance, as they have for many years.