Limitless Mind. Джо Боулер

do not know what approach countries use to bring about their results. Accordingly, a group of researchers studied the nature of math teaching by going into classrooms and recording a representative sample of the teaching in seven countries. This teaching study uncovered a number of noteworthy outcomes.¹⁰ One finding was that the mathematics curriculum in the US is “a mile wide and an inch deep” compared to the curriculum in more successful countries.

      Japan has always scored well in mathematics—it has always finished in one of the top-five TIMSS positions—and was one of the countries visited in the study. The researchers found that Japanese students spent 44 percent of their time “inventing, thinking, and struggling with underlying concepts,” whereas students in the US engaged in this kind of behavior less than 1 percent of the time.

      Jim Stigler, one of the authors of the study, writes that the Japanese teachers want the students to struggle—and recalls the times when they would purposely give the wrong answer so that students would go back and work with foundational concepts. In my thousands of observations of classrooms over many years in the US and the UK, I have never seen this kind of practice; more typically I have seen teachers who seem to want to save students from struggle. Many times I have observed students asking for help and teachers structuring the work for students, breaking down questions and converting them into small easy steps. In doing so they empty the work of challenge and opportunities for struggle. Students complete the work and feel good, but often learn little.

      I saw a very similar teaching approach, focused on struggle, in a visit to classrooms in China, another country that scores highly in mathematics. I had been asked to visit China to give a talk at a conference and managed, as I like to do, to sneak away and visit some classrooms. In a number of high-school math classrooms, lessons were approximately one hour long, but at no time did I see students working on more than three questions in one hour. This contrasts strongly with a typical US high-school math classroom, where students chug through about thirty questions in an hour—about ten times more. The questions worked on in Chinese classrooms were deeper and more involved than the ones in US classrooms. Teachers would ask provocative questions, deliberately making incorrect statements that students would be challenged to argue against.

      One of the lessons I watched was on a topic that is often uninspiring in US classrooms—complementary and supplementary angles. The teacher in China asked the students to define a complementary angle, and the students gave their own ideas for a definition. Often the teacher would push the students’ definition to a place that made it incorrect and playfully ask, “Is this right, then?” The students would groan and try to make the definition more correct. The teacher bantered with the students, playfully extending and sometimes twisting their ideas to push the students to deeper thinking. The students probed, extended, clarified, and justified for a long time, reaching depths that were impressive.

      Contrast this with the standard US lesson on the same topic. Teachers often give definitions of complementary and supplementary angles to students, who then practice with thirty short questions. The defining characteristic of the lesson in China was struggle—the teacher deliberately put the students in situations where they became stuck and had to think hard. The lesson was entirely consistent with researchers’ description of targeted, mistake-focused practice. As Coyle says, the best way to build a highly effective circuit is to “fire it, attend to mistakes, then fire it again.” This is what the teachers in China were enabling their students to do.

      Elizabeth and Robert Bjork are scientists at UCLA who have studied learning for decades. They point out that a lot of learning that happens is very unproductive, as the most important learning events often go against intuition and deviate from standard practices in schools. They highlight the importance of “desirable difficulties,” again suggesting that the brain needs to be pushed to do things that are difficult. They particularly highlight the act of retrieving information from the brain, as every time we retrieve something, it changes in the brain and is more accessible when needed later.¹¹

      Many people study for tests by rereading materials, but the Bjorks point out that this is not very helpful for the brain. A much more helpful way of reviewing material is to test yourself, so that you keep having to recall the material—and hopefully make mistakes and correct them along the way. Learning scientists point out that these tests should not be performance events, as these cause stress and reduce the learning experience. Nonevaluative self-testing or peer testing is most beneficial.¹²

      Teaching the Value of Mistakes

      As neuroscience becomes more established as a field, it seems that more and more evidence is revealing the value of mistakes and struggle. Good teachers have known this intuitively and impressed upon learners that mistakes are really good opportunities for learning. Unfortunately, I have found that this message is not strong enough to keep students from feeling bad when they make mistakes—often because of the performance culture in which many good teachers work. Even when the message is phrased more powerfully—that mistakes are good not only for learning, but for brain growth and connectivity—it is hard for teachers to send it in a system in which they are made to give students tests that penalize them every time they make a mistake.

      This highlights the challenge of changing education—it is a complex system that has many different parts, all of which impact each other. Teachers can give the right messages to students, but then witness their messages being undermined by a practice that is imposed by their school district. This is why I encourage any teacher who learns about effective messages and teaching ideas to share them not only with their students, but with administrators and parents as well.

      When teachers encourage students to make mistakes and struggle, it is incredibly freeing. New Zealand second-grade teacher Suzanne Harris began teaching in an era of procedural teaching and timed testing. When she read one of my books, she knew that what she felt was right was backed up by research and asked her principal if she could teach the “Jo Boaler way”! He agreed. Suzanne went on to make many changes, one of which was to explain the positive benefits of mistakes and struggle to her students. In my interview with Suzanne, she described how this and other messages had changed things for a young boy in her class.