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they are in a lower-track group, their achievement becomes a self-fulfilling prophecy.

      The same is true when teachers are told which tracks students are in; they treat students differently whether they intend to or not. Similar results were found in a study of nearly twelve thousand students from kindergarten to third grade in more than twenty-one hundred schools in the US.10 None of the students who started out in the lowest reading group ever caught up to their peers in the highest group. Such policies of placing students in groups based on their supposed level of ability may be defensible if it resulted in higher achievement for the low-, middle-, or high-achieving students, but it does not.

      Studies of schools’ tracking policies in reading show that those schools that use tracked reading groups almost always score lower on average than schools that do not.11 These results are echoed in mathematics. I have compared students learning mathematics in middle and high schools in England and the US, and in both school levels and countries the schools that taught students in mixed achievement groups outperformed those that used ability groups.12

      San Francisco Unified is a large and diverse urban school district whose school board voted, unanimously, to remove advanced classes until eleventh grade. This prompted a lot of controversy and opposition from parents, but within two years, during which all students took the same mathematics classes until tenth grade, algebra failure rates fell from 40 to 8 percent of students in the district and the number of students taking advanced classes after tenth grade went up by one-third.13

      It is hard to imagine that the teaching practices of the district teachers changed dramatically in two years, but what did change were the opportunities students received to learn and the ideas students believed about themselves. All students, instead of some students, were taught high-level content—and the students responded with high achievement. International studies of achievement in different countries across the world show that countries that use tracking the latest and the least are the most successful. The US and the UK, two countries in which I have lived and worked, have two of the most highly tracked systems in the world.

      Nobody knows what children are capable of learning, and the schooling practices that place limits on students’ learning need to be radically rethought. Someone whose story illustrates most clearly for me the need to change our expectations of young children is Nicholas Letchford. Nicholas grew up in Australia, and in his first year of school his parents were told that he was “learning disabled” and had a “very low IQ.” In one of his mother’s first meetings with teachers, they reported that he was the worst child they had seen in twenty years of teaching. Nicholas found it difficult to focus, make connections, read, or write. But over the next few years Nicholas’s mother, Lois, refused to believe that her son could not learn, and she worked with Nicholas, teaching him how to focus, connect, read, and write. The year 2018 was an important one for Lois Letchford. It was the year that she published a book describing her work with Nicholas, called Reversed,14 and it was also the year Nicholas graduated from Oxford University with a doctoral degree in applied mathematics.

      Research and science have moved beyond the fixed-brain era, but fixed-brain schooling models and limited-learning beliefs persist. As long as schools, universities, and parents continue to give fixed-brain messages, students of all ages will continue to give up on learning in areas that could have brought them great joy and accomplishment.

      The new brain science showing that we have unlimited potential is transformative for many—and that includes those diagnosed with learning disabilities. These are individuals who are born with or develop, through injury or accident, physical brain differences that make learning more difficult. For many years, schools have traditionally put such students into lower-level classes and worked around their weaknesses.

      Barbara Arrowsmith-Young takes an entirely different approach. I was fortunate to meet Barbara on a recent visit to Toronto, during which I toured one of the incredible “Arrowsmith” schools she has set up. It is impossible to spend time with Barbara and not realize that she is a force to be reckoned with; she is passionate not only about sharing her knowledge of the brain and how we develop it, but in using her knowledge to change the neural pathways of those diagnosed with special educational needs through targeted brain training.

      Barbara is someone who was herself diagnosed with severe learning disabilities. As she was growing up in Toronto in the 1950s and 1960s, she and her family knew she was brilliant in some areas, but they were told she was “retarded” in others. She had trouble pronouncing words and could not engage in spatial reasoning. She could not follow cause-and-effect statements, and she reversed letters. She was able to understand the words “mother” and “daughter,” but not the expression “mother’s daughter.”15 Fortunately for Barbara, she had an amazing memory and was able to memorize her way through school and hide what she knew was wrong.

      As an adult her own disabilities prompted her to study child development, and eventually she came across the work of Alexander Luria, a Russian neuropsychologist who had written about stroke victims who had trouble with grammar, logic, and reading clocks. Luria worked with many people with brain injuries, produced an in-depth analysis of the functioning of various brain regions, and developed an extensive battery of neuropsychological tests. When Barbara read Luria’s work, she realized she herself had brain injuries, became quite depressed, and started to consider suicide. But then she came across the first work on neuroplasticity and realized that particular activities could produce brain growth. She began months of detailed work on the areas she knew she was weakest in. She made herself hundreds of cards with clock faces and practiced so much she was reading them faster than “regular” people. She started to see improvements in her symbolic understanding and for the first time began grasping grammar, math, and logic.

      Now Barbara runs schools and programs that give brain training to students diagnosed with learning differences. Chatting with Barbara on my visit, I found it hard to imagine that this woman herself had had such severe disabilities in the past, as she is an impressive communicator and thinker. Barbara has developed over forty hours of tests that diagnose students’ brain strengths and weaknesses and a range of targeted cognitive exercises that enable students to develop brain pathways. Students come to her Arrowsmith schools with severe disabilities and leave without them.

      When I visited one of the Arrowsmith schools for the first time, I saw students sitting at computer screens intensely concentrating on their cognitive tasks. I asked Barbara if the students were happy doing this, and she replied that students stay motivated because they can feel the effects of the program very quickly. Many of the students I spoke to talked in the same terms—after they started on the cognitive tasks, they felt a “fog lifting” and were able to make sense of the world. When I visited the Arrowsmith school for the second time, I sat and talked to some adults going through the program.

      Shannon was a young lawyer who had become concerned after criticism for the length of time it took her to produce her work, as people typically pay for lawyers’ time by the hour. She was referred to Arrowsmith and decided to enroll for a summer. When I met her, a few weeks into the program, she told me that it was already “life changing” for her. Not only was Shannon thinking a lot more efficiently, but she was able to make connections she had not been able to make before. She was even making sense of events that had happened in her past, even though she had not been able to make sense of them at the time. Shannon, like the others, talked about a “fog lifting” from her mind; she said she used to be a passenger in conversations, but now “everything is clear” and she is able to participate fully.

      Barbara not only offers brain training for students who go to Toronto and enroll in the school; she has now developed a program that educators can be trained in and take back to their schools. Some students stay in the program for a few months, some for a few years, and now a remote program is being developed for students to work in different locations. Barbara is somebody who is leading the world in her brain-training approach. Like many groundbreakers, she has had to endure critiques from the people who do not accept the idea of neuroplasticity or that brains can be exercised and developed, but she has continued fighting for the rights of students who have been made to believe they are “broken.”

      Most of the students who contact

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