I lived in China for a few years and the education system there is pretty much all rote-memorization.
你好. I used to live in Taiwan, and I have a big bunch of mathematics textbooks from China, as well as some recent math students in my local mathematics classes who grew up in China. Mathematics instruction in China is not at all about memorization, in the sense used in this article. A good book on the topic of mathematics instruction in the United States and China is Knowing and Teaching Elementary Mathematics: Teachers' Understanding of Fundamental Mathematics in China and the United States by Liping Ma.[1] Her field study, with sponsorship by the United States federal government, made clear that elementary mathematics instruction in China is much richer and deeper and more conceptual than in the United States.
But the idea of the article is true: When you just memorize, it makes it difficult to apply the principals that you are learning to other situations/problems.
Yes. To memorize without underlying understanding is no more useful than not memorizing at all. Developing deep understanding of a topic usually brings along with it sufficient memorization of fundamental facts that the problem-solver will be able to solve some problems on the spot, and know when to look things up if needed.
Kids are ready for formal operations when their earlier experience has prepared them for formal operations. In some places around the world, students in fifth grade--including below-average fifth-graders--are already learning algebra. In quite a few whole countries around the world (for example, Taiwan, where my wife grew up when Taiwan was still a developing country) all seventh graders study algebra and geometry as part of their regular school math lessons, yes, including the below-average seventh graders. (In Taiwan, they also learned enough of the International Phonetic Alphabet to transcribe General American English at that age, but now that skill, which most United States reading teachers lack entirely even with a college degree, has moved into the elementary school curriculum.) Good education at the beginning produces better results in the middle grades.[1]
students do not have to study for 14 hours a day in their prime of their youth to acquire a stable career
Students don't have to do that anywhere. And they don't do that anywhere. I have lived in east Asia (and my three older children all have) and I challenge your assumption that pupils there study for fourteen hours a day (they most certainly do not) or that everything about schools there is a "pressure cooker environment." There are trade-offs involved in living anywhere, rather than living somewhere else, but you really owe it to yourself to find out more about how effective primary teaching is done before concluding that it shouldn't be tried in the United States. As they say in Chinese-speaking countries, "百聞不如一見" (hearing about something a hundred times isn't worth seeing it once). I offer for your reading pleasure a reading suggestion, full of food for thought, namely Liping Ma's book Knowing and Teaching Elementary Mathematics: Teachers' Understanding of Fundamental Mathematics in China and the United States.[1] Reviews of this book appear below the book link.
Anyway, we can get other reality checks on this issue by seeing what people who have studied the United States school curriculum say about secondary schools here, for example "What’s Holding Back American Teenagers? Our high schools are a disaster."[2] The last federal sample survey on the issue resulted in news reports such as, "School is too easy, students report,"[3] suggesting that a lot of learners here don't appreciate dumbed-down school lessons that waste their time without providing a return in new knowledge and skills.
你好. I used to live in Taiwan, and I have a big bunch of mathematics textbooks from China, as well as some recent math students in my local mathematics classes who grew up in China. Mathematics instruction in China is not at all about memorization, in the sense used in this article. A good book on the topic of mathematics instruction in the United States and China is Knowing and Teaching Elementary Mathematics: Teachers' Understanding of Fundamental Mathematics in China and the United States by Liping Ma.[1] Her field study, with sponsorship by the United States federal government, made clear that elementary mathematics instruction in China is much richer and deeper and more conceptual than in the United States.
But the idea of the article is true: When you just memorize, it makes it difficult to apply the principals that you are learning to other situations/problems.
Yes. To memorize without underlying understanding is no more useful than not memorizing at all. Developing deep understanding of a topic usually brings along with it sufficient memorization of fundamental facts that the problem-solver will be able to solve some problems on the spot, and know when to look things up if needed.
[1] http://www.amazon.com/Knowing-Teaching-Elementary-Mathematic...
http://www.aft.org/sites/default/files/periodicals/amed1.pdf
http://www.ams.org/notices/199908/rev-howe.pdf
[1] http://www.amazon.com/Knowing-Teaching-Elementary-Mathematic...
http://condor.depaul.edu/sepp/mat660/Askey.pdf
http://www.ams.org/notices/199908/rev-howe.pdf
Students don't have to do that anywhere. And they don't do that anywhere. I have lived in east Asia (and my three older children all have) and I challenge your assumption that pupils there study for fourteen hours a day (they most certainly do not) or that everything about schools there is a "pressure cooker environment." There are trade-offs involved in living anywhere, rather than living somewhere else, but you really owe it to yourself to find out more about how effective primary teaching is done before concluding that it shouldn't be tried in the United States. As they say in Chinese-speaking countries, "百聞不如一見" (hearing about something a hundred times isn't worth seeing it once). I offer for your reading pleasure a reading suggestion, full of food for thought, namely Liping Ma's book Knowing and Teaching Elementary Mathematics: Teachers' Understanding of Fundamental Mathematics in China and the United States.[1] Reviews of this book appear below the book link.
Anyway, we can get other reality checks on this issue by seeing what people who have studied the United States school curriculum say about secondary schools here, for example "What’s Holding Back American Teenagers? Our high schools are a disaster."[2] The last federal sample survey on the issue resulted in news reports such as, "School is too easy, students report,"[3] suggesting that a lot of learners here don't appreciate dumbed-down school lessons that waste their time without providing a return in new knowledge and skills.
[1] http://www.amazon.com/Knowing-Teaching-Elementary-Mathematic...
http://www.aft.org/pdfs/americaneducator/fall1999/amed1.pdf
http://www.ams.org/notices/199908/rev-howe.pdf
http://www.jstor.org/discover/10.2307/2695436?uid=2&uid=4&si...
[2] http://www.slate.com/articles/life/education/2014/02/high_sc...
[3] http://usatoday30.usatoday.com/news/education/story/2012-07-...