……States。http://math.berkeley.edu/~wu/ http://www.corestandards.org/the-standards/mathematics 一本由世界著名数学家所写、满是开放式问题的诱人教材的好例子，是已故的 Israel M. Gelfand 和 Alexander Shen 合著的《Algebra》。http://www.amazon.com/Algebra-Israel-M-Gelfand/dp/0817636773 这本书里有些题很难，但总体来说都是提得很好的问题……
…States. http://math.berkeley.edu/~wu/ http://www.corestandards.org/the-standards/mathematics A good example of a beguiling textbook by a world-famous mathematician with lots of open-ended problems is Algebra, by the late Israel M. Gelfand and Alexander Shen. http://www.amazon.com/Algebra-Israel-M-Gelfand/dp/0817636773 Some of the problems in this book are HARD, but they are generally well posed problems…
……才意识到 Israel Gelfand 刚刚去世。他是我最喜欢的数学教材作者，没有之一。（我甚至用他的照片做我第一个用 tokenadult 这个网名的网站上的头像。）他的《Algebra》http://www.amazon.com/Algebra-Israel-M-Gelfand/dp/0817636773 是一个鼓舞人心的例子，说明怎样把教材写得既幽默又有挑战性，也是一套出色的中学教材系列的开端……
…realize Israel Gelfand had just died. He is by far my favorite author of mathematics textbooks. (I even use his photograph as my avatar on the first website where I used the screenname tokenadult.) His book Algebra http://www.amazon.com/Algebra-Israel-M-Gelfand/dp/0817636773 is an inspirational example of how to make a textbook both humorous and challenging, and is the start of a great series of textbooks on secondary…
I don't think lack of realism is the worst thing about these types of problems. I think lack of fun is. I can recommend an algebra textbook with fun. And it was written by a mathematician with rather better credentials (theorems that bear his name in higher mathematics) than most algebra textbook authors. The book is Algebra by Israel…
…(which now have an edition aligned to United States curriculums standards) http://www.singaporemath.com/Primary_Mathematics_Stds_Ed_s/1... followed up by the Gelfand textbooks http://www.amazon.com/Algebra-Israel-M-Gelfand/dp/0817636773 http://www.amazon.com/Method-Coordinates-I-M-Gelfand/dp/0817... http://www.amazon.com/Functions-Graphs-Dover-Books-Mathemati... http://www.amazon.com/Trigonometry-I-M-Gelfand/dp/0817639144...…
真巧，上周六早上我刚教了分数比较那一课，不过我用的分数对稍微更有挑战性（出自已故的 I.M. Gelfand 和 Alexander Shen 合写的那本出色教材《Algebra》）。http://www.amazon.com/Algebra-Israel-M-Gelfand/dp/0817636773 我刚把书里的第 40 题放上去，那是我上周教给三年级到……的孩子们做的
Funny that I was just teaching that lesson about fraction comparison last Saturday morning, but I was using fraction pairs that are a bit more challenging (from the excellent textbook Algebra by the late I.M. Gelfand and Alexander Shen). http://www.amazon.com/Algebra-Israel-M-Gelfand/dp/0817636773 I just put problem 40 from the book, which I taught last week to children of third-grade to…
…(which now have an edition aligned to United States curriculums standards) http://www.singaporemath.com/Primary_Mathematics_Stds_Ed_s/1... followed up by the Gelfand textbooks http://www.amazon.com/Algebra-Israel-M-Gelfand/dp/0817636773 http://www.amazon.com/Method-Coordinates-Dover-Books-Mathema... http://www.amazon.com/Functions-Graphs-Dover-Books-Mathemati... http://www.amazon.com/Trigonometry-I-M-Gelfand/dp/0817639144...…
……States。http://math.berkeley.edu/~wu/ http://www.corestandards.org/the-standards/mathematics 一本由世界著名数学家所写、满是开放式问题的诱人教材的好例子，是已故的 Israel M. Gelfand 和 Alexander Shen 合著的《Algebra》。http://www.amazon.com/Algebra-Israel-M-Gelfand/dp/0817636773 这本书里有些题很难，但总体来说都是提得很好的问题……
…States. http://math.berkeley.edu/~wu/ http://www.corestandards.org/the-standards/mathematics A good example of a beguiling textbook by a world-famous mathematician with lots of open-ended problems is Algebra, by the late Israel M. Gelfand and Alexander Shen. http://www.amazon.com/Algebra-Israel-M-Gelfand/dp/0817636773 Some of the problems in this book are HARD, but they are generally well posed problems…
……才意识到 Israel Gelfand 刚刚去世。他是我最喜欢的数学教材作者，没有之一。（我甚至用他的照片做我第一个用 tokenadult 这个网名的网站上的头像。）他的《Algebra》http://www.amazon.com/Algebra-Israel-M-Gelfand/dp/0817636773 是一个鼓舞人心的例子，说明怎样把教材写得既幽默又有挑战性，也是一套出色的中学教材系列的开端……
…realize Israel Gelfand had just died. He is by far my favorite author of mathematics textbooks. (I even use his photograph as my avatar on the first website where I used the screenname tokenadult.) His book Algebra http://www.amazon.com/Algebra-Israel-M-Gelfand/dp/0817636773 is an inspirational example of how to make a textbook both humorous and challenging, and is the start of a great series of textbooks on secondary…
我不觉得缺乏现实性是这类问题最糟糕的地方。我觉得最糟糕的是缺乏乐趣。我可以推荐一本有趣的代数教材。而且它的作者资历比大多数代数教材作者都硬得多（高等数学里有以他命名的定理）。这本书就是 Israel…… 的《Algebra》
I don't think lack of realism is the worst thing about these types of problems. I think lack of fun is. I can recommend an algebra textbook with fun. And it was written by a mathematician with rather better credentials (theorems that bear his name in higher mathematics) than most algebra textbook authors. The book is Algebra by Israel…
……（现在有了对齐美国课程标准的新版）http://www.singaporemath.com/Primary_Mathematics_Stds_Ed_s/1... 接着是 Gelfand 的教材 http://www.amazon.com/Algebra-Israel-M-Gelfand/dp/0817636773 http://www.amazon.com/Method-Coordinates-I-M-Gelfand/dp/0817... http://www.amazon.com/Functions-Graphs-Dover-Books-Mathemati... http://www.amazon.com/Trigonometry-I-M-Gelfand/dp/0817639144...……
…(which now have an edition aligned to United States curriculums standards) http://www.singaporemath.com/Primary_Mathematics_Stds_Ed_s/1... followed up by the Gelfand textbooks http://www.amazon.com/Algebra-Israel-M-Gelfand/dp/0817636773 http://www.amazon.com/Method-Coordinates-I-M-Gelfand/dp/0817... http://www.amazon.com/Functions-Graphs-Dover-Books-Mathemati... http://www.amazon.com/Trigonometry-I-M-Gelfand/dp/0817639144...…
真巧，上周六早上我刚教了分数比较那一课，不过我用的分数对稍微更有挑战性（出自已故的 I.M. Gelfand 和 Alexander Shen 合写的那本出色教材《Algebra》）。http://www.amazon.com/Algebra-Israel-M-Gelfand/dp/0817636773 我刚把书里的第 40 题放上去，那是我上周教给三年级到……的孩子们做的
Funny that I was just teaching that lesson about fraction comparison last Saturday morning, but I was using fraction pairs that are a bit more challenging (from the excellent textbook Algebra by the late I.M. Gelfand and Alexander Shen). http://www.amazon.com/Algebra-Israel-M-Gelfand/dp/0817636773 I just put problem 40 from the book, which I taught last week to children of third-grade to…
……（现在有了对齐美国课程标准的新版）http://www.singaporemath.com/Primary_Mathematics_Stds_Ed_s/1... 接着是 Gelfand 的教材 http://www.amazon.com/Algebra-Israel-M-Gelfand/dp/0817636773 http://www.amazon.com/Method-Coordinates-Dover-Books-Mathema... http://www.amazon.com/Functions-Graphs-Dover-Books-Mathemati... http://www.amazon.com/Trigonometry-I-M-Gelfand/dp/0817639144...……
…(which now have an edition aligned to United States curriculums standards) http://www.singaporemath.com/Primary_Mathematics_Stds_Ed_s/1... followed up by the Gelfand textbooks http://www.amazon.com/Algebra-Israel-M-Gelfand/dp/0817636773 http://www.amazon.com/Method-Coordinates-Dover-Books-Mathema... http://www.amazon.com/Functions-Graphs-Dover-Books-Mathemati... http://www.amazon.com/Trigonometry-I-M-Gelfand/dp/0817639144...…