……数学教育中的二元对立》http://www.aft.org/pdfs/americaneducator/fall1999/wu.pdf 近期尝试将对基本技能的深刻概念理解融入数学教材的努力之一，是 Richard Rusczyk、David Patrick 和 Ravi Boppana 编写的《Prealgebra》，https://www.artofproblemsolving.com/Store/viewitem.php?item=... 它指出了低年级学生在不用计算器的情况下应该能做到什么，如果……
…dichotomy in mathematics education" http://www.aft.org/pdfs/americaneducator/fall1999/wu.pdf A recent effort to embody strong conceptual understanding of basic skills into a mathematics textbook is Prealgebra by Richard Rusczyk, David Patrick, and Ravi Boppana, https://www.artofproblemsolving.com/Store/viewitem.php?item=... which points to what young students should be able to do WITHOUT a calculator if…
数学缺乏直观的解释一直是我最受不了的痛点。我是个极度依赖视觉思考的人，这也是我喜欢 Art of Problem Solving 新出的这本教材《Prealgebra》（作者 Richard Rusczyk、David Patrick 和 Ravi Boppana）的原因之一——https://www.artofproblemsolving.com/Store/viewitem.php?item=... 书里充满了有趣的直观“解释”，并在一本书中替代了证明……
the lack of intuitive explanations for math is a major pet peeve of mine I'm a very visual thinker, and that is one reason I enjoy the new Art of Problem Solving textbook Prealgebra by Richard Rusczyk, David Patrick, and Ravi Boppana-- https://www.artofproblemsolving.com/Store/viewitem.php?item=... it is full of interesting visual "explanations" and substitute for proofs in a book…
……学期而且测试成绩超前好几年，对事物运作的原委有着非常直观的理解，我很想保持她的兴趣。然而，我们现在学到了初级代数，用的是这本书 [0]——《Prealgebra: The Art of Problem Solving》。第一章全都是公理、各种各样的证明，把“显而易见”的结论拆解回第一性原理的证明，这可就不太合她的胃口了……
…semester and tests several years ahead and has a very intuitive sense of why things work the way they do, I'd like to keep her interest. However, we're now on to pre-algebra and using this book [0], "Prealgebra: The Art of Problem Solving". The first chapter is all about axioms, proofs of some sort, breaking down "obvious" conclusions back to their constituent proof-from-first-principles and it's not agreeing…
……数学教育中的二元对立》http://www.aft.org/pdfs/americaneducator/fall1999/wu.pdf 近期尝试将对基本技能的深刻概念理解融入数学教材的努力之一，是 Richard Rusczyk、David Patrick 和 Ravi Boppana 编写的《Prealgebra》，https://www.artofproblemsolving.com/Store/viewitem.php?item=... 它指出了低年级学生在不用计算器的情况下应该能做到什么，如果……
…dichotomy in mathematics education" http://www.aft.org/pdfs/americaneducator/fall1999/wu.pdf A recent effort to embody strong conceptual understanding of basic skills into a mathematics textbook is Prealgebra by Richard Rusczyk, David Patrick, and Ravi Boppana, https://www.artofproblemsolving.com/Store/viewitem.php?item=... which points to what young students should be able to do WITHOUT a calculator if…
数学缺乏直观的解释一直是我最受不了的痛点。我是个极度依赖视觉思考的人，这也是我喜欢 Art of Problem Solving 新出的这本教材《Prealgebra》（作者 Richard Rusczyk、David Patrick 和 Ravi Boppana）的原因之一——https://www.artofproblemsolving.com/Store/viewitem.php?item=... 书里充满了有趣的直观“解释”，并在一本书中替代了证明……
the lack of intuitive explanations for math is a major pet peeve of mine I'm a very visual thinker, and that is one reason I enjoy the new Art of Problem Solving textbook Prealgebra by Richard Rusczyk, David Patrick, and Ravi Boppana-- https://www.artofproblemsolving.com/Store/viewitem.php?item=... it is full of interesting visual "explanations" and substitute for proofs in a book…
用于这个目的的话，artofproblemsolving.com 的任何一本书都极好。我建议从 Richard Rusczyk 的《Prealgebra》开始。
Any artofproblemsolving.com book will be outstanding for this purpose. I suggest starting with Prealgebra by Richard Rusczyk.
……学期而且测试成绩超前好几年，对事物运作的原委有着非常直观的理解，我很想保持她的兴趣。然而，我们现在学到了初级代数，用的是这本书 [0]——《Prealgebra: The Art of Problem Solving》。第一章全都是公理、各种各样的证明，把“显而易见”的结论拆解回第一性原理的证明，这可就不太合她的胃口了……
…semester and tests several years ahead and has a very intuitive sense of why things work the way they do, I'd like to keep her interest. However, we're now on to pre-algebra and using this book [0], "Prealgebra: The Art of Problem Solving". The first chapter is all about axioms, proofs of some sort, breaking down "obvious" conclusions back to their constituent proof-from-first-principles and it's not agreeing…