初等数学中的直观
Vision in elementary mathematics
W. W. Sawyer · 初版 1964 年
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正如书名所示，该方法利用视觉元素来探索数学中最具图形化且最不“令人望而生畏”的方面。作者观察到，大多数人的直观视觉只允许他们“看清”较小的数字。针对这一难题，作者面向趣味数学爱好者及教育工作者提出了多种方法：通过使数字可视化、戏剧化和分析化的技巧，吸引并保持注意力与理解力。主题涵盖从基础乘除法到代数，包含
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……她觉得那本书非常有帮助。至于数学，也就是我目前教的学科，我一直都非常看重数学概念的视觉化呈现，比如 W. W. Sawyer 的书《Vision in Elementary Mathematics》里所展示的那样 http://www.amazon.com/Vision-Elementary-Mathematics-W-Sawyer... http://www.marco-learningsystems.com/pages/sawyer/Vision_in_... 但其他教高等数学的数学家，比如 Serge……
…which she has found very helpful. As for mathematics, the subject I teach now, I have always cherished visual representations of mathematical concepts, for example those found in W. W. Sawyer's book Vision in Elementary Mathematics http://www.amazon.com/Vision-Elementary-Mathematics-W-Sawyer... http://www.marco-learningsystems.com/pages/sawyer/Vision_in_... But other mathematicians who taught higher mathematics, for example Serge…
……在我那个热爱数学的大儿子成长过程中，帮助他理解数学的书籍包括：Ian Stewart 的《Concepts of Modern Mathematics》（Dover 重印版）、John Stillwell 的《Numbers and Geometry》（Springer）、W. W. Sawyer 的《Vision in Elementary Mathematics》（Dover 重印版）、Sandor Lehoczky 和 Richard Rusczyk 的《The Art of Problem Solving》（Art of Problem Solving）。针对这种需求，经常被推荐的一本书是 Susan 的《Developing Math Talent》……
…understanding mathematics when my oldest son, a mathematics-lover, was growing up include Concepts of Modern Mathematics by Ian Stewart (Dover reprint) Numbers and Geometry by John Stillwell (Springer) Vision in Elementary Mathematics by W. W. Sawyer (Dover reprint) The Art of Problem Solving by Sandor Lehoczky and Richard Rusczyk (Art of Problem Solving) A frequently recommended book for this need is Developing Math Talent by Susan…
……社区大学水平的数学。那可不是大学初级数学；要是运气好，顶多也就是勾股定理和一元二次方程。W. W. Sawyer 的书，比如《Mathematician's Delight》[1] 和《Vision in Elementary Mathematics》[2]，似乎完全就是为这类受众量身定做的。[1] https://www.amazon.com/dp/0486462404/ [2] https://www.amazon.com/dp/048642555X/
…community college mathematics. That's not introductory university mathematics; if you are lucky it's Pythagoras' Theorem and quadratic equations. W. W. Sawyer's books, such as Mathematician's Delight[1] and Vision in Elementary Mathematics[2], seem to be exactly for this audience. [1] https://www.amazon.com/dp/0486462404/ [2] https://www.amazon.com/dp/048642555X/
……我最喜欢的学校数学读物作者之一曾写道：“家长最恰当的说法是：‘我以前数学学得很差，但那是因为我遇到了一个极差的老师。我真希望自己当年能遇到一个好老师。’”——W. W. Sawyer，《Vision in Elementary Mathematics》（1964年），第 5 页。哪怕你从没遇到过好老师，只要找到好的数学书，你也能找到一个好老师。很多在职程序员也没遇到过，这也是为什么他们中有些人不……
…One of my favorite authors on school mathematics wrote, "The proper thing for a parent to say is, 'I did badly at mathematics, but I had a very bad teacher. I wish I had had a good one.'" W. W. Sawyer, Vision in Elementary Mathematics (1964), page 5. You can find a good teacher by finding good books about mathematics, even if you have never had a good teacher. Many working programmers haven't either, which is why some of them don't…
……（也是我最初用这个网名时的个人签名）：“家长最恰当的说法是：‘我以前数学学得很差，但那是因为我遇到了一个极差的老师。我真希望自己当年能遇到一个好老师。’”——W. W. Sawyer，《Vision in Elementary Mathematics》（1964年），第 5 页。顺便提一句，引用的这本书学数学确实特别棒。
…tagline where I first started using this screen name): "The proper thing for a parent to say is, 'I did badly at mathematics, but I had a very bad teacher. I wish I had had a good one.'" W. W. Sawyer, Vision in Elementary Mathematics (1964), page 5. By the way, the cited book is indeed very good for learning math.
……一个我用“tokenadult”这个网名的在线论坛里：“家长最恰当的说法是：‘我以前数学学得很差，但那是因为我遇到了一个极差的老师。我真希望自己当年能遇到一个好老师。’”——W. W. Sawyer，《Vision in Elementary Mathematics》（1964年），第 5 页。是的，这句名言出处的那本书非常棒，尤其适合视觉型学习者。
…online forum where I used the screen name "tokenadult": "The proper thing for a parent to say is, 'I did badly at mathematics, but I had a very bad teacher. I wish I had had a good one.'" W. W. Sawyer, Vision in Elementary Mathematics (1964), page 5. Yes, the book from which the quotation comes is very good, and very good for learners with a visual learning style.