Vision in elementary mathematics
by W. W. Sawyer · first published 1964
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As the title suggests, this technique employs visual elements in its exploration of the most graphic and least "forbidding" aspects of mathematics. The author observes that most people possess a direct vision that permits them to "see" only the smaller numbers. In addressing this difficulty, both for those who like recreational mathematics and for those who teach, he suggests a variety of methods: techniques of visualizing, dramatizing, and analyzing numbers that attract and retain the attention and understanding. Topics range from basic multiplication and division to algebra, encompassing wor
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…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…
on “How to Ace Calculus: The Art of Doing Well in Technical Courses” ↗…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…
on “Ask HN: Books for Parents of Mathematics-Loving Children?” ↗…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/
on “OpenStax – openly licensed textbooks” ↗…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…
on “Ask HN: Is it necessary to learn maths to enter into programming?” ↗…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.
on “Algebra for All: Educators Challenge Idea That Math Skills Must Come Naturally” ↗…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.
on “Not Every Child Is Secretly a Genius” ↗…Distributive rule / algebra, to Quadratics then the Derivative, here : https://www.youtube.com/playlist?list=PLEInJ-Z4qBKYxbK1Mm13g... All of these things are covered in some great books : W W Sawyer Vision in Elementary Mathematics Algebra by Gelfand Calculus by Thomas We have superb resources now like 3Blue1Brown, KhanAcademy and ArtOfProblemsolving.com / BeastAcademy .. so you _can_ get your kids a superb math education,…
on “Simplifying and Refactoring Introductory Calculus” ↗…should start out in my reaction to both of these links you've kindly shared by pointing out that my own bent in thinking about mathematics is to think visually, and indeed that is why I like Sawyer's book Vision in Elementary Mathematics (which leads off my longer reply in this thread) so well. But although I like visual approaches to teaching mathematics very well, and use them in the mathematics classes I teach, I also like studies…
on “Teaching Kids to Love Math” ↗…Mathematician W. W. Sawyer wrote about this quite a while ago: "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. Elementary school teachers in the United States often fear mathematics themselves, http://news.uchicago.edu/article/2010/01/25/female-teachers-... http://www.jstor.org/discover/10.2307/41192533?uid=3739736&#...…
on “Teaching Kids to Love Math” ↗…am), and also chose a tagline quotation from Sawyer: "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. Sawyer didn't want parents to give their children an excuse for thinking "I don't have a head for mathematics." Instead, a learner can keep searching for an effective teacher, and learn…
on “"I can't do math" (2001)” ↗"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.
on “Ask HN: which is the most influencing quote you ever came across?” ↗Reading Bruner's "Toward a Theory of Instruction" and Piaget's "The Child's Conception of Number." Sawyer's "Vision in Elementary Mathematics" is next. Trying to get over my distaste for Objective-C so I can translate some of these ideas to the iPad. Teaching Scratch in Oakland.
on “Ask HN: What are you working on?” ↗