Knowing and teaching elementary mathematics
by Liping Ma · first published 1999
50% recommend50% neutral
Studies of teachers in the U.S. often document insufficient subject matter knowledge in mathematics. Yet, these studies give few examples of the knowledge teachers need to support teaching, particularly the kind of teaching demanded by recent reforms in mathematics education. Knowing and Teaching Elementary Mathematics describes the nature and development of the knowledge that elementary teachers need to become accomplished mathematics teachers, and suggests why such knowledge seems more common in China than in the United States, despite the fact that Chinese teachers have less formal educatio
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…Chinese-language textbooks about elementary mathematics for advanced learners, of which I have many at home, take care to introduce multiple representations of all mathematical concepts. The brilliant book Knowing and Teaching Elementary Mathematics: Teachers' Understanding of Fundamental Mathematics in China and the United States by Liping Ma http://www.amazon.com/Knowing-Teaching-Elementary-Mathematic... demonstrates with cogent examples just…
on “How to Ace Calculus: The Art of Doing Well in Technical Courses” ↗…In general, any reader of Hacker News could learn a lot about what is missing in the United States (or, more generally, in the English-speaking world) in elementary mathematics instruction by reading Knowing and Teaching Elementary Mathematics: Teachers' Understanding of Fundamental Mathematics in China and the United States by Liping Ma.[1] There is a lot to basic mathematics that is far from easy, if deep understanding is what you are looking…
…operations and why they work because WE BUILD FROM THERE." The longer story about understanding arithmetic--REALLY understanding it--and how that relates to learning beyond arithmetic can be found in the book Knowing and Teaching Elementary Mathematics by Liping Ma http://www.amazon.com/Knowing-Teaching-Elementary-Mathematic... (well reviewed by two mathematicians who study mathematics education) http://www.ams.org/notices/199908/rev-howe.pdf http://www.aft.org/pdfs/americaneducator/fall1999/amed1.pdf…
on “The mathematics generation gap” ↗…of fundamental mathematics (PUFM)" before starting the calculus course. A link that furthered my process of pondering how students might learn mathematics better was Richard Askey's review of the book Knowing and Teaching Elementary Mathematics by Liping Ma. http://www.aft.org/pdfs/americaneducator/fall1999/amed1.pdf Another review of that excellent book by mathematician Roger Howe http://www.ams.org/notices/199908/rev-howe.pdf is also food…
on “The Calculus Trap (2005)” ↗…teach. Fractions are not insuperably hard if they are well taught, but they are rarely well taught at any level of mathematics classes in the United States. If you'd like more background on this topic, see Knowing and Teaching Elementary Mathematics: Teachers' Understanding of Fundamental Mathematics in China and the United States by Liping Ma http://www.ams.org/notices/199908/rev-howe.pdf https://webstorage.worcester.edu/sites/rbisk/web/marlboro%20...…
on “Federal Research Suggests New Approach to Teaching Fractions” ↗…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…
on “Memorizers are the lowest achievers and other Common Core math surprises” ↗…learn as fast and effectively as possible. But you can also get by okay with just a typical trained professional teacher (ideally a specialist in mathematics education). I recommend Liping Ma’s book Knowing and Teaching Elementary Mathematics for some basic analysis.
on “Finland plans to replace classic school subjects with broader “topics” (2015)” ↗…American secondary school graduates entering tough college programs have more catching up to do than the (much more stringently selected) international undergraduates at American colleges. See the book Knowing and Teaching Elementary Mathematics http://www.amazon.com/Knowing-Teaching-Elementary-Mathematic... (or its review by mathematician Richard Askey) http://www.aft.org/pubs-reports/american_educator/fall99/ame... for example of ways American…
on “Senator To Microsoft: What Was That You Said About Wanting More H-1B Workers? ” ↗…high school. That's a mistake of the system in the United States. In many other countries, teachers specialize by subject in the elementary grades, the better to teach their subject effectively. See Knowing and Teaching Elementary Mathematics: Teachers' Understanding of Fundamental Mathematics in China and the United States http://www.amazon.com/Knowing-Teaching-Elementary-Mathematic... for a detailed discussion of elementary math teaching,…
on “Female teachers transmit math anxiety to female students” ↗…Mathematics Education"[1] (1999) by Hung-hsi Wu, for a discussion of what leads to deep understanding of mathematics. Another classic article on the topic is Richard Askey's review[2] of Liping Ma's book Knowing and Teaching Elementary Mathematics, a very good read indeed. [1] http://math.berkeley.edu/~wu/wu1999.pdf [2] http://www.aft.org/pdfs/americaneducator/fall1999/amed1.pdf
on “The trouble with Khan Academy (2012)” ↗…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…
on “U.S. Students from Educated Families Lag in International Tests” ↗…American society either.[4] The current efforts in preschools reported in the interesting article submitted here should be followed up by further reform of elementary school mathematics instruction. The book Knowing and Teaching Elementary Mathematics by Liping Ma[5] is especially informative about what to do to help all learners in the United States learn mathematics better in early schooling. [1] http://www.ets.org/Media/Education_Topics/pdf/TQ_full_report...…
on “Why Math Might Be the Secret to School Success” ↗…Hung-hsi Wu. His writings have been very influential on my thinking about math education. A link that furthered my process of pondering how to teach mathematics better was Richard Askey's review of the book Knowing and Teaching Elementary Mathematics by Liping Ma. http://www.aft.org/pubs-reports/american_educator/fall99/ame... Another review of that excellent book http://www.ams.org/notices/199908/rev-howe.pdf is also food for thought. Professor…
on “A Math Paradox: The Widening Gap Between High School and College Math” ↗…mathematics taught as music is taught to elementary-age pupils in the United States. For an eye-opening look at how elementary mathematics teachers could be prepared, and how that would help learners, see Knowing and Teaching Elementary Mathematics: Teachers' Understanding of Fundamental Mathematics in China and the United States by Liping Ma. http://www.amazon.com/Knowing-Teaching-Elementary-Mathematic... That book is a very enjoyable--but rather…
on “How Do You Spark a Love of Math in Children?” ↗What do students do in other mathematical areas if they don't do proofs? The book I already mentioned, Knowing and Teaching Elementary Mathematics, will give much of the sad story. A really sad description of how mathematics textbooks are written in the United States[1] and a contrasting description of what kinds of problems are found in Russian…