Through recounting clinical interviews taken with teachers in America and China, Ma highlights the differences of mathematical understanding between the two teacher groups. Ma illuminates the various strategies that Chinese teachers use which in turn reflects their deeper knowledge of mathematics. Many of the teachers from China employed vocabulary and teaching strategies that promoted deep learning. They reported allowing students to solve a problem on their own and then discuss their strategies to the class, before the teacher introduces formal algorithms. When students utilized manipulatives, they were asked to discuss and argue for their solutions and strategies after the exploration was over. Finally, most of the teachers from China reported making links between deep mathematical concepts while teaching simple algorithms, to help students comprehend the larger mathematical framework that their current work was situated in.
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Chinese students typically outperform U. Paradoxically, Chinese teachers seem far less mathematically educated than U. Most Chinese teachers have had 11 to 12 years of schooling--they complete ninth grade and attend normal school for two or three years. In contrast, most U. In this book I suggest an explanation for the paradox, at least at the elementary school level. My data suggest that Chinese teachers begin their teaching careers with a better understanding of elementary mathematics than that of most U.
Their understanding of the mathematics they teach and--equally important--of the ways that elementary mathematics can be presented to students continues to grow throughout their professional lives. I document the differences between Chinese and U. I also document some of the factors that support the growth of Chinese teachers' mathematical knowledge and I suggest why at present it seems difficult, if not impossible, for elementary teachers in the United States to develop a deep understanding of the mathematics they teach.
I shall begin with some examples that motivated the study. In , I was a graduate student at Michigan State University.
Imagine that you are teaching division with fractions. To make this meaningful for kids, something that many teachers try to do is relate mathematics to other things. Sometimes they try to come up with real- world situations or story-problems to show the application of some particular piece of content. An unknown error has occurred. Please click the button below to reload the page. If the problem persists, please try again in a little while.
Knowing and Teaching Elementary Mathematics
I have been meaning to read this book for years. This summer I assigned it to a student, so I had to read it myself. It's very good. Liping Ma. Chinese students typically outperform U. Paradoxically, Chinese teachers receive far less education than U.
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