One of the ways to connect concepts in mathematics is to make use of the same representation to teach mathematics. Let me take for an example the visual representation of the square of a sum, . This concept is usually ‘concretized’ using algebra tiles. However, if you have facility for computer technology I would recommend using the…

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As a result of her research, Liping Ma developed the notion of profound understanding of fundamental mathematics (PUFM) as the kind of mathematical knowledge teachers should possess. She discusses this kind of knowledge in her book Knowing and Teaching Elementary Mathematics: Teachers’ Understanding of Fundamental Mathematics in China and the United States (Studies in Mathematical Thinking…

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One popular way of introducing the negative numbers is through the number line. Most textbooks start with the whole number on the number line and then show to the students that the number is decreasing by 1. From there, the negative numbers are introduced. This seems to be something easy for students to understand but…

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