Tag Archives: making connections

What kind of mathematical knowledge should teachers have?

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… Read More »

Teaching negative numbers via the numberline with a twist

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… Read More »

To understand mathematics is to make connection

I’m sharing in this post some of the “theories” underpinning the lessons, learning tasks, and math teaching ideas that I blog here.  This is part of the literature review of my dissertation titled “A Framework of Growth Points in Students Developing Understanding of Function”. If you are a researcher and wants to see the references,… Read More »

Introducing negative numbers

One of the ways to help students to make connections among concepts is to give them problem solving tasks that have many correct solutions or answers. Another way is to make sure that the solutions to the problems involve many previously learned concepts. This is what makes a piece of knowledge powerful. Most important of… Read More »

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