Tag Archives: making connections

How to orchestrate a mathematically productive class discussion

Show and tell activity (aka lecture method) may work for some but never in a mathematics class. Getting students to explain and ask questions are nice but only when the explanation and the questions are mathematical. Reasoning and justifying are good habits of mind but they are only productive if they are based on mathematical… Read More »

NCTM Process Standards vs CCSS Mathematical Practices

The NCTM process standards, Adding it Up mathematical proficiency strands, and Common Core State Standards for mathematical practices are all saying the same thing but why do I get the feeling that the Mathematical Practices Standards is out to get the math teachers. The NCTM’s process standards of problem solving, reasoning and proof, communication, representation, and connections describe for me… Read More »

What is an inverse function?

In mathematics, the inverse function is a function that undoes another function. For example,  given the function f(x) = 2x. If you input a into the function f, the output is 2a. The inverse function of  f(x) is the function g(x) such that if you input 2a into g(x) its output is a. Now what is g(x) equal to? How does its… Read More »

Making connections: Square of a sum

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… Read More »

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