Tag Archives: fractions

Math knowledge for teaching fractions and decimals

No one can teach mathematics without knowing mathematics but not everyone who knows mathematics can teach it well. Below are two tasks about teaching fractions and decimals that would give us a sense of the kind of mathematical knowledge we teachers need to knowapart from knowledge of the content of mathematics. As teachers it is… Read More »

What are fractions and what does it mean to understand them?

Negative numbers, the irrationals, and imaginary numbers are not that easy to make sense of for many students. But this is something understandable. One only needs to check-out the histories of these numbers. The mathematicians themselves took a long time to accept and make sense of them. But fractions? How can something so natural, useful,… Read More »

Technically, Fractions are Not Numbers

It is misleading to put fractions alongside the sets of numbers – counting, whole, integers, rational, irrational and real. The diagram below which are in many Mathematics I (Year 7) textbooks is inviting misconceptions. Fraction is a form for writing numbers just like the decimals, percents, and other notations that use exponents and radicals, etc.… Read More »

Math War over Multiplication

The post It Ain’t No Repeated Addition by Devlin launched a math war over the definition of multiplication. Here’s an excerpt from that post: “Multiplication simply is not repeated addition, and telling young pupils it is inevitably leads to problems when they subsequently learn that it is not. Multiplication of natural numbers certainly gives the same… Read More »