Category: maths education

Simple wikipedia

This gives simple explanations for things like Pythagoras’ Theorem.

In mathematics, the Pythagorean theorem or Pythagoras’ theorem is a statement about the sides of a right triangle.

One of the angles of a right triangle is always equal to 90 degrees. This angle is the right angle. The two sides next to the right angle are called the legs and the other side is called the hypotenuse. The hypotenuse is the side opposite to the right angle, and it is always the longest side.

The Pythagorean theorem says that the area of a square on the hypotenuse is equal to the sum of the areas of the squares on the legs. In the picture below, the area of the blue square added to the area of the red square makes the area of the purple square. It was named after the Greek mathematician Pythagoras:

If the lengths of the legs are a and b, and the length of the hypotenuse is c, then, a^2+b^2=c^2.

Carol Dwek

Has a website on Mindset:

In a fixed mindset, people believe their basic qualities, like their intelligence or talent, are simply fixed traits. They spend their time documenting their intelligence or talent instead of developing them. They also believe that talent alone creates success—without effort. They’re wrong.

In a growth mindset, people believe that their most basic abilities can be developed through dedication and hard work—brains and talent are just the starting point. This view creates a love of learning and a resilience that is essential for great accomplishment. Virtually all great people have had these qualities.

Teaching a growth mindset creates motivation and productivity in the worlds of business, education, and sports. It enhances relationships. When you read Mindset, you’ll see how.

This is the basic message that I want to get across to all my tutees. Maths can be tamed, and your understanding, and your grade, improved by the right effort.

Her section on Test your Mindset though is a bit disappointing, basically it is the same question asked 16 times. I tried it and came out with a fixed mindset, but I could just have easily responded in such a way as to be informed at the end of the “test” that I had an open mindset. The test is far too simplistic to be of any use.

Maths teaching in China

…mathematics in the Chinese curriculum is not seen as an elite subject. It is viewed as an essential of life, and one in which everyone can be highly competent if you work at it. ‘Maths gets you everywhere’ is a common phrase used in China and far from turning pupils off the subject, this focus and respect for it gives their pupils confidence and purpose.

Sean Harford HMI, National Director, Initial Teacher Education, Ofsted

Mathematics teaching in China: reflections from an Ofsted HMI

The greatest mathematicians of all time

I have just come across this list and find it pretty unsurprising although Newton at #1 ahead of Gauss and Euler seemed a bit much. Emmy Noether is at #27. Maxwell is not given a ranking but is on the list. A shame I think although I do take the point about JCM working in mathematical physics more than in pure maths.

The Thirty Greatest Mathematicians

Is mathematics beautiful and does it (mathematics) matter?

Understood or not, tapping the aesthetic component of mathematics is a crucial and neglected component of mathematical education. See Simon Fraser mathematical educator Nathalie Sinclair’s 2006 book Mathematics and Beauty: Aesthetic Approaches to Teaching Children. Given that basing mathematical education on utility and importance has not worked very well, perhaps introducing the aesthetic is past overdue.

Huff post article on Why Mathematics is beautiful and why it matters