Aprender sin reflexionar es malgastar la energía.
A pesar de que ya soy mayor, sigo aprendiendo de mis discípulos.
El que ama la lectura tiene todo a su alcance.
William Godwin

Classic mistakes.

For many people Mathematics is a very difficult subject and they make an effort with it because people simply don't know how to study Mathematics. This is not because people are not capable of studying Maths, but because they've never really learned how to study Maths. That is why it is common for students to do lots of mistakes.

See if you can find the mistake that I have made in the work below. Tip: You cannot pide by zero so don't do it!

b = a

We'll start assuming this to be true.

ab = a2

Multiply both sides by a.

ab - b2 = a2 - b2

Subtract b2 from both sides.

b (a - b) = (a + b)(a - b)

Factor both sides.

b = a + b

Divide both sides by a - b.

b = 2b

Recall we started off assuming a = b.

1 = 2

Divide both sides by b.

So, we've managed to prove that 1 = 2! Now, we know that's not true so clearly we have made a mistake somewhere. Can you see where the mistake was made?

A mistake in Maths earns "Classic Mistake" status if it is regularly made by successive classes of students, in classrooms. I'm convinced that many of these are mistakes given there are caused by people getting lazy or getting in a hurry and not paying attention to what they're doing. By slowing down, paying attention to what you're doing and paying attention to proper notation you can avoid the vast majority of these mistakes!


If you visit http://www.calculatorsoftware.co.uk/classicmistake/about.htm, you will find a big list of classic mistakes. I hope you enjoy it.

Categorías:  Noticias