According to Apple’s documentation when I setup an input element with a type of number I should get a number keypad.
<input type="number"/>
number:
A text field for specifying a number. Brings up a number pad keyboard in iOS 3.1 and later.
Looks damn near impossible to mess up. However, when I view this simple fiddle on my iPhone or the simulator (both iOS6) the number keypad does not appear, and I get the standard alphabetic keyboard instead.
What on earth could I possibly have messed up here?

You need to specify the pattern:
As a
numbercan be negative or with floating point, so the - and . and , should be available in the keyboard, unless you specify a digits only pattern.