Question

why does the connecting rod of an electric heater not glow while the heating element does

Answer 1

because heating element and connecting are made from different elements.Heating element is generally made from Nichrome and connecting rod is from copper.
Nichrome has higher electrical resistivity than copper.so the heating element of heater glows but connecting rod does not.

Answer 2

The the heating element of a heater is made up of an alloy and has high resistance. Thus when current is passed through it, it becomes to hot and glows.
But the resistance of a chord which is usually made of copper, aluminium, etc. is not so high to glow.