Should computer coding be taught at more schools?

Google's chief executive, Eric Schmidt, claims that the ICT curriculum does not give pupils insight into how software is made.
A survey for a UK newspaper showed that only 33% of boys and just 17% of girls had learned any computer coding skills at school. Rather than focusing on aspects of ICT such as Word, Excel and PowerPoint he argues that computer programming and understanding computer coding should be part of the primary school maths curriculum.
Learning to code should be seen in the same way as learning the skill of handwriting so children can then use it as a tool for solving problems in a wider context.
Do you think this is really a skill that everyone needs to know, or should we leave this to the ICT experts?