Well people are wrong.
One of my many personal failings is in pea growing; it never goes well.
As a result, I had all but given up on sowing any more peas, until I discovered pea shoots. If you're not aware of their work, these early-harvested shoots are the ultimate 'posh veg' and are showing up in hoity-toity restaurants all over the land. They are also as cheap and easy to grow as anything out there which makes them ideal for a gardening - or in my case pre-school gardening - activity.
In terms of the seeds, I have been using up my existing packets from the garden centre, but there is a far cheaper way of doing things: just buy a packet of dried peas from the supermarket. As long as these aren't split, you should be able to soak them in water for about 24 hours and plant away with no problem - great if you're running a gardening club and need seeds enough for a whole load of children.
When I did this activity with the pre-schoolers they filled up pots with compost and then used their planting fingers (AKA their index fingers) to make half a dozen holes before dropping a seed into each. They then covered them over with more compost, gave them a water and took them home to place on a sunny windowsill.
If you are doing this with slightly older children though they should have the dexterity to grow seeds 'on show'. For this, stuff a jar with kitchen roll or paper napkins, give these a water until the paper is damp all over, and then carefully slot peas, at 2cm intervals, around the side. This way children can watch the germination of the seed take place rather than just seeing the shoot above ground.
The shoots appear within a week and are ready to harvest 2-3 weeks from sowing - which is useful because kids aren't renowned for their patience. You cut them when there are about 15cm above ground, snipping them off about 3cm above the soil level. Oh and don't throw the peas away yet because you'll find you'll get another crop - albeit slightly smaller - about 3 weeks later.
Of course, in the warmer weather you can do this activity outside in the garden, but in colder months these are the ideal windowsill crop - plus this means they are close to hand for all those hoity-toity recipes - or just to munch on there and then (possibly in a hoity-toity manner).