DeHe we have been using typing club. It's very basic but my kids have actually chosen that. There is some degree of timing involved in that the more advanced you get the more there are time goals involved in progressing to further levels. However this is very discreet early on. My DD could not handle the timed aspect of timez attack but is not phased by this at all. Well, she did get antsy when she reached the point of levels being for speeds like 30+ WPM rather than for new keys, but that was WELL into the process. My younger 6yr old (grade 1) girl is nowhere near any overt time issues like that.
