I have taught hand embroidery in English primary schools but am not sure what age group you are referring to. The youngest I taught were four to 5 years, which was a real learning curve having spent most of my teaching life teaching post 16 up to over 80!
I suspect children are the same the world over. Firstly the boys in my classes were always more interested than the girls because it was different. They all enjoy bold bright designs and colours. I always gave them large eyed needles, the bigger the better and for the very young would just put one knot immediately under the eye until they got to grips with keeping the thread in the eye!
Where I was given the option to select a subject, my selection was always 'stitch your own picture', so they could select or create a picture that they wanted to sew, this way they are interested in the subject. I also found it useful to work with other media, so that as complete beginners they were able to use sewing as a highlight to their work rather than all of it, embroidery of any sort can become boring when you are doing the same stitch in the same colour for many lessons, and you're only 6 years old. So I might use paints, dye sticks, or overlays of fine organza type fabrics to cover large areas. Of course each class is different but I hope this helps.
Cross stitch is easy to teach with any age, using Binca or 11 count Aida are the options I would suggest. I used Perle, Soft Cotton, wools and thrums with the children to give texture as well as colour. Blackwork should be easy too as children love repeating things, so filling stitches are easy and they could design it themselves on graph paper before they begin, which will make it that much more personal. You can begin them on the colour of threads traditionally used in Blackwork and let them experiment, children have a wonderful way of putting together things that shouldn't work but do!