I'm in the process being the "technical advisor" for my granddaughter's 1st grade class. They'll draw directly on the muslin squares with fabric markers.
I experimented, using masking tape to tape the cut square with border marked on to a piece of cardboard, worked great & granddaughter had control of her drawing because fabric not moving around.
I did the same thing a few years ago for another class, they loved it & came out so cute.

It would require using a poly blend but there are fabric crayons that the kids could use to draw on paper and then you iron it to transfer it to fabric - I have a set of these crayons and it is really easy. I have all kinds of project ideas for my kids. If they wrote words, it would transfer backwards, of course. The finished project is washable in cold water but cannot be put in the dryer. The crayons are available at Hobby Lobby and possibly your LQS (that's where I found mine).

I did this for my daughter's teacher. I taped fabric to cardboard square and used fabric crayons and had the kids draw and sign their names right on the fabric. You then iron the sqares to set the crayon. It worked really well and I knew it was appreciated because it brought tears to the teacher's eyes.

and it was a beauty,,, i can see what made Gramma smile...

Using a 3-in-1 inkjet printer you can copy their pictures directly onto white muslin that has been ironed onto freezer paper. Be sure the leading edge is well attached before running it through the printer or it will jam. I do my quilt labels this way. Much cheaper than printer fabric.

You can get permanent fabric markers and have the kids draw directly onto fabric. We did that at my sons' school and they turned out so cute! Put a sashing between the blocks, a couple of borders and you're there. You can follow a theme if you want too. Bears or frogs or something.

My GD class did one. They used Fabric Crayons and it came out so cute

Trace the drawings, using a light box, on the fabric you want to use. If you want to color it, use Crayola crayons and heat set the colors by turning the fabric picture face down on a paper towel or piece of white copy paper and dry ironing. Quick, pretty, easy and fun. froggyintexas

Yes, you can scan the picture into the computer and then print them on special fabric that goes through the computer. I've done that already. Also, MANY, MANY years ago, when my children were in the first and third grades, I made a quilt for the first grader's teacher, who was getting married. What I did was cut squares on white fabric - I think 8x10 or something like that, took them to school in envelopes with fabric markers and a note to their parents to have each child draw and color a picture for their teacher's wedding and sign the block. I collected them and just added sashing and a binding and tied the quilt. That teacher still has the quilt, which she has hanging up in one of her "studios".

We used to recreate children's drawings with fabric. Each grade in the primary school was given a topic that fit in with the overall theme of the quilt. We then raffled it off. You'd be amazed at how much fun that can be, as well as frustrating. My son's teacher once gave them sponges to sponge paint snow flakes, I think it was. I ended up cutting pieces of netting the size of sponges to recreate the drawing. You also gotta enjoy applique if you go this route! (and be will to simplify if needed in the name of sanity!)