Process, Not Product
These art activities are designed to teach a toddler how to handle tools, learn about color and texture and have fun. There is no wrong or right way. It is simply their way. You need to praise the effort, not the results. Finger painting is a perfect example of process instead of product art. While you have the paint out, let them drive little cars across their paper. They can also drag a small branch through the paint or a zillion other objects. Here are a few more ideas:
Bubble painting: pour bubble mix in a small bowl and add a little powdered tempera paint. With a straw, let them blow colored bubbles on paper.
Mosaics: whether they are with solid paper colors or magazine pages are great for toddlers.
Feet painting: they can use finger paint and paint with their feet. Make sure they don’t slip.
Feet painting 2: they can use the feet of their toy animal and people to paint with.
Ribbon or string painting: they can drag it through their paint then their project.