Puzzles for young children come in many types:
1. Single piece to single hole. Sometimes the hole has a matching picture in it. This can aid the learning of the concept "Same", and the correct orientation of the picture. When there is no matching picture underneath, then the child will use their knowledge of matching the shape and problem solving by turning the piece to find the fit.
2. Multiple pieces making up a simple picture, ranging for 3 pieces to many. Young children will use their knowledge of matching and shape to help them complete the puzzle. It is later on that they use the idea of joining the pieces of the picture. Some puzzles have an outline underneath. this means that the child just needs to use their knowledge of matching to complete the puzzle. When there is no outline underneath then a child needs to use more skills.
3. Traditionally cut picture puzzles require the child to be more advanced and able to match the picture rather than the shape.
An experienced person can learn many things about a child's abilities when observing them do a puzzle. Completing a puzzle requires an integration of cognition, problem solving skills, and fine motor planning. It is this integration which can create difficulties for some children, as well as the motor planning itself. A child needs to think about the shape and find the same. However, once the child can complete single piece puzzles and moves on to picture puzzles of several pieces, then the child needs to match the shape of part of the piece only at first. This can confuse the child because a piece has a few edges and this multiplies the possibilities. Then the child has to hold in his/her mind what part of the piece has already been tried - so they need a accurate working memory, as well as an ability to compare the memories. Some children randomly move the piece around and by trial and error, find the right place. With puzzles of increasing numbers of pieces, this method only works for a limited amount of time and puzzles with a limited number of pieces.
So, it is useful for the child's learning, that the supporting adult does not focus on getting the puzzle completed quickly, but rather, slows down, and focuses on the skills involved. When needed, give specific instructions such as which part to look at, pointing out the match between part of a piece and part of the hole, to turn the piece all the way round or just a little round, to try another place, to look at the shape of the part of the piece. Most importantly, give time for the child to process your instructions and give them time to experiment, putting into words what they are doing and commenting on the shape of the piece.
There is much learning taking place with puzzles. It is worthwhile taking the time to observe the skills the child is using and learning to support the detail of the learning, because it can be transferred to other learning situations.