The following summary of Thinking About Alternative Procedures and Algorithms for Computation is from Supporting School Mathematics: How to Work with Parents and the Public by Ruth Parker and Joan Akers Mitchell (Heinemann Press, 2006):
When children are given frequent opportunities to reason with numbers while solving problems, it is often surprising what they are able to do. Many teachers and parents comment that they are amazed to see the sophisticated thinking children use and how they are able to solve problems with relative ease.
When children are taught standard paper and pencil algorithms that they do not understand, they often come to believe that math is about memorizing recipes that don’t make sense. Many end up feeling that they are not any good at math. On the other hand, children who have been taught to reason with numbers know that mathematics is not about memorizing recipes. It is about understanding relationships. They know they can make sense of mathematics, and they are confident in explaining how they know their answers make sense.
What can parents do to help? They can play with numbers with their children whenever possible—when riding in the car or even at the dinner table; explore new ways of doing addition, subtraction, multiplication and division problems mentally; explain to their child how they know their approach to a problem makes sense, and listen to their child explain his or her thinking. They can make this a fun time as a family, and model being a willing problem solver. This sends the important message that mathematics is both engaging and useful.” From Article Summary.
Excerpt from Building Support for School Mathematics: Handbook for Working with Parents and the Public by Ruth Parker and Joan Akers Mitchell (Heinemann Press, 2006).