You want these letters to show that the writers know of your current plans and goals. These programs are generally easier to get into than most Ph.D. programs. They often attract those who want postgraduate training, but who are not ready to try for a Ph.D. program or undecided on a specific area. Many students use good performance in a Masters level program to get into a better Ph.D. program than would have been possible on the basis of their undergraduate work. After all, the best predictor of performance in a graduate program is performance in a graduate program.
Careful selection is important.
Most M.A. programs emphasize the terminal M.A., which means they are primarily job oriented. There are also predoctoral M.A. programs that match the first year or two of standard doctoral programs. Probably fewer courses would transfer from a terminal program. Many psychology majors are interested in children with learning and social problems. Masters programs in education and social work would be worth investigating.