I recently read a study published in the February 2014 Music Teachers National Association (MTNA) E-Journal on the practice habits of 2nd year piano majors at a university. These were all pianists who knew how to play the piano and could play it well. The researchers were interested in finding out exactly how did each student practice and how effective was that practice.
What was interesting was there was a direct relationship between how they practiced and whether or not they continued on in piano or dropped out of piano.
One student (student #1) identified mistakes and worked out one mistake at a time, listening closely to his playing. When he mastered it and could play it three times in a row well, he moved on to the next spot where he made a mistake. This is how he spent the majority of his practice session. At the end of the session he played through the whole piece and made a note of any remaining mistakes and that is what he would address in his next practice session. He mastered music quickly. Two years later he graduated in piano and was looking at continuing to study piano in graduate school.
On the opposite end of the spectrum was a young woman who said she enjoyed the piano and practicing. However, it was noted by the researchers that this student made faces (probably out of frustration) when practicing. She also spent more time practicing than student #1 and instead of focusing on small chunks of the music and fixing one mistake at a time, she practiced bigger chunks with multiple errors in it. The down side to this method was that she reinforced her errors as she was attempting to fix an error at the end of a passage. It took her longer to master the music. She ended up dropping out of piano lessons before graduation.
How you practice has an impact on your success and enjoyment at the piano. If you are not getting the results you want within a few tries, talk to your teacher about different practice techniques. This goes for all piano students, whether a beginner or more advanced student. When you are able to pinpoint a problem and choose an appropriate technique to solve it, the results are astounding. You deserve to have astounding results. Your child deserves to have astounding results.