I personally found the Schaum series slightly easier to follow than the Aaron and Thompson books. What attracted me the most were the catchy arrangements of popular classical tunes. Since most of the teaching pieces fit in just two-thirds of a page, it gave me the impression that I was progressing rather quickly. In one minute, I could play three to four pieces!
On the other hand, the Schaum series divides each grade prior to Grade 3 into two parts. Thus, one goes through Grade 1, 1 1/2, 2 1/2, half-steps as it were, with specific colors for each grade (the "Red Book", "Blue Book", etc.). While this gradual approach in piano pedagogy has its merits, I feel that there were a lot of extraneous pieces that were neither appealing, offered new difficulty, nor worth taking the trouble. Why there are no half steps for the higher grades (3-6) is a little strange to me--all the more reason to progress slowly in the upper grades in my opinion.
Another thing I have observed about the series is that it very much emphasizes the skill of sight reading. In the beginning of each book, there are tips, drills, and reminders about the importance of sight reading. I suppose Mr. Schaum himself may have been an excellent sight reader and may have wanted to impart his secrets to the young pianist. However, I do feel that undue emphasis is given to this skill more than technique and artistic development.
Edit: I've decided to expand the list to "Top 40" and replaced some of the pieces based on familiarity to today's listeners. I've also included the composer from whom these pieces were adapted. As you may notice, I'm partial to popular classical music from opera, symphony, and solo works.
I have picked my Top 40 pieces from the Schaum Series (books A to H). Most of them I studied in childhood but the more advanced ones (F to G), I have discovered on my own. I mostly picked two-page pieces but there are a couple of one page piece too:
A - Red Book - 11. Brahm's Lullaby (Brahms)
2. Swinging Along (Behr)
3. Snake Dance
4. Bells are Ringing (Beethoven)
B - Blue Book - 1.55. The Elevator
6. The Harpsichord Player (Bach)
7. Magic Flute (Mozart)
8. The Spider Dance
C - Purple Book - 29. Come On, Rangers (Rossini)
10. Wishing Well (Mozart)
11. AM and PM (Grieg-Chopin)
12. It Was in the Good Old Summertime (Spindler)
13. From Pole to Pole (Chopin-Paderewski)
14. Estrellita (Ponce)
15. Lilac Time Serenade (Schubert)
16. Gertrude and Elizabeth (Beethoven)
17. Hawaiian Love Song (Truax)
18. Dangerous Journey (Koelling)
D - Orange Book - 2.519. A Harvest Melody (Beethoven)
20. El Caballero (Moszkowski)
21. The Masked Horseman (Schumann)
22. In the Hall of the Mountain King (Grieg)
23. Pals of the Saddle (von Suppe)
24. Garden of the Stars (Saint-Saens)
25. The Waltz King (Strauss)
26. Two Military Heroes (Strauss-Berlioz)
27. The Swan (Saint-Saens)
28. In an Eighteenth Century Flower Garden (Mozart)
29. The Cuckoo (Daquin)
E - Violet Book - 330. Camp of the Gypsies (Behr)
31. The Bullfighter's March (Bizet)
32. The Crystal Ballroom (Chopin)
33. Purple Sunset (Liszt)
34. Magic Carpet of Dreams (Debussy)
35. 1812 Overture (Tchaikovsky)
F - Brown Book - 436. With Love in My Heart (Chopin)
37. The Great Gates of Kiev (Moussorgsky)
38. Clog Dance (Dvorak)
G - Amber Book - 539. Norwegian Concerto (Grieg)
H - Grey Book - 6
40. Russian Concerto (Rachmaninoff)
Of these books, my favorite would have to be C, D, and E in that order. These three books could be fully taught to the student. I very much enjoyed studying, practicing, and playing them for family and friends. Some of them sound difficult and sophisticated though they are quite manageable arrangements. In a minute or two, one gets instant applause!
For me, the weakest of the bunch would have to be Book F. Beginning at this level, Schaum seemed to have dispensed with the Baroque and Classical Periods and concentrated on the Romantic repertoire. I feel that this is premature as most students would still be in their teens by this time. They may overcome the technical difficulties but very few would have the level of musical maturity required in these works.
I feel that the student could skip this book without serious impairment. Perhaps the teacher could substitute it with Thompson or Aaron Grade 3 and 4 which have much better piece selection appropriate for the adolescent students in my opinion.
Books G and H are not bad. My problem with them is that many of the pieces in these books are almost exactly the same as the original but often shortened or the ending simplified. The level of difficulty of the original pieces and the Schaum-edited pieces are almost the same in these grades, so why not just study the original?
I wish that Schaum had focused more concert transcriptions of popular ensembles, operas, concertos, and symphonies at these levels, just as he did with the Norwegian Concerto (based on Grieg's Piano Concerto in A minor) and the Russian Concerto (based on Rachmaninoff's Second Piano Concerto). These are wonderful concerto transcriptions for the advancing pianists who are not quite ready for the real version but good enough to sound majestic and virtuosic among the general audience. They make excellent party pieces for the non-classical crowd too.
Suggestions to the teacher: After the student learns any primer piano book, you may follow the list above in assigning pieces. The assigned piece must be played very well before advancing to the next piece. It does not only mean zero wrong notes but more importantly, artistic playing--beautiful tone, engaging tempo, "color", etc. Each piece must be learned and played as if it were the recital piece.
I recommend supplementing the lessons with A Dozen A Day by Edna-Mae Burnam. I've never studied these books but many teachers and performers swear by them and use them in tandem with method books. When taught properly, the series should address basic technical needs and enhance sight reading.
Suggestions to intermediate and advanced students: If you are using Aaron, Thompson, or any other method book and have reached Grade 3 or higher, the Schaum series is still very useful for sight reading. As I have mentioned above, it seems that the Schaum was designed for sight reading more than performance. Try the exercises, drills, and tips mentioned in the books. Gradually read through the pieces in Books A to F. Many of the pieces in Book G and H are too hard to sight read but if you can do it, then so much the better.