DISCLAIMER: Learn your traditional fingerings first! There are plenty of sites out there which offer free downloads of traditional scale fingerings. Find them first and master them before tackling alternative fingerings.
Practicing scales with alternative fingerings provides better situational awareness for improvising pianists. Have you ever heard something in your head that you just couldn't quite get to come out in your playing? Most likely you were limited by your technique (or lack there of). By practicing scales with alternative fingerings you will be able to better handle any idea that comes to you while playing not just ideas you've worked out or predetermined in your practice.
I first came across this concept while reading about Lennie Tristano's teaching methods. However, the idea of alternative fingerings isn't unique to the jazz world. Chopin, Liszt, and Czerny all produced etudes with alternative scale fingerings for their students. After all, you don't often find yourself running up and down basic scales in Classical repertoire either. At least not in pieces not specified as technical etudes.
Please enjoy the free .pdf document listed below. I recommend practicing them at 40-80bpm with hands separate at first. You could apply the 1-2 (thumb-index) fingering to virtually any other scale as well. Be sure to practice slow and concentrate on good timing and tone. Enjoy!
If you're interested in a complete guide to Tristano's methods, check out this excellent book.
PDF Link
Lesson #1: Major Scales with Alternate Fingerings (1-2)
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