You should claim both federal and provincial tuition and edutional amount. They are two different tax credits, and most likely the amount you can claim is different (e.g., you claim federal amount 5000, and provicial amount 4000). It's not that you add the two numbers to 6000.
Federal: Fill in Schedule 11 to calculate the amount (tuition, educational amount and text book allowance) available. Then calculate the amount that can be transferred to you, any unused amount can be carried forward to next year. see Line 323 - Tuition, education, and textbook amounts for details.
Provincial: Fill in Schdule ON (S11) to calculate the amount (tuition, educational amount and text book allowance) available. Then calculate the amount that can be transferred to you, any unused amount can be carried forward to next year.