With "approach to" you normally use the ing form. You can only use the infinitive when "to" means "in order to" . Ex.: A different approach is needed to solve the problem "To" =in order to solve (verb) A new approach to learning =a new way/method used for learning. A new approach to something (noun, or gerund which works as a noun)

Hi Angela, this is a gerund. Your action is continuous (so you are learning). Your gerund can also be used to replace some of the nouns after the preposition "to". For example: I'm accustomed to filter coffee Gerund example: I'm accustomed to drinking filter coffee. I'm not used to heavy clothes. Gerund example: I'm not used to wearing heavy clothes. I look forward to your letter. Gerund example: I look forward to receiving a letter from you. I'm opposed to excessive spending on cosmetics. Gerund example: I'm opposed to spending excessively on cosmetics.