Although automaticity (from repetition and practice) with math facts is great, counting on fingers at the very least is a strategy that indicates that a student knows what they are doing.
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Stopping students from using their fingers when they count could, according to the new brain research, be akin to halting their mathematical development. Fingers are probably one of our most useful visual aids, and the finger area of our brain is used well into adulthood. The need for and importance of finger perception could even be the reason that pianists, and other musicians, often display higher mathematical understanding than people who don’t learn a musical instrument.