Plank was born in Wilmington, Delaware.[5] As a child, she grew up in a schist quarry and was the youngest member of the Delaware Mineralogical Society in third grade.[5][6] She graduated from Tatnall High School in 1981 and then graduated summa cum laude in Earth Sciences from Dartmouth College in 1985 with her thesis Magmatic Garnets from the Cardigan Pluton, NH under the supervision of John B. Lyons. She received her Ph.D. in Geosciences with distinction in 1993 from Columbia University, Lamont-Doherty Earth Observatory with her thesis Mantle Melting and Crustal Recycling at Subduction Zones under the advising of Charles H. Langmuir.