In a mixing bowl, cream shortening and 3/4 cup sugar. Beat in extract. Combine flour, baking soda and salt; gradually add to creamed mixture. Stir in gumdrops. In a small mixing bowl, beat egg whites until soft peaks form. Gradually add remaining sugar, beating until stiff peaks form. Fold into dough.
Drop by heaping teaspoonfuls 2 inches apart onto ungreased baking sheets. Bake at 350 degrees for 12-15 minutes or until golden brown. Cool for 1 minute before removing from pans to wire racks to cool completely