The 1928 Olympics saw the first women’s gymnastics competition held. The hosts pre-selected 14 gymnasts for the all-around team competition, which would feature 10 gymnasts. Nordheim placed 5th in the selection event and competed in the Games where the Dutch won with a comfortable margin. A year later, Nordheim came 6th in the individual all-around at the inaugural Dutch Gymnastics Championships.
Like several of her team mates in the 1928 Dutch team - Stella Agsteribbe, Ans Polak, Elka de Levie, alternate Judikje Simons and coach Gerrit Kleerekoper - Nordheim was Jewish. With the exception of De Levie, they did not survive World War II. Nordheim was killed at Sobibor on 2 July 1943, along with her husband, Abraham Kloot, and their 10-year-old daughter, Rebecca.