Anaerobic respiration reactions are of fundamental importance to global biogeochemical cycling of elements. Yet, the idea that cellular respiration can occur not only in the absence of oxygen but also involve the oxidation of inorganic substrates (e.g., AsO[subscript 3 superscript 3-], Fe[superscript 2+], H[subscript 2], H[subscript 2]S,…

Physics experts and students commonly use a variety of representations when working with partial derivatives, including symbols, graphs, and words. One especially powerful representation is the contour graph. In open-ended problem-solving interviews with nine upper-division physics students, we asked students to determine derivatives from contour…