This image depicts a Mathematics class being taught by the head of the Math Department, David Eugene Smith. Dr. Smith originally joined the Normal faculty during the 1890-91 school year and would remain in his position until 1898, when he moved back to his home state of New York to be the principal of the Normal School in Brockport. During his seven years at the MSNS, Smith co-authored and published four textbooks relating to mathematics. Today, Smith is considered to be one of the founders of the field of mathematics education, and he was able to make students see the true beauty and depth of mathematics.
The student in the second to the last row, first seat left of the aisle, appears to be Fred W. Green, future Governor of Michigan. Green took a class in arithmetic, probably Teacher's Review of Arithmetic, in Fall 1892, so that is likely the class pictured here.