Connaway, a marine painter, first studied under William Forsyth at the John Herron School of Art in Indianapolis. He then traveled to California and Maine. He entered the antique class at the Academy school in 1912, but was suspended for not submitting a drawing, that is, defaulted rather than take the "examination," a common occurance among Academy students in the earlier years of the twentieth century. The next year he studied with George Bridgman and at the New York Art Students League, and with William Merritt Chase.
During World War I Connaway served with a medical unit and made a series of medical drawings illustrating wounds. In 1920 he went to Paris and studied at the Acad‚mie Julian under Jean Paul Laurens, and at the Ecole des Beaux-Arts. Returning to America in 1921, he settled in Head Island of Jonesport on the Maine coast where he studied rock formations; he served in the U.S. Coast Guard and painted.
It was 1923 when Connaway established himself in New York, taking up residence in the Tenth Street Studio Building and showing at the Macbeth Gallery; later his work would be regularly seen at the Milch Gallery. Five years later, with his new wife, he went to France for two years of painting in Paris, and, again drawn to a rugged coastline, in Brittany. Upon their return in 1931, they settled on Monhegan Island, Maine, where Connaway started a school. In 1948 he moved to Dorset, Vermont, where he continued to paint and teach.
The Academy awarded Connaway a Hallgarten prize in the annual exhibition of 1926.
