Joanna
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Below are links to oil painting class demonstrations from the Art Students League a very old and apparently still a traditional art school. What you are being taught are two different approaches closely tied together that evolved from late 19thC representational art. Just about everybody in art books from about Manet to Franz Kline learned to paint this way. And that includes both de Koonings, Gorky, on up to Diebenkorn, and the SF, LA west coast schools through most of the 1950s.