With a sharp knife cut peel and pith from oranges. Working over a bowl, cut sections free from membranes and squeeze enough juice from membranes to measure 1/4 cup. In a bowl whisk together orange juice, curry powder, salt, cumin, sugar, and vinegar. Add oil in a stream, whisking until emulsified. Peel jicama and halve lengthwise. Thinly slice jicama crosswise and add to vinaigrette, tossing to combine. Halve, pit, and peel avocados and thinly slice crosswise.
Lift jicama from vinaigrette and arrange on 4 plates with orange sections and avocado. Pour remaining vinaigrette over and around salads.
Recipe courtesy of Gourmet Magazine