In a medium-size bowl, sprinkle the yeast over the water and add a teaspoon of whole wheat flour. Cover and set in a warm spot for 5 to 10 minutes to proof.
Stir in 1 cup of the wheat flour to form a batter. Cover and set it aside for 30 minutes, or until a sponge develops.
Stir the salt and oil into the sponge. Add the flour, ½ cup at a time, stirring well after each addition, until the dough pulls away from the sides of the bowl and balls up in the center.
Turn the dough out onto a lightly floured surface and cover it for a few minutes. Thoroughly knead the dough, adding flour only as necessary to keep it from sticking.
When the dough is smooth and elastic, form it into a ball and place it in a lightly oiled bowl. Cover with a clean tea towel (see note) and set it in a draft-free spot for 1 to 2 hours, or until the dough has risen and does not rebound when pressed with a finger.
Turn the dough out onto the lightly floured surface again and knead it briefly. Put the dough back in the bowl, cover, and set it aside to rise for another 1 to 2 hours, until it does not spring back when pressed.
Divide the dough into 6 equal balls. Arrange on the floured surface; cover with the tea towel for 30 minutes.
On the lightly floured surface, use a rolling pin to roll each ball into an 8-inch circle slightly less than ¼ inch thick. Arrange these on baking sheets lightly dusted with cornmeal and cover them for 30 minutes.
Move a rack to the lowest position (leaving lots of space above it) in the oven and preheat to 500º F.
Before baking, make sure that the dough circles are not sticking to the baking sheet. If they are, gently lift them away and sprinkle more cornmeal under them.
Bake the pita breads for 5 minutes. They should puff up like balloons and be lightly browned. Do do not open the oven door before the 5 minutes is up, and make sure the oven has reheated to 500º F. before putting in another batch, in case you couldn’t fit all onto your baking sheet at once.
If a bread doesn’t puff, it will still taste good but won’t have a pocket to fill
Wrap breads with a dry tea towel as soon as you remove them fro the oven. Serve them warm. Thoroughly cool breads before storing them.
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