1. Preheat the oven to 350º. In a medium bowl, mix the flour and 1/4 cup of the confectioners' sugar. Add the butter and, using your hands, a pastry cutter, or two knives, mix well until the butter breaks down into small pealike shapes. Press the crust (it will appear dry and crumbly) into the bottom and 1/2 inch up the sides of an 8 x 8 x 2-inch baking pan or a rectangular tart pan with a removable bottom. Bake on the middle rack for 20 minutes.
2. Meanwhile, in a large bowl, beat the eggs with a whisk or electric mixer. Slowly add the granulated sugar, baking powder, salt, lemon peel, and lemon juice, and beat until light and fluffy, about 5 minutes.
3. Remove the crust from the oven. Pour the lemon mixture over the crust. Bake for another 15 minutes on the middle rack. Scatter the berries over the lemon mixture and bake another 10 to 20 minutes. If the tart begins to brown, cover very loosely with a sheet of aluminum foil. The tart is done when a toothpick inserted in the center comes out clean. Remove from oven and let cool. Sift remaining confectioners' sugar on top, if desired.
How kids can help: Measure ingredients; mix lemon filling; scatter berries on crust; sift confectioners' sugar over cooled tart.