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Directed orientationOn the second day of the geometry lesson, the class reviewed the attributes that we had discovered by sorting the blocks into categories the day before (see ftg. 1). After the review, students engaged in a series of activities that are consistent with the second Van Hiele phase of learning, the directed-orientation phase. Directed orientation is characterized by structured activities that challenge students to formally recognize and verbalize their understanding of the new geometric concepts that were introduced in the information phase ( Van Hiele-Geldof 1984). Through teacher- directed activities, students should gain an understanding of the attributes and the connections among them. For the first learning activity, students were required to categorize the attribute blocks into sets of two with one attribute difference (see ftg. 2).The objective of the first activity was to deepen students’ understanding of the basic shapes by encouraging students to make meaningful connections among the various attributes. To begin, we held up two triangles: a big, thick, blue triangle and a small, thick, blue triangle. Students were to examine these shapes and describe their similarities. Raising a hand to answer, students were able to describe that both shapes were blue, thick, had three sides and three corners, and were triangles. However, one student in particular shouted out, “One shape is big, and one shape is small.” This led the class to discuss the distinction between similarities and differences among the attributes of the blocks. The class agreed that the last statement referred to the difference between the two triangles. These triangles contained one difference: one was big, and the other was small. This discovery led us into the next activity for this phase.Every student was instructed to find two blocks that contained only one difference. After finding the shapes, students held their blocks up. They were instructed to describe the difference between the pair of blocks that they chose. As students shared their descriptions, other students listened to ensure that their findings were correct. Some findings included the following:• “I have two squares, but they are different colors.”• “I have two circles, but one is skinny, and one is fat.”• “I have a small square and a small circle.”
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