Overview:  The teacher tells students that they are going to be working on a problem where they will need to think like an artist, and she brings up the idea of trying to draw pictures that are 3-dimensional.  The teacher invites Harriet to the board to draw a box, and Harriet draws a very basic cube by overlapping two squares and connecting the vertices.  Then the teacher asks if anyone in the class draws landscapes where the view extends very far.  None of the students respond, so the teacher shares a memory of her sister who used to draw a boat sailing in the water.  The teacher asks what it means to draw things in perspective, and students share their thoughts.  Before students begin working on the problem, the teacher tells them that perspective includes important elements – a vanishing point, a horizon, and some diagonal lines.

Prior knowledge:  The teacher attempts to establish a connection with students’ prior knowledge of the mathematical practice of drawing in 3 dimensions.  The teacher knows that there are some students in the class who are interested in art, so the teacher may expect that some students will know something about drawing in perspective.  When Harriet comes to the board, she illustrates a practice for making a 3-dimensional cube that does not identify a vanishing point or perspective lines.  The teacher shares the memory of her friend drawing landscapes, perhaps to make the idea of a horizon more salient.  With the examples of the cube and the sailboat on water, the teacher tries to connect with different practices students have used for drawing 3-dimensional objects, which they can build upon for their work on the perspective drawing problem.

Other points of interest:  When some students in the class tell the teacher that they have done perspective drawing, the teacher tells those students not to give too much away while working on the problem.  With this comment the teacher seems to be trying to limit the collective memory (González, 2009) of the class.  Even though some students have prior knowledge of the practice of drawing in 1-point perspective, the teacher may not want to “give away” the solution to the problem by telling everyone how to do 1-point perspective drawing.  The teacher seems to want students to limit their prior knowledge in some ways so that they can discover the mathematical aspects of 1-point perspective drawing through their work on the problem.