Overview:  In this summary, the teacher tries to connect the practice of paper folding and tracing with the mathematical concept of perpendicular bisector.  A student, Sophie, shares her work from part I, and it is projected at the front of the room.  Sophie had used paper folding to construct the right half of the leaf from the left half.  After Sophie shares her strategy for solving part I of the problem, the teacher makes the point that the “fold line” Sophie had used to fold and trace the leaf is actually the line of reflection.  By picking one specific point and its image, the teacher also points out that the line of reflection is the perpendicular bisector of the segment connecting a point to its reflection.  The end of the summary indicates that the class will next apply the concept of perpendicular bisector to reflect the images in parts II and III.

Prior knowledge:  The teacher begins to build a bridge between students’ prior knowledge of the mathematical practice of paper folding and the school mathematics concept of perpendicular bisector.  The students seem to have knowledge that what they are calling the “fold line” is the same thing as the “line of symmetry” or “line of reflection”.  The teacher pushes students to use formal mathematical vocabulary to describe the relationships between the points and line segments.

Other points of interest:  The teacher makes the choice in this summary to use a student’s work as a starting point to make a connection with a new idea.  After Sophie presents her solution, the interaction in the classroom transitions to more teacher exposition with IRE/IRF (Mehan, 1979; Wells, 1993) interactions.  The teacher calls on students until they offer the terms “perpendicular” and “bisector” to describe the relationship between the line segments.  To help students remember the word “bisect” the teacher recalls an event from earlier in the school year.