Instruction and Construction of Mathematics at Home: An Exploratory Study

Abstract

In this paper, we draw on data from a longitudinal study of mathematics engagement during adult-child joint activity at home. Drawing from across case and within case analysis of 44 videotaped activities, gathered in 6 middle class homes over 2 years, this paper provides evidence of either Instruction or Construction being predominate in each activity. Examination of one Instruction (i.e., Play-Doh pizza) and one Construction activity (i.e., family photos) suggests each activity shared common characteristics, but there were also distinct characteristics pertaining to concepts, control, and interactions. We discuss two considerations (i.e., blending across experiences and valuing big ideas) to stimulate further reflection and research.

Appendix A

Pizza Activity

The Adam mother and her preschooler are seated at adjacent sides of the child’s table. Once the mother assists her daughter in getting a “lump” of Play-Doh onto the table, the child begins to roll a wooden dowel onto it. When the Adam mother asks what the child plans to make, she answers pizza. At times, the mother helps flatten the dough to make it easier for the roller and converses with her daughter as the child concentrates on rolling out the pizza. Initially the mother asks what shape she is trying to make (“what’s the shape of a Pizza?”) and the daughter responds (“triangle”) in such a way that the mother qualifies it (“when it is sliced”) before turning their attention to cutting the pizza to share with friends who visit. As the episode unfolds, the child is encouraged to cut the circular Play-Doh pizza into equal-sized slices for various numbers of imagined visitors. The mother’s questions ensue about the number of pieces and on occasion about whether the sizes are fair (“same size for each visitor”) while the child makes the cuts and counts the slices (Fig. A.1).

Fig. A.1 Excerpt from Adam mother-daughter Play-Doh activity transcript

NOTE: As the mother repeatedly asked math (number) related questions, explicitly directed the child’s actions for cutting equal pieces, redirected the child’s attention to the problems being posed, and maintained a focus on a mathematical goal, the tenor of the session was deemed Instruction.

Photos Activity

The Pimm grandmother and her preschool granddaughter sit side by side on the edge of the child’s bed, with large sheets of paper on the floor or bed near them. Multiple photos of various family members, captured in groups or alone, with or without other props, have been printed on these sheets. The grandmother holds one sheet at a time, at a slight angle while resting the bottom edge on her lap, so as to be readily visible to her and the child. The child is able to point to, and readily touch, most of the photos. The Pimm mother is behind the camera and videotaping the conversation between the grandmother and her preschooler. She comments on one occasion only, although the child is seen looking in the direction of the camera (her mother) on a few occasions typically when the grandmother speaks of the mother’s (Eema) presence in the photos. The grandmother shares varied information about selected photos and those captured, asks the child questions, answers the child’s questions, and at times expands on the child’s statements (Fig. A.2). In the latter third of the session, the older sibling joins her grandmother and sister, and all three continue to view and talk about the family photos together.

Fig. A.2 Excerpt from Pimm grandmother-daughter Photos activity transcript

NOTE: As the grandmother repeatedly identifies the persons in the pictures, providing details about relationships to each other and the child, sharing short stories of related events, interweaving math-related terms on occasion when quantity, age or size were invoked to describe the photo, the tenor of the session was deemed Construction