Various levels of representation: Parents assisting children with mathematics homework.

摘要

Parents play an important role in the educational development of their children. Little research, however, has been reported on how parents can best help their children with mathematics homework. Parents want to help their children with mathematics homework but often do not know how.;Through ethnographic techniques of participant observation, interviewing, and document collection, a family of five was investigated for twenty-one months as they engaged in mathematics homework. The aim of the research was to learn about mathematics homework from the participants' perspectives. The objectives of the research were to produce a detailed description of: (1) How each parent in the family assisted the children with mathematics homework; (2) Each child's level or levels of representation and each parent's level or levels of representation--enactive, ikonic, or symbolic--as described by Jerome S. Bruner; (3) The relationship between the children's level of representation and the level at which the parents were helping the children with homework; (4) The connection between levels of representation and problem solving strategies; (5) Information and instructions for the parents and children about operating at appropriate levels of representation and utilizing various levels of representation and problem solving strategies; and (6) The extent to which each family member operated at appropriate levels of representation utilizing various problem solving strategies and the effect on mathematics homework.;The study was conducted in three parts. Part 1 identified that the family members had a difficult time completing mathematics homework because they operated at various levels of representation and utilized few problem solving strategies. In Part 2 the researcher tutored the family in ways to improve the homework situation. In Part 3 the children operated at appropriate levels of representation and utilized various problem solving strategies, and the parents did not impose abstract ways onto the children. Ultimately, the children developed understanding about mathematics concepts, completed their homework independently, became more confident and motivated about mathematics, and experienced an improvement in mathematics grades.