Mathematical ability

Current studies are rapidly investigating strategy choice on tasks such as math and reading that children encounter in day to day life; it follows that strategy development should also be examined in the naturalistic settings where children actually perform these tasks. From a sociocultural learning perspective, we examined five year old children's arithmetic strategy use, in a game context, with the most likely of mentors for a young child, his or her parents. Children played three games of a modified version of "Chutes and Ladders" with one of their parents. Children's strategy use and parents' behavior were coded and analyzed. Results indicate that parents usually provided appropriate support to their children, providing more direction and assistance to the children who required them, and less to those who did not.

Developmental and contextual effects on children's addition strategies were assessed in two experiments. The first experiment examined developmental differences in preschool, kindergarten, and first grade children's strategy use during a nonschool-related task, a board game. The children showed a developmental progression in their strategy use during the game as would be predicted by Siegler's strategy-choice model, with children overall showing multiple and variable strategy use, and a progression toward more sophisticated strategy use with age. The second experiment compared the game context with a comparable school-related math context in first graders. Three testing sessions separated by about a week, included the game, aural math problems, and a series of diagnostics designed to measure verbal IQ and working memory. The children showed great variability in their strategy use between the two contexts and were faster and more accurate during the game. Within each context, verbal IQ and working memory displayed some interesting relationships with strategy use.

This thesis was prepared out of the necessity for an identification
of the concepts of mathematics used in PSSC physics. First,
a survey of past and current educational journals was used to
establish general mathematical prerequisites for PSSC physics. Then
the necessary mathematical concepts as conceived by the authors of
the PSSC textbook are discussed, with no attempt to state the level
of proficiency required in behavioral terms for the identified
topics. A survey of the literature was made in order to suggest
provisions for the teaching of these concepts. These suggestions
take the form of mathematics-physics curriculum changes such as
integrated mathematics-physics courses, fusion of science applications
into the mathematics curriculum, and the institution of a
mathematics course specifically designed to prepare students for the
study of physics.