Showing papers by "Australian Catholic University published in 1990"
TL;DR: In this paper, children's solutions to a variety of multiplication and division word problems were analysed in a cross-sectional pilot study of 34 children from Grades K to 2, and responses indicated a wide range of strategies used and these were further classified into developmental levels of strategy use.
Abstract: Children’s solutions to a variety of multiplication and division word problems were analysed in a cross-sectional pilot study of 34 children from Grades K to 2. Responses indicated a wide range of strategies used and these were further classified into developmental levels of strategy use. Because these data reflected the SOLO Taxonomy developmental model for classifying responses, a SOLO mapping procedure was used for further analysis. In this paper, the mapping procedure is applied to only one multiplication problem strategy, repeated addition, to exemplify the procedure. The mapping device employed in the analysis isolated three components of the problem-solving procedure: the cues given by the problem, the concepts and processes used by the children, and the responses given by the children. Responses to mathematical problems from children in this age group have not previously been used to elucidate the earlier modes of functioning in the SOLO Taxonomy. In particular this paper considers the Ikonic mode and the transition into the concrete Symbolic mode.
13 citations
TL;DR: In this paper, a class of spaces for which Gateaux and Frechet differentiability of a continuous convex function coincide with Mazur's theorem implies that all Montel Frechet spaces are Asplund spaces.
Abstract: In this paper topological linear spaces are categorised according to the differentiability properties of their continuous convex functions. Mazur's Theorem for Banach spaces is generalised: all separable Baire topological linear spaces are weak Asplund. A class of spaces is given for which Gateaux and Frechet differentiability of a continuous convex function coincide, which with Mazur's theorem, implies that all Montel Frechet spaces are Asplund spaces. The effect of weakening the topology of a given space is studied in terms of the space's classification. Any topological linear space with its weak topology is an Asplund space; at the opposite end of the topological spectrum, an example is given of the inductive limit of Asplund spaces which is not even a Gateaux differentiability space.
5 citations