Mathematical Modeling in the Primary School: Children's Construction of a Consumer Guide

This paper examines 6th grade children's local conceptual development and mathematization processes as they worked a comprehensive mathematical modeling problem (creating a consumer guide for deciding the best snack chip) over several class periods. The children and their teachers were participating in a 3-year longitudinal teaching experiment in which sequences of mathematical modeling problems were implemented from the 5th grade (10 years of age) though to the 7th grade. In contrast to traditional problem solving, mathematical modeling requires children to generate and develop their own mathematical ideas and processes, and to form systems of relationships that are generalizable and reusable. Reported here is a detailed analysis of the iterative cycles of development of one group of children as they worked the problem, followed by a summary of the mathematization processes displayed by all groups. Children's critical reflections on their models are also reported. The results show how children can independently develop constructs and processes through meaningful problem solving. Children's development included creating systems for operationally defining constructs; selecting, categorizing, and ranking factors; quantifying quantitative and qualitative data; and transforming quantities.     

The development of the ability to recognize the meaning of iconic signs

Early developmental psychologists viewed iconic representation as cognitively less complex than other forms of symbolic thought. It is therefore surprising that iconic signs are not acquired more easily than arbitrary signs by young language learners. One explanation is that children younger than 3 years have difficulty interpreting iconicity. The current study assessed hearing children's ability to interpret the meaning of iconic signs. Sixty-six 2.5- to 5-year-olds who had no previous exposure to signs were required to match iconic signs to pictures of referents. Whereas few of the 2.5-year-olds recognized the meaning of the iconic signs consistently, more than half of the 3.0-year-olds and most of 3.5-year-olds performed above chance. Thus, the ability to recognize the meaning of iconic signs gradually develops during the preschool years. Implications of these findings for sign language development, receptive signed vocabulary tests, and the development of the ability to interpret iconic symbols are discussed.     

对非线性规划的一类Di Pillo-Grippo增广拉格朗日函数的进一步研究

1 Introduction Duringthe past several decades ,considerable atten-tion has been given to devising methods for solvingconstrained opti mization problemsviaunconstrainedmini mization techniques and a number of researchwork in the area of nonlinear programmi…