Reports and surveys by the U.S. government and international organizations have repeatedly acknowledged the achievement problem in math in K-12 regardless of various efforts (e.g., by the U.S. Department of Education) to diminish it. To address the problem in math achievement in K-12, teachers, scholars, and the U.S. government have developed…

The distinction between procedural and conceptual learning has long been a topic of discussion in mathematics education and the idea of compression into thinkable concepts that enable the individual make links between them (Tall, 2007). In addition to, the compression to thinkable concept was to be thinking mechanism arising naturally and…

Although a large part the Physics Education Research (PER) literature investigates students' conceptual understanding in physics, these investigations focus on qualitative, conceptual reasoning. Even in modeling expert problem solving, attention to conceptual understanding means a focus on initial qualitative analysis of the problem; the equations…

This study examined the relation between symbolic play training and conservation in 30 middle-class nonconserving 4-year-old children. Results showed that 13 experimental subjects manifested some change in solving conservation problems after symbolic play training while only one control subject showed any change toward conservation on the…

Investigated the effects of model status and various symbolic modeling procedures on brainstorming behavior in female undergraduate education majors (N=136). Results indicated that more solutions were produced by the experimental and higher-status model groups than by the control and peer model groups. (LLL)

After describing desirable characteristics of a student's first encounter with proof, and listing skills prerequisite for the proposed lesson (knowledge of some operational systems), the author describes in detail an introductory session in which students prove consequences of commutativity and associativity for a system supposedly encountered on…

Discusses implications for emergent literacy of a study of children two to three years old that examined how age and differing mnemonic cues are related to problem-solving strategies. The study found a transitional stage between older children's symbolic problem solving and younger children's reliance on trial and error. Suggests ways to…

In the pair of experiments reported here the authors investigated the relationship between meaningfulness of problem statements and subjects' use of these statements in problem-solving tasks. Subjects (96 university students) were required to memorize meaningful formulae such as "volume = area x height" or corresponding symbolic formulae such as…

"A new sort of concept attainment or decoding-encoding experimental paradigm based on the model is developed and an experiment on 5-, 7-, and 9-year-olds is reported. (Author)

Discusses development of symbolic thinking in toddlers as a step in language acquisition and skill development. Examines means of encouraging this symbolic problem solving, such as setting the stage for problems, helping children plan problem-solving strategies, and encouraging children in self-evaluating their skills. Examines development of…

Examined whether toddlers would use information presented through video to solve a retrieval problem. Found that 2.5-year-olds were very successful at finding a hidden toy based on viewing a televised hiding event, but 2-year-olds were not. Substantially better performance was achieved by other 2-year-olds who either watched or believed they were…

Children's Television Workshop (CTW) is an experiment in the instruction of preschool children through the medium of broadcast television. This document, which incorporates, extends, and supersedes an earlier report of a meeting to establish priorities among goals for CTW, serves six related purposes: (1) it attempts to reflect the suggestions of…

Reviews approaches to machine learning (development of techniques to automate acquisition of new information, skills, and ways of organizing existing information) in symbolic domains. Four categorical tasks addressed in machine learning literature are examined: learning from examples, learning search heuristics, learning by observation, and…

A review of research on children's symbolic play discusses ways for teachers to (1) defend the inclusion of play in the curriculum; (2) understand and respect differences in the ways children play; and (3) facilitate play in the classroom. Discusses the complexity of play and the controversy about play as part of the curriculum. (GLR)

This paper examines sixth-grade children's thinking related to solving ratio and proportion problems before these children had received any instruction in the domain. It explores unitizing and norming, one of the processes identified by both content analyses (Behr, Harel, Post, & Lesh, 1990); Harel, Behr, Post & Lesh, 1990) and research in…