Concrete experience should be a first step in the development of new abstract concepts and their symbolization. Presents concrete activities based on Hyde and Nelson's work with egg cartons and Steiner's work with money to develop students' understanding of partitive division when using fractions. (MDH)

Presents a series of activities developed from the "Arithmetic Teacher's" regular feature entitled "Problem Solving: Tips for Teachers" to help students develop skills in each of the four steps of Polya's problem-solving process: (1) Understanding the Problem; (2) Making a Plan; (3) Carrying Out the Plan; and (4) Reflecting…

Over a 10-month period, normal children showed an increased reliance on memory retrieval and a decreased reliance on counting when they solved addition problems. There was an increase in speed of counting and of retrieving addition facts from long-term memory. Children with a mathematical learning disability showed no change in problem-solving…

Middle school students (n=267) were designated as gifted, honors, or average; divided into problem-solving treatment or comparison groups; and assessed on creative problem-solving ability and potential giftedness. Treatment students showed significant gains in problem-solving ability compared with comparison groups, with no significant differences…

Results from 40 high school students on the mathematics subtest of the Scholastic Aptitude Test (SAT) support the prediction that successful students would have more prior knowledge and would be better at defining problems, assembling strategies, and avoiding computational errors. Results are discussed in terms of a cognitive processing model.…

Responses of students in grades K-10 (42 interviewed; 98 written) to 4 common fractions problems were analyzed for iconic mode processes in relationship to concrete symbolic mode development. Concludes that progress in the latter, without development of complementary iconic support, limits both understanding and flexibility in solving problems.…

Students (n=40) who had experienced cooperative and individualistic concept-mapping experiences performed significantly better in solving three biological problems than did control students (n=20). No significant differences were found between students who mapped concepts cooperatively and those who mapped individually. There were mixed results…

A study examined the effects of differing degrees of bilingualism (English monolingual, English-French balanced bilingual, Bengali-English partial bilingual) on nonverbal problem-solving abilities of 71 grade-three children. The groups were compared on control of attention and analysis of knowledge. Results indicate the balanced bilinguals…

Scientists and students often believe that if they just think harder about a problem, a solution will follow. However, thinking about one's thinking, or using metacognition, can be a more productive expenditure of mental energy. Introducing students to metacognition allows them to discover the value of reflection. This article presents a lesson on…

A cognitive/metacognitive framework is presented for analysing applications tasks and responses to these. Conditions facilitating or impeding access to such tasks at the upper secondary level were identified using qualitative data analysis techniques within this framework. Strategies employed in exploiting, or overcoming these conditions were…

The author believes that information technologies are powerfully heuristic in addressing one of education's deepest ambitions. Following Engelbart's paradigm, he sees these technologies as augmenting human intellect, not simply because they permit high-speed calculations but also because they externalize our own cognitive processes in a way that…

This book provides a comprehensive review of teaching-learning models used in the development and implementation of a curriculum for gifted students. The models described were selected for their demonstrated or potential success with gifted children and their widespread use. For each model, the following types of information are provided:…

There is an emphasis on meaningmaking, problem solving, and discovery in contemporary educational settings--facts and concepts integrated into the curriculum by unifying themes that connect to real-world experiences. Using graphics to represent the thinking of students in learning and the thinking of teachers in integrated planning can be…

The domination of the information processing approach has shifted research from problem solving strategies to the structure and organization of knowledge that characterizes expertise. The purpose of this study was to compare the reasoning processes of 12 clinicians and 40 medical students as they responded to 6 positively stated multiple choice…

In Computer-Supported Intentional Learning Environments (CSILE), students use a computer-database system as a tool to store and organize their curriculum-related knowledge as a means of sharing information and thoughts with peers, supporting both individual and collaborative learning. This study contrasts two conditions: face-to-face collaboration…