The paper argues that a relationship between visualization and mathematical problem solving ability exists. Research suggests that visual imagery leads to increased understanding of mathematical concepts at both the primary and secondary levels. Mathematical potential is not necessarily "born." Potential can be created in the least likely students…

Noting that the ability to think critically and creatively can be encouraged even in the very young, this book provides practical strategies and lesson plans for introducing children in kindergarten through grade 3 to the fun and rigors of skillful thinking. The first set of four lessons is designed to start children thinking and to lay the…

The PRODIGY/EBL system [Minton88] was one of the first works to directly attack the problem of strategy utility. The problem of finding effective strategies was reduced to the problem of finding effective rules. However, this paper illustrates limitations of the approach. There are two basic difficulties. The first arises from the fact that the…

A psycholinguistic approach to listening was used in this study of listening skills in second language (L2) acquisition. The study tried to identify and classify the problem-solving processes and strategies used by L2 listeners. The processes were categorized from a perspective that took into account the processes underlying their use rather than…

The purpose of this exploratory study was to examine the effectiveness of learner manipulation of visuals with and without organizing cues in computer-based instruction on adults' factual, conceptual, and problem-solving learning. An instructional unit involving the physiology and the anatomy of the heart was used. A post-test only control group…

Fifty-five college students were assessed on four types of cognitive and metacognitive measures in math, language, and visual/spatial tasks. They were measures on self-reported general metacognitive skills, predicted performance, metacognitive behaviors, and actual performance. The students' self-reported assessments of their ability on a general…

This analysis of 44 research studies concerned with word problems contains: (1) a brief overview; (2) 44 major findings and conclusions; (3) 64 suggestions and questions for further research; and (4) a reference list. The author suggests that the experimental research of the 1980s seemed to focus on the children, the instruction, and the word…

Although it is difficult to predict which mathematical ideas will be most important to the citizens of the 21st century, most mathematics educators agree that problem solving will become an even more important skill. This booklet is designed to provide teachers with ideas on helping students learn to: (1) use problem solving thinking skills; (2)…

There has long been dispute in mathematics between the drill and practice orientation that focuses primarily on memorizing mathematics as meaningless rote algorithms and the approach based on understanding and making creative use of mathematics. This 25-chapter book, based on a 7-year study at the University of Illinois, seeks to explain and…

The Preparing Elementary Teachers to Teach Mathematics Project is a cooperative university/school effort to improve the teaching of mathematics by elementary teachers. Although the primary focus of the project is the improvement of the university training of preservice teachers (PSTs) in mathematics, there are two important collaborative aspects…

Attempts to train learning strategies have not produced marked or lasting increases in academic IQ, probably because current training models fail to recognize the evolutionary nature of strategies acquisition. Empirical and theoretical evidence supports an incidental learning model, which engineers the instructional environment following study…

Early adolescence is a time when students require adult assistance to become accurate and effective decision makers and problem solvers. Because of the fragmented nature of society, the family structure, and the schooling process, schools need to establish a nonthreatening environment in which students can discuss the issues related to growing up.…

Indicates that only 21% of respondents (secondary school math teachers) used computer-assisted instruction for tutorial work, physical models to interpret abstract concepts, or real-life application of the arithmetic or algebraic manipulation. Recommends that creative teaching methods be applied to problem solving. (NKA)

Discusses the differences between problems and exercises in chemistry, and some of the difficulties that arise when the same methods are used to solve both. Proposes that algorithms are excellent models for solving exercises. Argues that algorithms not be used for solving problems. (TW)

Discusses the difference between a generic chemistry problem (one which can be solved using an algorithm) and a harder chemistry problem (one for which there is no algorithm). Encourages teachers to help students recognize these categories of problems so they will be better able to find solutions. (TW)