A trend at U.S. colleges and universities in teaching first-year science courses is discussed. An approach in the classroom and lab in which students engage in science through observation and hypothesis is emphasized. Hands-on science, experiential science, and constructing science through cooperative learning are discussed. (KR)

Number sequences are useful complements to traditional drill and practice. Described is an activity in which the basic rule, add the tens digit to five times the ones digit, is used to generate a sequence of numbers. The dialogue between teacher and student discussing characteristics of emerging patterns is given. (MDH)

Describes a classroom experience in which the teacher experiments with integrating mathematics history into a calculus class by presenting a historical problem taken from L'Hopital to be solved by the students. Extracts the role that history can play in teaching mathematics from the experience. (MDH)

This article recommends a holistic approach to student problems in mathematics. Teachers need to be aware of all paradigms (e.g., developmental, behaviorist, psychoanalytic) explaining causes of problems in mathematics. Examples of misunderstandings resulting from insufficient knowledge, insufficient mathematical vocabulary, and overgeneralization…

French tenth grade physics classes were observed as they studied electric circuits over a one-year period. An analysis is presented of tests taken during the year. The main point separating "average" students from "good" ones is their performances in "implicitly difficult exercises," that is, in what appears…

Compares seven positions on media influences on learning that were presented in a previous journal issue; discusses the conflict between advocates of a given approach versus integrated approaches to the solving of complex problems; and presents a model that links cognitive processes to computer-based prescriptions for improvements in learning. (35…

Presented is a proof where special attention is accorded to rigor and detail in proving the lemma that relates ruler-and-compass constructions to arithmetical operations. The idea that some angles cannot be trisected by a ruler and compass is proved using three different cases. (KR)

Presented is the theorem proposed by Volterra based on the idea that there is no function continuous at each rational point and discontinuous at each irrational point. Discussed are the two conclusions that were drawn by Volterra based on his solution to this problem. (KR)

Describes the design and implementation of a major collaborative assignment in which students investigate and produce written and oral solutions to a problem with a national perspective experienced by a community corporation, business, governmental, or not-for-profit organization. (KEH)

Various examples of open-ended problems and ways to obtain them are presented. Suggestions for incorporating open-ended problems and some of the benefits and difficulties encountered by teachers and students are discussed. Examples are from courses on mass and energy balances, communications, kinetics and ideal reactors, and reactor design. (KR)

Presents a model that relates Polya's ideas on problem solving to teaching practices that help create a mathematics learning environment in which students are actively involved in doing mathematics. Illustrates the model utilizing a high school geometry problem that asks students to measure the width of a river. (MDH)

Student problem-solving behaviors are analyzed using a four-dimensional framework with related detrimental factors identified for each dimension. General approaches and specific techniques developed to address negative factors are reviewed. Examined are means of developing the components of problem-solving teaching. (KR)

A technique for studying various properties of soap bubbles subjected to deformation, accompanied by some representative experiments to illustrate the versatility of the method, is presented. The measurement of the change of force that occurs when a bubble is stretched is calculated. (KR)

The soliciting-and-reacting-moves questioning technique used in science classrooms is described. The importance of using both higher-order and lower-level questions during a lesson is discussed. An example of a dialogue between a student and teacher using this technique is included. (KR)

Study compared the effects of classroom management instruction emphasizing technical skills versus instruction emphasizing reflective and constructive processes on 67 preservice teachers' reasoning and problem solving. Participants receiving reflective instruction used strategies more often to solve problems, provided more reasons for decisions,…