Describes teaching methods employed in German elementary school classrooms that develop discovery, creativity, and a spirit of cooperation in students learning mathematics. Methods included free choice of learning activities by students and small group cooperative activities. Students' motivation, self-confidence, social and communications skills,…

Presents a lesson using chocolate chip cookies to involve children in scientific investigation and mathematical reasoning. (Author/MKR)

This article gives a comprehensive description of a theory for efficient assessment of knowledge. The essential concept is that the knowledge state of a subject, with regard to a specified field of information, can be represented by a particular subset of problems that the subject is capable of solving. (SLD)

Among 32 ESL students who received training in metacognitive strategies for mathematics problem solving, those students who were the highest achievers in mathematics and whose teachers were involved extensively in project activities were better problem solvers than less able math students or students in low implementation classrooms. Includes…

"The Systemic Initiative for Montana Mathematics and Science," based on a successful Dutch nontraditional curriculum, was used by a mathematics teacher to help ninth graders apply previously learned skills. Creative learning modules provided hands-on experience and helped students carry concrete knowledge to more abstract levels,…

Presents an alternate form of assignment, called "Special Problems," that incorporates writing in journals into the mathematics classroom. The method requires students to provide process narratives to accompany selected homework exercises. Allows the teacher to monitor the student's thought processes and development. (MDH)

Describes two lessons in which a fifth grade teacher emphasized the mechanics of mathematics, such as carrying out various computational procedures, to her students. The first lesson introduced students to the concept of averages. In the second lesson, the teacher conducted class surveys to provide data for computing averages. (BB)

Challenges the readers comprehension of mathematical induction by presenting four examples of arguments that misrepresent the concept. Discusses the reasons why the arguments lead to false conclusions. (MDH)

Presented is an activity which shows how mathematics is used in real life and helps to establish a need for mathematics in students' futures. Adapted from a scavenger-hunt idea, this activity helps students to discover that almost every career makes use of mathematics. (KR)

Small group work has grown in use throughout the 1980s. Reported are six issues that were raised concerning small groups resulting from a series of workshops for university students in which the students worked on problems in groups, jointly planned tasks, and critiquing their use during their practice experience. (MDH)

Presents a series of hands-on activities for grades K-2, 3-4, 5-6, and 6-8 using the common theme of kites to develop number sense in basic operations and fractions. Teachers' guides and worksheets are provided. (MDH)

Presents activities that integrate story telling, history, and problem solving as a stimulus for discussion and creativity in the elementary mathematics classroom, and a way to relieve children's anxiety in an escalating curriculum. (MDH)

To test the Lewis and Mayer simulation model (1987) for understanding compare problems, 3 experiments involving 39 college students and 15 third graders used registration of eye movements. Two experiments somewhat support the model, suggesting it holds true only when the task puts cognitive demands on the subject. (SLD)

This study examines the effect of formal representation of blue and yellow color mixtures as rational numbers on students' ability to solve ratio problems comparing the mixtures. Sixty subjects participated, 20 from each of grades 7, 8, and 9 from a Haifa (Israel) junior high school. Introducing the formal representation improved performance for…

A mathematics achievement test was taken by 132 U.S. and 110 Japanese fifth graders. Scores were higher for the Japanese, and relatively better for computation than problem solving. The reverse was true for the U.S. students. Results are discussed in terms of amount and kind of exposure to mathematics. (SLD)