This study examined effects of gamified comparison on sixth graders' performance of algebra word problem solving and attitude toward algebra learning. Seventy-two sixth graders were invited to participate in a four-week experimental instruction and assigned to three groups: gamified comparison, comparison, and control. The results showed (1) a…

Discussed is the meaning of the word "of" as is found in mathematical expressions that involve fractional numbers. The conceptual rather than numerical distinction is stressed. Teaching techniques regarding difficulties with this concept are suggested. (CW)

Reports unique solutions given to five problems from individual students in mathematics courses for prospective elementary school teachers oriented toward problem solving. Concludes that such courses are feasible, promote problem-solving abilities and strategies, and develop appreciation and confidence in preservice teachers. (MDH)

The history of formal mathematical proofs is sketched out, starting with the Greeks. Included in this document is a chronological guide to mathematics and the world, highlighting major events in the world and important mathematicians in corresponding times. (MP)

Presented is an account of a day-and-a-half seminar which was held for selected mathematics educators from six states. It was sponsored by the Regional Exchange (RX), a National Institute of Education (NIE) dissemination project headquartered at the Southwest Educational Development Laboratory (SEDL). The seminar had two important purposes: (1) to…

Children's solutions to simple word problems requiring addition or subtraction skills develop through four stages: (1) modeling with objects; (2) utilization of both modeling and counting strategies; (3) reliance on counting strategies; and (4) reliance on number facts. The current primary mathematics curriculum fails to capitilize on rich…

Boundary value problems (BVPs) for partial differential equations are common in mathematical physics. The differential equation is often considered in simple and symmetric regions, such as a circle, cube, cylinder, etc., with global and separable boundary conditions. In this paper and other works of the authors, a general method is used for the…

The purpose of this report is twofold. The first is to deliver an accurate portrayal of students' achievement in geometry and measurement as gleaned from the results of the 1986 Massachusetts Educational Assessment Program (MEAP). The second is to provide K-12 teachers of mathematics with activities that have proven to be helpful in encouraging…

Reports examples of the behaviors, including kinetic and vocal, used to facilitate problem-solving based on observations of four seventh-grade students. Discusses the use of the behaviors in problem-solving teaching. (YP)

Discusses the problems American students have learning math. Describes the new learning in mathematics that synthesizes new content and methods that restructure the curriculum in a way that resolves design and quality control problems. Presents examples of effective programs. (JS)

Argues that proving something begins with an assumption and proceeds logically to a conclusion, thus convincing by offering arguments. Describes some pitfalls involved in proving through examining several case histories. Offers suggestions for teaching the proof process. For example, sometimes an extreme example or counterexample will do more to…

Mathematics plays an exceptionally important role in biological education and the history of biology. Ten equations and descriptions of their historical importance are presented to draw students' and faculty's attention to mathematical models that have been intrinsic to many of the significant discoveries in biology in the 20th century. Each…

Explores mathematical methods children use to find answers for themselves. Describes some methods used for multiplication and subtraction problems. (YP)

Presents a process model developed for interaction and mathematical level raising focusing on the individual learning process and relates this model to research. The model is meant to show how level raising can be realized by allowing students to work in small groups on a mathematical problem. Contains 24 references. (Author/ASK)

After noting that research and development reports indicate that there are strong psychological arguments for approaching algebraic concepts through the use of computer programming, the work of the Nottingham Programming in Mathematics Project with pupils aged 11-13 is briefly described. What is meant by understanding of a concept and how pupils…