Explores the mathematical abilities of human infants compared with various species of animals. Studies indicate that human infants enter the world capable of doing simple mathematical operations. Nonhuman animals can discriminate among sets of objects based on the number of items in each set. Further studies may pinpoint the age at which children…

Discusses the teaching of "big ideas" in mathematics in an environment that accommodates special learning differences. With multiple approaches that capitalize on the learning differences of students, those with special needs can respond within their specific limitations and succeed at levels previously considered beyond their reach. (SLD)

Discusses the benefits of dynamic geometry software in helping students learn to write proofs. The software allows students to create simple geometric figures, explore relationships, make conjectures about their properties, and test those conjectures. (AIM)

Presents three problems based on the price of aluminum designed to encourage students to be cooperative and to use an investigative approach to learning. Students collect and synthesize information, analyze results, and draw conclusions. (AIM)

Argues that although differential equations are billed as applied mathematics, there is rarely any hands-on experience incorporated into the course. Presents a laboratory project that requires students to obtain data from a physics lab and use that data to compute the coefficients of the second order differential equation, which mathematically…

Presents facts about a super-jumbo jet and poses 11 questions on different subjects, including estimation and comparison, concerning the super-jumbo jet. Gives hints and solutions for the answers to those questions. (ASK)

Describes an examination of arithmetic problem posing designed to examine the behaviors of 63 prospective elementary school teachers. Findings indicate that the test effectively evaluates arithmetic problem posing. Most subjects were able to pose solvable, complex problems. Performance improved when the task contained specific numerical…

Examines Australian students' conceptions of ordering decimals. Fifty secondary students studied over 12 months showed little change in their misconceptions. Whole number misconceptions are important in earlier years but disappear with time. The fraction misconception persists however, being displayed by approximately 20% of year 10 students. The…

Investigated relationship between students' classroom experiences and how they construct mathematical meanings. Suggests that students determine meaning or correctness of mathematical activity according to teacher, intuition, familiarity, and procedural knowledge. The teacher emerged as playing the most valued role in sense making and ratifying of…

Argues that children need to be given regular opportunities to gather, organize, display, and interpret their own data. They should have regular opportunities to pose their own questions and represent the results in their own way. Offers five sample survey questions children can pose to each other and examples of data representation by children.…

Describes a study of young children's thinking about numbers and operations with numbers. Issues explored include how young students interpret mathematical questions, aspects having to do with the language of mathematics, the mathematical potential of some children, and the range of procedures that children use when solving problems. Stresses…

Describes a classroom activity designed to give students hands-on experience using technology and geometric visualization, as well as to explore fractal geometry in a cooperative classroom environment. Natural phenomena is the context of these activities. Enriches understanding of Euclidean geometry and infinite sequences. Lists materials,…

A teaching experiment involving 30 third graders investigated the transformation of their concepts of numbers. Observations of their notations and problem-solving procedures show development that progresses from a focus on states to a type of reasoning in which changes become quantifiable "objects of awareness." (SLD)

Investigates consumer research through an activity that helps students distinguish between qualitative and quantitative data. (KHR)

Recommends skillful use of language arts to help students make sense of scientific and mathematical concepts. Suggests that connecting language arts with science and mathematics explicitly and intentionally strengthens teaching and learning in all three areas of the curriculum. (Author/NB)