Presents remarks adapted from the Presidential address from the 1999 annual meeting of the National Council of Teachers of Mathematics (NCTM). Argues that the mathematics classroom teacher must create an environment that supports students' interests and mathematics growth at many different levels and ways in which to achieve this. Considers…

Researchers from four projects with a problem-solving approach to teaching and learning multidigit number concepts and operations describe a common framework of conceptual structures children construct for multidigit numbers, and categories of methods children devise for multidigit addition and subtraction. Conceptions include unitary, decade and…

Presents longitudinal analyses of the mathematical achievement and beliefs of three groups of elementary pupils. The groups were designated according to those students who had received two years of problem-centered mathematics instruction, those who had received one year, and those who had received textbook instruction. Results indicate that the…

Studies the developmental process of how the concepts of ratio and proportion do not develop in isolation, but rather are part of the individual's multiplicative conceptual field, which includes other concepts such as multiplication, division, and rational numbers. Follows one fifth-grade student as he attempts to schematize his…

Presents the assessment and grading practices of 19 mathematics classes in five high schools in three states. In each class the most frequently used assessment tools were tests and quizzes, with these determining approximately 77% of students' grades. In 12 classes other forms of assessment such as written projects or interviews were also used.…

Reports on the results of the reform curriculum of the University of Chicago School Mathematics Project's elementary curriculum, Everyday Mathematics, for third-grade students. Results included the fact that only 2% of UCSMP students failed to meet state goals. UCSMP students also scored well in all mathematical areas including number skills and…

Mathematical problems generated by 509 middle school students who were given story-problem descriptions and asked to pose questions that could be answered using the information were examined for solvability, linguistic and mathematical complexity, and relationships within the sets of posed problems. The multiple-step data analysis scheme can be…

Elementary number theory is investigated with the main focus on the concept of divisibility and its relation to division, multiplication, prime and composite numbers, factorization, divisibility rules, and prime decomposition. Preservice teachers' responses indicated dispositions toward procedural attachments even when conceptual understanding was…

Reports evidence of construction and coordination of units in a measurement setting using data gathered from four students during individual problem-solving sessions near the end of their fourth-grade year. Proposes the task of measuring two-dimensional regions becomes possible when a student can construct two-dimensional units and coordinate…

Reports a case study set in the context of a "function" curriculum approach to introductory algebra. The expectation that the teacher's actions would reflect the philosophy implied in the curriculum was not supported. The teacher gave priority to curriculum content coverage, emphasized methods and procedures, and adopted teacher-focused…

Remarks adapted from the Presidential Address at the 74th Annual Meeting of the National Council of Teachers of Mathematics in April 1996 charge educators with believing that every student can learn mathematics, every teacher must have adequate support and professional development opportunities, and every parent must have a vested interest in…