In some situations, memorisation is useful, even necessary. It can give students enough concrete facts on which to reflect; it can limit anxiety by reducing mathematics to a set of simple facts, rules and procedures; and it can help to develop fluency with numbers early in a child's development, before the child is asked to tackle more complex…

This article presents two classroom episodes in which students were exposed to the value of asking questions and to the different roles played by proof in mathematics. The conversation in the two episodes is outlined in the article. The setting was a classroom of fifteen good high-school students, who were studying calculus. These episodes…

MathWings is the mathematics program of the Success for All Foundation, a non-profit organization that develops and disseminates school reform programs originally developed at Johns Hopkins University. MathWings, based on NCTM standards, emphasizes the use of cooperative learning, problem solving, and metacognitive strategies to help all children …

Presents the complete Applesoft listing of a traditional adventure program. The unique feature of the program is the incorporation of mathematics word problems into the adventure. Students aged 10 and up should be able to solve these problems with little or no effort. (JN)

Presents a conceptual framework for analyzing students' mathematical understanding, reasoning, problem solving, and communication. Analyses of student responses indicated that the tasks appear to measure the complex thinking and reasoning processes that they were designed to assess. Concludes that the QUASAR assessment tasks can capture changes in…

The Program for International Student Assessment (PISA) is a system of international assessments that measures 15-year-olds? capabilities in reading literacy, mathematics literacy, and science literacy every 3 years. PISA was first implemented in 2000 and is carried out by the Organization for Economic Cooperation and Development (OECD), an…

This paper documents the achievement monitoring component of a three-year study on the acquisition of addition-subtraction problem-solving skills by young children. A set of performance objectives contained in or ancillary to ten instructional units on sentence-writing for verbal problems and algorithms specified test content. Tests measuring…