Helps teachers explore the generative nature of traditional curriculum topics and shows how teachers can come to a better understanding of why an individual topic is important, how that topic helps build mathematical power, and what opportunities exist for making connections and supporting transfer. Discusses using generative questions to address…

Exemplifies a model of a conceptual-support net in the domain of multidigit addition that provides guidance in making curricular and classroom teaching choices about what kinds of conceptual supports to provide in a particular setting. Presents summaries of several different multidigit addition solution methods that indicate how different quantity…

Discusses the implementation and influence of the National Council of Teachers of Mathematics (NCTM) three standards-focused documents since they were published eight years ago. (Author/ASK)

Discusses what is important in teaching and learning mathematics, mathematics curriculum, types of mathematical knowledge, and reform movements in these areas. (ASK)

Mathematics curriculum for students in grades 5 through 8 should include explorations of statistics in real world situations. Provides a sample data-exploration activity. (ASK)

Views the mathematics curriculum in terms of things that can be worked out by someone (necessary) and things about which everyone needs to be informed (arbitrary). This view clarifies the roles that teachers and students have within the complexities of teaching and learning. (Contains 11 references.) (ASK)

Highlights a debate concerning reform calculus between Professor Thomas W. Tucker on the reform side and Professor Howard Swann on the traditional side. (ASK)

Observes some children as they went through middle school from two perspectives: as a parent, and as a college mathematics teacher. Contemplates why American children learn so little arithmetic in the middle grades. (ASK)

Develops in detail implications for teaching of the arbitrary and necessary curriculum divide. Discusses practical ways forward for teachers who plan lessons and work in the classroom with sensitivity to this divide. Concentrates on teaching and learning arbitrary aspects of the curriculum. Arbitrary is in realm of memory and students have the job…

Presents a critique of the multimedia package for the secondary mathematics classroom, World of Number, which was sponsored by the National Curriculum Council. Also makes suggestions for future development based on this critique, the experience of classroom use, and sociocultural learning theory. (AIM)

Presents reflections on experiences in teaching mathematics class, especially what to teach and how to teach it. (ASK)

Links the use of Computer Algebra Systems (CAS) to an existing classification scheme for mathematical tasks called the MATH Taxonomy. Illustrates through concrete examples how the goals of teaching and learning mathematics can be set using this classification together with the CAS. (Author/MM)

In many countries, the traditional processes of algebra have received criticism from educational reformers. Current reform policies, national frameworks, and local implementing statements have encouraged an algebra-for-all curriculum for students. After years of effort to improve the teaching of algebra, studies indicate that students usually do…

Summarizes and integrates the lessons learned from the last decade of professional development efforts based on the standards of the National Council of Teachers of Mathematics. Identifies fundamental challenges to such reform and indicates strategies that have been helpful in overcoming these obstacles. (Author/MM)

Study examines whether the implementation of an instructional management system served to improve student math achievement and the classroom instructional environment. In addition, the study examined the extent to which adding a curriculum-based monitoring system to an ongoing math curriculum would result in positive changes in the classroom…