The curriculum resources used for teaching secondary mathematics vary considerably from school to school. Some schools base their teaching largely on a single published scheme, while others design their own schemes of learning, curating their resources from a range of (often free) online sources. Both approaches seem problematic from the…

Recent "reform" curricula both ignore the absence of supporting data and completely misunderstand the role of problem solving in cognition. If, the argument goes, teachers are not really teaching people mathematics but rather are teaching them some form of general problem solving, then mathematical content can be reduced in importance. According…

The Childcare Act 2006 provides the underpinning legislation for a single quality framework for supporting children's learning development and care from birth to five. This is encompassed in the early years foundation stage (EYFS). EYFS has been designed to deliver improved outcomes for all children, by providing a flexible, play-based framework,…

The author criticizes an exploratory study of mathematics curricula for 6-13 year olds for its neglect of the needs of students with learning difficulties. He cites the importance of better assessment strategies, use of the problem-solving approach, development of an intersubject emphasis, and encouragement of estimating abilities. (CL)

Topics which should be emphasized in the secondary school mathematics curriculum are noted. The importance of problem solving is stressed, with some specific illustrations. (MNS)

The California Mathematics Standards are cynical, mind-numbing, and shallow. Instead of balancing problem solving, concept development, and skill acquisition, the standards are full of obsolete mathematics and devoid of problem solving. Students offering only an algorithm when asked for meaning have style without substance. Blind memorization is…

Discusses four major issues related to the mathematics curriculum and what research says about each of them, namely questions of content, tracking, problem-based curricula, and the role of proof. (23 references) (MKR)

Historical issues concerning the role of mathematics in the school curriculum are considered, with numerous examples illustrating varying emphases. (MNS)

This paper examines to show how an investigative approach to mathematics teaching can honor its two important dimensions--a thinking and reasoning side to go with the skill development. The paper addresses the question of why a problem solving approach has failed, makes the case for investigations as an overarching organizer, and discusses the…

The relationship between logic and mathematics is examined. Four basic concepts inherent in symbolic logic that are typically included in ninth- and tenth-grade mathematics programs are reviewed. Symbolic logic is advocated for all students who will study algebra and/or geometry. (MP)

Profiles a middle school mathematics teacher and examines her use of two problems from a pilot version of a 6th grade unit developed by a mathematics curriculum project. Reports that problem-solving-oriented curricula provide opportunities for students to make mathematics connections and leads to student confusion and uncertainty. Contains 35…

There are selected philosophies in the teaching of mathematics which can provide guidance to the teacher in developing the curriculum and also a framework for teaching and learning. This paper discusses four such philosophies of teaching mathematics: Idealism, Realism, Experimentalism, and Existentialism. Idealism stresses that students live in an…

Incorporating problem solving as an integral part of mathematics programs in the classroom is discussed. The teacher's focus is seen as stretching pupil thinking. (MP)

Some important issues related to teaching problem solving in the elementary grades are addressed, with particular emphasis on the intermediate grades. Presents one point of view and some specific questions often raised by teachers who wish to incorporate problem solving into the mathematics program. (MP)

Contends that, although the introduction of problem solving, intended to involve students more actively in their learning and understanding of the nature of mathematics, is a positive factor, the need for proof, which is an integral part of mathematics, must not be overlooked. (25 references) (MKR)