An analysis of everyday use of mathematics by working youngsters in commercial transactions in Recife, Brazil, revealed computational strategies different from those taught in schools. Performance on mathematical problems embedded in real‐life contexts was superior to that on school‐type word problems and context‐free computational problems involving the same numbers and operations. Implications for education are examined.

We examine issues that arise in students' making of generalizations about geometrical figures as they are introduced to linear functions. We focus on the concepts of patterns, function, and generalization in mathematics education in examining how 15 third grade students (9 years old) come to produce and represent generalizations during the implementation of two lessons from a longitudinal study of early algebra. Many students scan output values of f(n) as n increases, conceptualizing the function as a recursive sequence. If this instructional route is pursued, educators need to recognize how students' conceptualizations of functions depart from the closed form expressions ultimately aimed for. Even more fundamentally, it is important to nurture a transition from empirical generalizations, based on conjectures regarding cases at hand, to theoretical generalizations that follow from operations on explicit statements about mathematical relations.

No abstract

No abstract

No abstract

Early research in everyday mathematics lent support to diverse and often contradictory interpretations of the roles of schools in mathematics education. As research has progressed, we have begun to get a clearer view of the scope and possible contributions of learning out of school to learning in school. In order to appreciate this view it is necessary to carefully scrutinize concepts of real (as in "real life"), utility (or usefulness), context, as well as the distinction between concrete and abstract.These concepts are crucial for determining the relevance of everyday mathematics to mathematics education; yet each concept is deeply problematic. The tension between knowledge and experience acquired in and out of school is not a topic of mathematics.But it deserves to be a fundamental topic in mathematics education. Everyday and Academic Mathematics 239We share with the other contributors to this monograph a number of premises about the nature of mathematical learning. We view mathematics, for example, as both a cultural and personal enterprise. It is cultural because it draws upon traditions, symbol systems, ideas, and techniques that evolved over the course of centuries, having originated in human activities such as surveying, astronomy, building, commerce, and navigation and eventually becoming a partially autonomous field of endeavor with its own subject matter, purposes, tools, and concerns. It is personal Everyday and Academic Mathematics 240 insofar as it demands from learners constructive processes and creative rediscovery even when they are apparently engaged in mere assimilation of facts and conventions.We also share a number of ideas and beliefs about the purposes and spirit of mathematics education. We tend to distrust rote, unquestioning learning. We favor situations in which students themselves must decide how to frame and represent problems, but we realize that, left to their own devices and inventiveness, students are not going to discover many important concepts of elementary mathematics. We value problems that promote engaging discussions among students. We recommend that students and teachers pursue multiple paths of reasoning when solving problems. We encourage educators to make frequent comparisons between everyday language and symbolism and the formal language and symbolism of mathematics. These value premises are rooted in our personal backgrounds, in the economic and political Zeitgeist, and in our theoretical lenses as well as in the legacies of Plato's Meno, Rousseau's Émile and Piaget's constructivism (even though they may at times push and pull in somewhat opposed directions). Some hallmarks of these influences include the belief that mathematical concepts are "out there" to be discovered but require the careful questioning and guidance of the more learned (Plato), faith in the capabilities of children to learn provided we are sensitive to their views and motivations (Rousseau), and the importance of painstakingly documenting children's reasoning and handling of mathematical invariants...

No abstract

No abstract