A high-school English teacher deplores barking-media sound bites of politicians pretending to resolve complex educational problems with one-dimensional "solutions." Highlighting specific classroom learning situations, he ponders three paradoxes: justice is not necessarily fair; freedom comes with limits; and clarity comes through…

Observed four fifth-graders who collaboratively solved problems integrating concepts related to fractions and area. Compared features of learning through peer collaboration with teacher-directed learning, including whole solution versus component parts, appropriation versus scaffolding, analysis versus synthesis, conflict versus errorless…

In this interview, psychologist Andrew Meltzoff dispels some popular myths and discusses insights from cognitive developmental psychology to enlighten educators. Studying infants and listening to young children has led experts to revise their ideas about the thought/language relationship. Play activities are profound learning experiences. (MLH)

One hundred forty fourth graders were asked to solve proportion problems about juice-mixing situations both before and after an intervention that used a manipulative model or other materials in three experiments. Results indicate different approaches appear to be necessary to facilitate children's proportional reasoning, depending on the reasoning…

Explains cognitive apprenticeship models. Highlights include modeling; coaching; scaffolding; metacognition; learning through social interaction; placing learning in an authentic context with authentic activities; information literacy and problem solving; and implementing apprenticeship approaches in library media centers. (LRW)

The Internet, an exciting and radically different medium infiltrating pop culture, business, and education, is also a powerful educational tool with teaching and learning potential for mathematics. Web-based instructional tools allow students and teachers to actively and interactively participate in the learning process (Lynch, Moyer, Frye & Suh,…

Traditional assessment methods are not always suitable for diagnosing learners' knowledge structures at different levels of their expertise. This paper describes an alternative schema-based rapid assessment technique and its application in the area of arithmetic word problem solving. The technique is based on an assessment of the extent to which…

This paper stems from the ESRC TLRP Learning How to Learn--in Classrooms, Schools and Networks Project, and explores how Assessment for Learning (AfL) relates, conceptually, to learning how to learn (LHTL). The term LHTL was intended to draw attention to a primary focus on learning practices, and we have related the processes of AfL to LHTL. A…

Metacognition has been accorded a role in both mathematical problem solving and in the learning of mathematics. There has been consistent advocacy of the need for the promotion of metacognitive activity in both domains. Such advocacy can only be effective if the advocated process is well understood. In this paper we have four goals: to describe a…

Students frequently misconceive the process of problem-solving, expecting the linear process required for solving an exercise, rather than the convoluted search process required to solve a genuine problem. In this paper we present an activity designed to foster in students realization and appreciation of the nature of the problem-solving process,…

Reuven Feuerstein's theory of Mediated Learning Experience was developed to explain individuals' different propensities for learning by linking those differences to an individual's exposure--through specific experiences--to his or her own culture, irrespective of its nature or level of conceptualization, technology, or institutionalized education.…

This paper proposes a theory that can account for differences between everyday and formal mathematics knowledge and a set of processes by which informal knowledge is transformed into formal mathematics. After an introduction, the paper is developed in five sections. The first section lays out the nature of informal, everyday mathematics knowledge.…

Previous research has cast doubt on children's ability to use specified evidence when making causal inferences, or, indeed, to differentiate between the specified evidence and their own preconceptions, or "prior theories." The present study continues previous work by distinguishing between children's reasoning in conditions where…

This paper identifies the bases and rationale for the concept of cooperative learning; describes the dynamics of the cooperative learning approach; and proposes methods that college faculty can use to enhance student motivation and learning. Cooperative learning is defined and is reported to have positive effects on student achievement, human…

The project's purpose was to revise the introductory biology material in a freshman course for biology majors so that it is based on Piagetian learning theory and incorporates the three phases of the learning cycle teaching strategy: (1) exploration; (2) concept formation; and (3) concept application. The approach presented concepts structured so…