In the framework of a long term teaching experiment we present an Educational approach based on the use of a dynamic geometry software and a symbolic manipulator. Here we present the general ideas of the followed approach focusing on how meanings can originate from phenomenological experience and evolve under the guidance of the teacher. In…

According to Kilpatrick (1987), in the mathematics classrooms problem posing can be applied as a "goal" or as a means of instruction. Using problem posing as a goal of instruction involves asking students to respond to a range of problem-posing prompts. The main goal of this article is a classification of mathematics questions created by Years 8…

We address the telling/not-telling dilemma in mathematics education. Telling is instructionally important, but has been downplayed because of (a) perceived inconsistencies between telling and constructivism, (b) increased awareness of the negative consequences of relying too heavily on telling, and (c) a focus on "non-telling" actions as…

In individual interviews, 220 students in grades 4, 6, 8, and 9 were given one task, and 72 eighth graders were given three tasks to answer two questions: (a) Is a square the unit of measurement for an area for students in grades 4-8? and (b) Does a square have a space-covering characteristic for students in grade 8? The answers to both questions…

Research conducted during the Trends in International Mathematics and Science Study (TIMSS) and later (Stigler et al. 1999; Stigler and Hiebert 1999) undertook a thorough analysis of lessons in the United States, Japan, and Germany. This article focuses on certain aspects of mathematics lessons in Russia. Specifically, the attempt is made to…

Two hundred and thirty-one students in six Grade 9 classes in two government secondary schools located near Chiang Mai, Thailand, attempted to solve the same 18 quadratic equations before and after participating in 11 lessons on quadratic equations. Data from the students' written responses to the equations, together with data in the form of…

The purpose of this study is to investigate the effect of one year of regular "LEGO" training on pupils' performances in schools. The underlying pedagogical perspective is the constructivist theory, where the main idea is that knowledge is constructed in the mind of the pupil by active learning. The investigation has been made in two…

Violence among American youth is a significant societal problem. The past decade witnessed juvenile arrests for violence, weapons, drugs, and curfew violations peak in the mid 90's. Analogous to the arrest trends for older juveniles, the arrest rate for young offenders rose 63% from 1987 until 1994 when it declined slightly. Since that time,…

"Harvard Education Letter" is published bimonthly at the Harvard Graduate School of Education. This issue of "Harvard Education Letter" contains the following articles: (1) Telling Tales Out of Charter School: What Educators and Policymakers Can Learn from the Successes and Failures of Charters (Robert Rothman); (2) One Charter School's Formula…

Reading is an essential part of science literacy, yet teachers often face challenges in incorporating reading in science classrooms. In this article, the authors share how they brought reading back into their science classrooms. They designed four quarterly reading projects with yearlong literacy routines that they used successfully with their…

In this paper, we suggest that case-based resources, which are used for assisting cognition during problem solving, can be structured around the work of narratives in social cultural psychology. Theories and other research methods have proposed structures within narratives and stories which may be useful to the design of case-based resources.…

Introduction: The Maui Hawaii Educational consortium (the Maui School District and Maui Community College) sought scientifically based evidence for the effectiveness of the Cognitive Tutor (CT) Algebra I Curriculum to inform adoption decisions. Decision makers were particularly interested in whether the use of the CT program affects achievement of…