With student numbers decreasing and traditional teaching methods having been found inefficient, it is widely accepted that alternative teaching methods need to be explored in tertiary physics education. In 2006 a different teaching environment was offered to 244 first year students with little or no prior formal instruction in physics. Students…

NIER (National Institute of Educational Research, 2004) survey revealed that the most common attitude of Japanese high school students to mathematics is that "it is not useful in daily life but must be learnt for entrance examinations". It was also clarified that only 3.2 percent of mathematics teachers use computers in their classes.…

The purpose of this paper is to present the mechanism for effective communication when the mathematical objects of learning are equations and functions. The presentation is based on data collected while the same object of learning is presented in two classes, and it includes two teachers and 45 students. Among other things, the data consists of…

This dissertation explores fifth and eighth grade students' interpretations of three kinds of mathematical representations: number lines, the Cartesian plane, and graphs of linear functions. Two studies were conducted. In Study 1, I administered the paper-and-pencil Linear Representations Assessment (LRA) to examine students'…

Every student should understand and use all concepts and skills from the previous grade levels. The standard is designed so that new learning builds on preceding skills. Communications, Problem-solving, Reasoning & Proof, Connections, and Representation are the process standards that are embedded throughout the teaching and learning of all…

Every student should understand and use all concepts and skills from the previous grade levels. The standard is designed so that new learning builds on preceding skills. Communications, Problem-solving, Reasoning & Proof, Connections, and Representation are the process standards that are embedded throughout the teaching and learning of all…

Following the Guidelines for Assessment and Instruction in Statistics Education (GAISE) recommendation to use real data, an example is presented in which simple linear regression is used to evaluate the effect of the Montreal Protocol on atmospheric concentration of chlorofluorocarbons. This simple set of data, obtained from a public archive, can…

Three classrooms of Grade 4 students from different schools and diverse backgrounds collaborated in early algebra research to solve a series of linear and quadratic generalizing problems. Results revealed that high- and low-achieving students were able to solve problems of recognized difficulty. We discuss Knowledge Building principles and…

This article presents the partial results obtained in the first stage of the research, which sought to answer the following questions: (a) What is the role of intuition in university students' solutions to optimization problems? (b) What is the role of rigor in university students' solutions to optimization problems? (c) How is the combination of…

Taking part in the United States Department of Energy's Real World Design Challenge (RWDC), the author describes how four technology education students at Cumberland Valley High School in Mechanicsburg, Pennsylvania, took on the challenge to redesign an aircraft wing, attempting to make it more efficient than one currently in operation. The…

The aim of this article is to illustrate how students, through collaborative small-group problem solving, appropriate the concept of geometric series. Student appropriation of cultural tools is dependent on five sociocultural aspects: involvement in joint activity, shared focus of attention, shared meanings for utterances, transforming actions and…

Two studies investigated the effects on students' perceptions (Study 1) and learning and motivation (Study 2) of different levels of feedback in mathematical problems. In these problems, an error made in one step of the problem-solving procedure will carry over to the following steps and consequently to the final solution. Providing immediate…

Before instruction, children solve many arithmetic word problems with informal strategies based on the situation described in the problem. A Situation Strategy First framework is introduced that posits that initial representation of the problem activates a situation-based strategy even after instruction: only when it is not efficient for providing…

According to the intuitive rules theory, students are affected by a small number of intuitive rules when solving a wide variety of science and mathematics tasks. The current study considers the relationship between students' Piagetian cognitive levels and their tendency to answer in line with intuitive rules when solving comparison tasks. The…

As English-only efforts continue in the US schooling system, dual-language programs have served as attempts to preserve students' home language. An after-school, dual-language, Spanish-English, mathematics program, Los Rayos was developed in a predominantly Mexican/Mexican-American neighborhood in Chicago. As participant observers with a…