This article presents a designed learning environment intended to engage students in learning about the relationships among multiple representations as they work together on a shared task. Over the course of several extended problem-solving sessions, groups developed several successive alignments of participants and representations as they learned…

Latinas/os, the largest and fastest growing minority ethnic group in the United States (impels research that focuses on the education of Latinas/os and the need to reduce the achievement gap that persists between Latinas/os and other groups. Such research has gained in popularity; however, it is still very limited. I use my teaching experience…

The study documents the extent to which high school teachers reflect on their need to revise and extend their mathematical and practicing knowledge. In this context, teachers worked on a set of tasks as a part of an inquiring community that promoted the use of different computational tools in problem solving approaches. Results indicated that the…

This article continues a fairly recent trend of research examining the teaching practice of university mathematics lecturers. A lecturer's pedagogical practices in a course in linear algebra were discussed via a supportive community of inquiry. We use Schoenfeld's framework describing the relationship of resources, orientations and goals to…

The key questions are: is it true that persons with Down's syndrome can study mathematics only at a very elementary level? Might it be possible that their difficulties are mainly restricted to some fields, such as numeracy and mental computation, but do not encompass the entire domain of mathematics? Is the use of a calculator recommended? Is…

Taiwanese students consistently rank near the top on international exams on mathematics and science. In 2007, Taiwan recorded the highest TIMSS math score for eighth grade. The central education agency in Taiwan publishes detailed mathematics curriculum guidelines, which textbooks and national exams follow closely. In May each year, all ninth…

"Harvard Education Letter" is published bimonthly by the Harvard Graduate School of Education. This issue of "Harvard Education Letter" contains the following articles: (1) Money and Motivation: New Initiatives Rekindle Debate over the Link between Rewards and Student Achievement (David McKay Wilson); (2) An Inexact Science: What Are the Technical…

"Destination Math" is a series of computer-based curricula designed to be used for at least 90 minutes a week. Featuring sequenced, prescriptive, step-by-step instruction, "Destination Math" is designed for the development of fluency in critical skills, math reasoning, conceptual understanding, and problem-solving skills.…

The Isis problem, which has a link with the Isis cult of ancient Egypt, asks: "Find which rectangles with sides of integral length (in some unit) have area and perimeter (numerically) equal, and prove the result." Since the solution requires minimal technical mathematics, the problem is accessible to a wide range of students. Further, it is…

Generalising arithmetic structures is seen as a key to developing algebraic understanding. Many adolescent students begin secondary school with a poor understanding of the structure of arithmetic. This paper presents a theory for a teaching/learning trajectory designed to build mathematical understanding and abstraction in the elementary school…

A group of teachers involved in embedding NRICH tasks into their everyday practice decided they needed to address the (im)balance between teacher and student activity in their classrooms. In this article they share the issues they identified, and what they have been doing to address them.

While others have focused on gender-based language and the workplace, this research study explores gender-based language, in this case women's language, and the classroom. The study specifically examines examples of women's language and how this language affects student response in the classroom. Five variables have been identified as…

Many exercises in mathematical induction require the student to prove a divisibility property of a function of the integers. Such problems are generally presented as being independent of each other. However, many of these problems can be presented in terms of difference equations, and the theory of difference equations can be used to provide a…

The K-W-L method of teaching is a simple method that actively engages students in their own learning. It has been used with kindergarten and elementary grades to teach other subjects. The authors have successfully used it to teach physics at the college level. In their introductory physics labs, the K-W-L method helped students think about what…

If you take a circle with a horizontal diameter and mark off any two points on the circumference above the diameter, then these two points together with the end points of the diameter form the vertices of a cyclic quadrilateral with the diameter as one of the sides. We refer to the quadrilaterals in question as diametric. In this note we consider…