Elapsed-time problems are notoriously difficult for children. Instruction on techniques for teaching and learning elapsed time is not emphasized in current mathematics education literature. Nor is it addressed in "Curriculum Focal Points for Prekindergarten through Grade 8 Mathematics: A Quest for Coherence" (NCTM 2006). This absence of…

This study examines 8th grade students' coordination of quantitative units arising from word problems that can be solved via a set of equations that are reducible to a single equation with a single unknown. Along with Unit-Coordination, Quantitative Unit Conservation also emerges as a necessary construct in dealing with such problems. We base our…

This study sought to determine the effect of the problem-solving approach on academic achievement of students in mathematics at the secondary level. The secondary school students studying mathematics constituted the population of this study. The students of 10th class of Government Pakistan Girls High School Rawalpindi were selected as a sample…

In a small-scale, 8-month teaching experiment, the author aimed to establish and maintain "mathematical caring relations" (MCRs) (Hackenberg, 2005c) with 4 6th-grade students. From a teacher's perspective, establishing MCRs involves holding the work of orchestrating mathematical learning for students together with an orientation to…

This study investigated whether children's inversion shortcut use (i.e., reasoning that no calculations are required for the problem 4 x 8 divided by 8, as the answer is the first number) is related to their analogical reasoning ability, short-term memory capacity, and working memory capacity. Children from Grades 6 and 8 solved multiplication and…

In this article the authors describe their efforts to support teachers' development of deep, connected understandings of school mathematics and to find ways to make use of the teachers' learning as a context for subsequent mathematical and pedagogical development. The authors detail the evolution of their model for Online Asynchronous…

Ms. Thomas, the general educator, and Ms. Merced, the special education teacher, plan to co-teach mathematics classes during the upcoming school year. Based on previous interactions with students and knowledge of students' abilities from school records, they know that several students, including students with disabilities, struggle with…

A method is developed in which an analytical solution is obtained for certain classes of second-order differential equations with variable coefficients. By the use of transformations and by repeated iterated integration, a desired solution is obtained. This alternative method represents a different way to acquire a solution from classic power…

This study implemented a three-stage problem-based estimation instruction scenario and combined it with mobile technology to provide elementary teachers with an effective e-tool for observing student estimation and leading effective class or group discussions on the selection and assessment of appropriate strategies for solving daily estimation…

We answer a geometric question that was raised by the carpenter in charge of erecting helical stairs in a 10-story hospital. The explanation involves the equations of lines, planes, and helices in three-dimensional space. A brief version of the question is this: If A and B are points on a cylinder and the line segment AB is projected radially onto…

Research in the didactics of mathematics has shown the importance of the problem of the particular and its relation to the general in teaching and learning mathematics as well as the complexity of factors related to them. In particular, one of the central open questions is the nature and diversity of objects that carry out the role of particular…

This article describes a simple alternative unified method of solving nonlinear regular perturbation problems. The procedure is based upon the manipulation of Taylor's approximation for the expansion of the nonlinear term in the perturbed equation. An essential feature of this technique is the relative simplicity used and the associated unified…

Although word problems pose greater language demands, they also encourage more meaningful problem solving and mathematics understanding. With proper instructional support, a student-centered, investigative approach to contextualized problem solving benefits all students. This article presents a lesson built on an author-adapted version of the…

This study investigated middle school students' conceptual understanding of algebraic equations. Participants in the study--257 sixth- and seventh-grade students--were asked to solve one set of algebraic equations and to generate story problems corresponding with another set of equations. Structural aspects of the equations, including the number…

The authors document their experience of working with 6-year-olds over several weeks. They share some observations that arise from weekly sessions they conducted which have been under way for several years and which have been widely reported. These observations show the payoff of a problem-solving approach to learning.