Students struggling with mathematics may benefit from early interventions aimed at improving their mathematics ability and ultimately preventing subsequent failure. This guide provides eight specific recommendations intended to help teachers, principals, and school administrators use Response to Intervention (RtI) to identify students who need…

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…

Aim: Subcortical band heterotopia (SBH) or "double cortex" is a malformation of cortical development resulting from impaired neuronal migration. So far, research has focused on the neurological, neuroimaging, and genetic correlates of SBH. More recently, clinical reports and small sample studies have documented neuropsychological dysfunction in…

This article proposes an instructional idea where students can figure out an individual's secret personal information using the power of mathematics, particularly the power of algebraic thinking. The proposed examples in this article start with a personalized context that other people do not know and end up with generalized patterns of solutions.…

Background: Understanding and solving problems involves different levels of representation. On the one hand, there are logico-mathematical representations, or problem models (PMs), which contain information such as "the size of the flock changed from 31 sheep to 42" while, on the other hand, there are more qualitative representations, or…

There is debate as to the relationship between mathematical ability and language. Some research has suggested that common processes underlie arithmetic and grammar while other research has suggested that these are distinct processes. The current study aimed to address this issue in a large group of 68 left hemisphere stroke patients who were all…

The purpose of this study was to determine prospective teachers' knowledge about the concept of division. One focus of interest was whether the prospective teachers were able to represent division of fractions. The participants were introduced to an alternative model for representation of fractions based on a rate or ratio model of division…

Algebraic reasoning stands as a formidable gatekeeper for students in their efforts to progress in mathematics and science, and to obtain economic opportunities (Ladson-Billings, 1998; RAND, 2003). Currently, mathematics education research has focused on algebra in order to provide access and opportunities for more students. There is now a growing…

The aim of this series of four articles is to look critically, and in some detail, at the primary strategy approach to written calculation, as set out on pages 5 to 16 of the "Guidance paper" "Calculation." The underlying principle of that approach is that children should use mental methods whenever they are appropriate, whereas for calculations…

This article discusses the difficulties preservice teachers experience when they try to make sense of the standard long-division algorithm, describes a realistic context that we have found productive in helping our students think about why the algorithm works and the role of place value in the algorithm, and suggests the applicability of this…

The objectives of this study were to (1) evaluate group differences in specific arithmetic competencies among students with various types of learning difficulties (LD) and (2) to examine the influence of attention behaviors on possible group differences. Participants were a community sample of 291 third- and fourth-grade students with reading…

Presents a defense of traditional teaching methods during the progressive education movement. Reprint from April 1931 "Elementary School Journal." (JMB)

This textbook is a course in mental arithmetic that is essentially based on the object-lesson plan. It is believed that the pupil in the primary school can more readily acquire a familiarity with numbers from the use of objects and pictures than from an uninterrupted drill on the tables. It also includes suggestions for teachers how to use the…