In this paper we investigated the contribution of a dynamic testing procedure, including multiple graduated prompts protocols, in identifying differences in need for instruction of second grade children (N = 120) with arithmetic difficulties. The training was adaptive and prompts were provided according to one of six protocols, each focusing on a…

This study describes the word-problem solving instruction of one elementary special education teacher of Latino English Language Learners (Latino ELLs) with mathematics learning disabilities (MLD) in an urban school setting. This study was situated in a culturally responsive teaching framework. In investigating this instruction with Latino ELLs…

As the use of educational technology becomes more ubiquitous, an enormous amount of learning process data is being produced. Educational data mining seeks to analyze and model these data, with the ultimate goal of improving learning outcomes. The most firmly grounded and rigorous evaluation of an educational data mining discovery is whether it…

This paper reports on a study that investigated the ways that young children interact with discrete programmable digital toys in a free play setting. One intention was to see whether this interaction would address some of the requirements of the Digital Technologies subject in the Australian Curriculum. The study was implemented in two phases in…

What is important for citizens to know and be able to do? The OECD Programme for International Student Assessment (PISA) seeks to answer that question through the most comprehensive and rigorous international assessment of student knowledge and skills. The PISA 2015 Assessment and Analytical Framework presents the conceptual foundations of the…

Collaborative and individual learning are both frequently used in classrooms to support learning. However, little research has investigated the benefits of combining individual and collaborative learning, as compared to learning only individually or only collaboratively. With our study, we address this research gap. We compared a combined…

A continuous representation of a hybrid method with three "off-step" points is developed via interpolation and collocation procedures, and used to obtain initial value methods (IVMs) for solving initial value problems. The IVMs are assembled into a single block matrix equation which is convergent and A-stable. We note that accuracy is improved by…

Many optimization problems can be solved without resorting to calculus. This article develops a new variational method for optimization that relies on inequalities. The method is illustrated by four examples, the last of which provides a completely algebraic solution to the problem of minimizing the time it takes a dog to retrieve a thrown ball,…

For a suitably nice, real-valued function "f" defined on an open interval containing [a,b], f(b) can be expressed as p[subscript n](b) (the nth Taylor polynomial of f centered at a) plus an error term of the (Lagrange) form f[superscript (n+1)](c)(b-a)[superscript (n+1)]/(n+1)! for some c in (a,b). This article is for those who think that not…

The title question has at least two natural answers, one "global" and one "local." Global: "when they can be made to coincide by a rigid motion of the whole plane;" local: "when there is a one-to-one distance preserving mapping of one onto the other." Self-evidently global implies local. We show that in fact these different notions lead to…

Separate a three-digit number into its component digits. After raising each digit to the third power and computing the sum of the cubes, determine how often the original number reappears. Modular arithmetic is used to reduce the number of potential solutions to a more manageable quantity. (Contains 4 tables.)

In this note, we present an interesting approach to sum subseries in closed form. This approach seems to be not widely known and remains under-appreciated. Our study will lead to the discovery of results some of which have been known for a long time, some which were found only recently, as well as those which appear to be new.

This article analyzes the findings from an 18-section experiment studying the effect of homework-completion tutoring on community college students' remedial mathematics performance. The experiment involved 529 students registered for two remedial math courses: math skills and algebra. For each course, the experiment studied nine sections: three…

Edited by National Math Panel veteran Russell Gersten with contributions by all of the country's leading researchers on RTI and math, this cutting-edge text blends the existing evidence base with practical guidelines for RTI implementation. Current and future RTI coordinators, curriculum developers, math specialists, and department heads will get…

School librarians occupy a space rich in resources and numeracy. They are thus positioned to offer resources and standards that promote inquiry, drawing conclusions, real world connections, and aesthetic enjoyment. Part of their task with teachers is to create those connections with curriculum and students. School librarians' collections are aswim…