This dissertation involved a series of training sessions where parents from a Title I middle school participated in the learning and practice of Algebra Readiness skills. The project was based on a series of six weekly trainings for parents to learn home-based activities to increase their child's Algebra Readiness. I administered an initial…

In this paper the augmentation of worked examples with animations for teaching problem-solving skills in mathematics is advocated as an effective instructional method. First, in a cognitive task analysis different knowledge prerequisites are identified for solving mathematical word problems. Second, it is argued that so called hybrid animations…

The study focused on the relationship of English proficiency and math performance in a sample of high school students, including 47% English language learners (ELLs). Data sources included state math test scores, study-specific pre- and posttest scores, problem solving in an online math tutorial, and responses to a self-report assessment of…

Much like the shifting landscape in K-12 educational technology, this year's "Technology Counts" issue is changing to address the challenges of covering schools in the digital age. The 2010 report does not issue state report cards or state policy reports. Instead, the report takes a more district- and school-level look at educational…

In the Netherlands, as in many other countries, the algebraic expertise of students graduating from secondary education is an issue. The use of digital tools for algebra education is expected to change epistemologies, activity structures and student achievement. Therefore, a study was set up to investigate in what way the use of ICT in upper…

This article presents lesson plans that use downloadable spreadsheet tools that relate symbolic and graphical representations of functions. Instructions and a template allow readers to create personalized tools without programming. (Contains 14 figures.)

Students learn to use linear algebra covered in their first algebra course to design mobiles like those created by artist Alexander Calder. (Contains 17 figures and 2 tables.)

In the context of a three-year professional development program in mathematics, practicing elementary teachers persistently engaged in collaborative inquiry and reflection to build connected meanings for slope. One teacher invented a compelling representation for slope as a process of repeated addition, using Cuisenaire rods, based on teachers'…

We report a dissociation between higher order mathematical ability and language in the case of a man (SO) with severe aphasia. Despite severely impaired abilities in the language domain and difficulties with processing both phonological and orthographic number words, he was able to judge the equivalence of and to transform and simplify…

This paper explores the development of the method of partial fraction decomposition from elementary number theory through calculus to its abstraction in modern algebra. This unusual perspective makes the topic accessible and relevant to readers from high school through seasoned calculus instructors.

The article deals with issues concerning the abductive-inductive reasoning of 42 preservice elementary majors on patterns that consist of figural and numerical cues. We discuss: ways in which the participants develop generalizations about classes of abstract objects; abductive processes they exhibit which support their induction leading to a…

This article presents a project for a differential equations class using an inverse problem based on the second order differential equation that models an electrical circuit. (Contains 2 footnotes.)

Sometimes it becomes a matter of natural choice for an observer (A) that he prefers a coordinate system of two-dimensional spatial x-y coordinates from which he observes another observer (B) who is moving at a uniform speed along a line of motion, which is not collinear with A's chosen x- or y-axis. It becomes necessary in such cases to develop…

This article describes concepts exhibited by seventh-grade prealgebra students as they approached algebraic-thinking tasks. (Contains 7 Figures.)

Two related sequences of definite integrals are considered. By mixing hand-work, computer algebra system assistance and websurfing, fine connections can be studied between integrals and a couple of interesting sequences of integers. (Contains 4 tables.)