Teacher research--often called "action research"--is an intentional and systematic inquiry into one's own classroom practice with the goal of improved student learning (Cochran-Smith and Lytle 1993). In this article, the authors present a teacher research project undertaken to improve student understanding of the gas laws in a high…

The NCTM calls for the use of rich tasks that encourage students to apply their own reasoning to problem situations. When students work through algebraic generalization tasks, their reasoning often elicits a variety of strategies (Lannin 2003; Stacey 1989; Swafford and Langrall 2000). Challenges for teachers include facilitating student awareness…

This proceedings volume of InCoTEPD 2018 covers many ideas for handling a wide variety of challenging issues in the field of education. The outstanding ideas dealing with these issues result in innovation of the system. There are many innovation strategies resulting from recent research that are discussed in this book. These strategies will become…

Solving indeterminate algebraic equations in integers is a classic topic in the mathematics curricula across grades. At the undergraduate level, the study of solutions of non-linear equations of this kind can be motivated by the use of technology. This article shows how the unity of geometric contextualization and spreadsheet-based amplification…

This article describes one seventh-grade teacher's classroom efforts to integrate traditional exercises from different content areas to form more robust questions that provide genuine problem-solving opportunities for students. These exercises are illustrated by connecting the Pythagorean theorem with a variety of prealgebra topics. Since the…

Using sticky notes and number lines, a hands-on activity is shared that anchors initial student thinking about absolute value. The initial point of reference should help students successfully evaluate numeric problems involving absolute value. They should also be able to solve absolute value equations and inequalities that are typically found in…

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…

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.)

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…

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…

Teachers use action research in order to improve their teaching and student learning. This action research will analyze students' algebraic reasoning in finding values of variables in systems of equations pictorially and algebraically. This research will look at students solving linear systems of equations without knowing the algebraic algorithms.…

The purpose of this study was to assess algebra and geometric prerequisites skills as incorporated into the Applied Calculus Optimization Problem (ACOP) solution. The difficulties that students encounter in applying algebraic and geometric prerequisites at the early stages of the ACOP solution were identified. The study analyzes errors related to…

Computer algebra systems (CAS) have been around for a number of years, as has dynamic geometry. Symbolic geometry software is new. It bears a superficial similarity to dynamic geometry software, but differs in that problems may be set up involving symbolic variables and constants, and measurements are given as symbolic expressions. Mathematical…