The author was asked to develop a list of actions that teachers could take to build students' mathematics abilities. Too many students fail to graduate and fail to pass state assessments as a result of weak mathematics skills. Even many students who do graduate leave high school lacking sufficient understanding of mathematics to pass college…

Extending a recent paper by Derek Holton, we show how to represent the algorithm for the Frog Problem diagrammatically. This diagrammatic representation suggests a simpler proof of the symmetrical case (equal numbers of frogs of each colour) by allowing the even and odd cases to be treated together. It also provides a proof in the asymmetrical…

Elementary school students often misinterpret the equal sign (=) as an operational rather than a relational symbol. Such misunderstanding is problematic because solving equations with missing numbers may be important for the development of higher order mathematics skills, including solving word problems. Research indicates equal-sign instruction…

This study determined the working memory (WM) components (executive, phonological short-term memory [STM], and visual-spatial sketchpad) that best predicted mathematical word problem-solving accuracy in elementary schoolchildren (N = 392). The battery of tests administered to assess mediators between WM and problem-solving included measures of…

The aim of this study was to investigate the effect of the Scratch and Lego Mindstorms Ev3 programming activities on academic achievement with respect to computer programming, and on the problem-solving and logical-mathematical thinking skills of students. This study was a semi-experimental, pretest-posttest study with two experimental groups and…

The purpose of this research is to develop a hands-on spatial geometry learning system to facilitate the learning of geometry. The development of this system was based on Duval's four critical elements of geometric learning: perceptual apprehension, sequential apprehension, operative apprehension, and discursive apprehension. The system offers…

Gaps between science, technology, engineering, and mathematics (STEM) education and required workplace skills have been identified in industry, academia, and government. Educators acknowledge the need to reform STEM education to better prepare students for their future careers. We pursue this growing interest in the skills needed for STEM…

In recent years, learning progressions (LPs) have captured the interest of educators and policy makers. There have been numerous efforts to develop LPs aligned to college and career readiness standards, to unpack these standards, and to provide more clarity on the pathways students follow to reach them. There is great variation, however, in the…

We conducted a qualitative research of case studies based on think-aloud protocols. The aim was to carry out in-depth analyse secondary students' cognitive difficulties appearing in early stages of transfer processes in problem-solving. The task was to relate several source problems to a target problem, in order to solve it effectively. Source and…

To learn from an error, students must correct the error by engaging in sense-making activities around the error. Past work has looked at how supporting collaboration around errors affects learning. This paper attempts to shed further light on the role that collaboration can play in the process of overcoming an error. We found that good…

The Math Forum Problems of the Week Library is designed to leverage the power of interactive technology to hold student interest while increasing their success as strategic thinkers. The Math Forum Library is an online source of non-routine challenges in which problem solving and mathematical communication are key elements of every problem. This…

Sixth grade students come to MS 331 with strong mathematics backgrounds from elementary school. Nevertheless, students often come with a dearth of skills when performing basic math computations. The focus of this study is to investigate the use of the 24 Game in quickening the ability of sixth graders to perform basic computations. The game…

A number of schools have recently introduced new courses dealing with various aspects of iteration theory or at least have found ways of including topics such as chaos and fractals in existing courses. In this note, we will consider a family of functions whose members are especially well suited to illustrate many of the concepts involved in these…

The study of the number of intersection points of y = a[superscript x] and y = log[subscript a]x can be an interesting topic to present in a single-variable calculus class. In this article, the authors present a classroom presentation outline involving the basic algebra and the elementary calculus of the exponential and logarithmic functions. The…

The purpose of this study is to investigate teachers' understanding and knowledge of computational estimation, and teaching practice toward to computational estimation. There are six fifth-grade elementary teachers who participated in this study; three teachers with mathematics/ science major and three teachers with non-mathematics/science major.…