In school, at least in the US, we were taught to multiply by hand according to a standard algorithm. Most people find that algorithm difficult to use, and many children fail to learn it. We propose a new way to make sense of this difficulty: to treat explicit computation as perceptually supported physical and mental action. Based on recent work in…

The eight mathematical practices explored in the Common Core Math Standards are the following: (1) Make sense of problems and persevere in solving them; (2) Reason abstractly and quantitatively; (3) Construct viable arguments and critique the reasoning of others; (4) Model with mathematics; (5) Use appropriate tools strategically; (6) Attend to…

There have been calls in the literature for reforms to assessment to enhance student learning (Shepard, 2000). In many instances, this refers to the need to move from traditional assessment procedures that are characterized as content-heavy, summative, and norm-referenced approaches to more constructivist and student-centred approaches, often…

Could problem solving be the object of teaching in early education? Could appropriate teaching interventions develop to scaffold children's efforts to solve problems? These were the central questions of this article. The sample consisted of 18 children attending public pre-school in Cyprus. The problem they were asked to solve was to find all…

The author presents a strategy for helping students with emotional and behavioral disorders become more proficient at solving math word problems. Math word problems require students to go beyond simple computation in mathematics (e.g., adding, subtracting, multiplying, and dividing) and use higher level reasoning that includes recognizing relevant…

The purpose of this study was to explore instructors' perspectives on the effect of using pen-based technology in the online mathematics courses and understand instructors' experiences in online mathematics teaching with pen-based technology. In this study, two instructors who taught online mathematics courses in fourteen weeks used digital pen as…

The study was a quasi-experimental research project conducted to investigate the effect of performance assessment-driven instructions on the attitude and achievement in mathematics of senior high school students in Ghana at Ghana National College in Cape Coast. Two Form 1 science classes were used for the study and were assigned as experimental…

The Dodgson winner seems very intuitive and reasonable: when a Condorcet winner doesn't exist, pick the candidate that is closest, under some measure, to being a Condorcet winner. However, Dodgson's method is computationally intensive. Approximate methods are more tractable. By placing these methods in a geometric framework, we can understand how…

This article illustrates the power of Bloom's revised taxonomy for teaching, learning, and assessing in aligning our curriculum expectations and our assessment tools in multivariable calculus. The particular assessment tool considered involves a common matching problem to evaluate students' abilities to think about functions from graphical and…

Part of the power of algebra is that it provides students with tools that they can use to model a variety of problems and applications. Such modeling requires them to understand patterns and choose from a variety of representations--numeric, graphical, symbolic--to construct a model that accurately reflects the relationships found in the original…

After learning how to trace the principal rays [Fig. 1(i)] through a thin lens in order to form the image in the conventional way, students sometimes ask whether it is possible to use other rays emanating from the object to form exactly the same image--for example, the two arbitrary rays shown in Fig. 1(ii). The answer is a definite yes, and this…

Problems in projectile motion are a time-honored staple of high school and even first-year university physics. They can become confusing for some students, yet boring for the stronger students. Herein we present two alternative approaches to such questions, one we call "breaking down gravity," which makes these questions easier to solve, and the…

Children playing in damp sand invariably try to make a tower or a tunnel. By providing experiences with a variety of materials, alone and together, teachers set up the conditions for children to learn through their senses and ensure that a class approaches a topic with a common set of experiences to build on. Learning about the properties of…

The nature of vocational education needs has changed. In authentic vocational classroom contexts, there is a rising need to develop new ways to integrate ongoing and overlapping processes of students' personal learning environments and collaborative knowledge construction. However, there is currently very little knowledge about how teachers…

International Financial Reporting Standards (IFRS) are accepted throughout the world, particularly in the European Union, Australia, New Zealand and Canada. Emerging economies are also are aligning their practices with IFRS. Historically, the USA has been cautious about accepting IFRS. However, following acceptance of IFRS worldwide, the US…