"I liked to grab things on the graphics and see it first hand, see what we were doing on the problem. It makes more sense." These words were from a student who completed a series of lessons on lines of best fit. She made this comment after comparing a hands-on approach using a strand of spaghetti with a high-tech approach using a calculator. To…

The present study examines the cognitive activity that is evoked in young children when they are read a picture book that is written for the purpose of teaching mathematics. The focus of this study is to explore the effects of pictures on children's spontaneous mathematical cognitive engagement. The study is based on the assumption that the…

A computer algebra system is used to derive a theorem on the existence of roots of a quadratic equation on any bounded real interval. This is extended to a cubic polynomial. We discuss how students could be led to derive and prove these theorems. (Contains 1 figure.)

When teachers provide students with every opportunity to visually understand a mathematical concept, process, definition, or notation, they allow them to construct and manipulate relevant and useful images in their minds. Visual understanding has a dynamic character that they do not easily develop with alphanumeric symbols alone despite the…

Imagine a mathematics instructor and English instructor sharing an office; scribbled equations litter one desk, snatches of poetry the other. Our learning community, "Space on Earth," grew from conversations in just such an office where we bridged our own disciplinary gap and discovered a shared passion for helping students apply the concepts and…

Mathematics specialists play a significant, meaningful, and integral role in supporting elementary school teachers in this mathematically connected world. These teacher leaders (coaches, resource teachers, math leads, and so on) work closely with all members of the school community--students, teachers, and administrators--and have a range of…

There has been an increasing interest in and hence a growing number of research studies on content and language integrated learning (CLIL) over the past two decades. One of the on-going debates in CLIL is on bilingualism versus monolingualism, or the role of the first language (L1) in subject teaching. So far, very few research projects have been…

In this article we examine how students engage in learning mathematical concepts in the middle grades of an urban public school in the Southwestern United States. In the context of a 3-year National Science Foundation-funded longitudinal study of the development of students' rational number understanding, we encountered differing levels of…

It is a bitter reality that the curricula and traditional pedagogy prevailing in public schools of Pakistan in general and Sindh in particular do not incorporate the algebraic concepts properly. Both the content and the presentation therein cannot be considered up to the mark, thereby making "Algebra" a tough and dry subject. This…

Professional teachers can guarantee the progress and the promotion of society because fostering the development of next generation is up to them and depends on their professional knowledge which has two kinds of sources: content knowledge and teaching skill. The aim of the present research was studying the effect of integrating problem-based…

Although much educational research has investigated the relative effectiveness of different educational interventions and policies, little is known about the absolute net benefits of K-12 schooling independent of growth due to chronological age and out-of-school experience. The nearly universal policy of age tracking in schools makes this a…

In the run-up to 2015 and beyond, the global education community must work together to improve learning and propose practical actions to deliver and measure progress. In response, UNESCO through its Institute for Statistics (UIS) and the Center for Universal Education (CUE) at the Brookings Institution have co-convened the Learning Metrics Task…

"Bars, Lines, & Pies" is a dynamic math program designed to build graphing skills in students, while also showing them the relevance of math in their lives. Developed by The Actuarial Foundation along with Scholastic, the graphing lessons and activities involve engaging, real-world examples about the environment and recycling. In these lessons,…

This brief is directed to researchers and adds to the research base about instructional practices that are related to student achievement. Additional evidence on these relationships can suggest specific hypotheses for the future study of such instructional practices, which, in turn, will provide research evidence that could inform professional…

Algebra is the language that must be mastered for any course that uses math because it is the gateway for entry into any science, technology, engineering, and mathematics (STEM) discipline. This book fosters mastery of critical math and algebraic concepts and skills essential to all of the STEM disciplines and some of the social sciences. This…