While proof is central to mathematics, difficulties in the teaching and learning of proof are well-recognised internationally. Within the research literature, a number of theoretical frameworks relating to the teaching of different aspects of proof and proving are evident. In our work, we are focusing on secondary school students learning the…

Although research on the effectiveness of differentiated and enriched instruction in improving the achievement of diverse students is still emerging, some studies suggest that students in academically diverse classrooms benefited academically from differentiated learning experiences. The primary research question explored in this study was…

"Achieving Fluency" presents the understandings that all teachers need to play a role in the education of students who struggle: those with disabilities and those who simply lack essential foundational knowledge. This book serves teachers and supervisors by sharing increasingly intensive instructional interventions for struggling students on…

We propose the development of a "population" of high-quality assessment tasks that cover the performance goals set out in the "Common Core State Standards for Mathematics." The population will be published. Tests are drawn from this population as a structured random sample guided by a "balancing algorithm."

Taiwanese students consistently rank near the top on international exams on mathematics and science. In 2007, Taiwan recorded the highest TIMSS math score for eighth grade. The central education agency in Taiwan publishes detailed mathematics curriculum guidelines, which textbooks and national exams follow closely. In May each year, all ninth…

This article describes the process of development of assessment instruments for a three-year longitudinal comparative study that focused on evaluating American high school students' mathematics learning from two distinct approaches to content organization: curriculum built around a sequence of three full-year courses (Algebra 1, Geometry, and…

Children who learn math fundamentals in preschool and kindergarten have the best chance of later achievement in school--but too often, children don't get the effective early math instruction that makes all the difference. Now there's a core early childhood textbook that helps current and future educators teach the most critical math concepts to…

New Mexico Mathematics Content Standards, Benchmarks, and Performance Standards identify what students should know and be able to do across all grade levels, forming a spiraling framework in the sense that many skills, once introduced, develop over time. While the Performance Standards are set forth at grade-specific levels, they do not exist as…

The purpose of this paper was to describe the process of development of assessment instruments for the Comparing Options in Secondary Mathematics: Investigating Curriculum (COSMIC) project. The COSMIC project was a three-year longitudinal comparative study focusing on evaluating high school students' mathematics learning from two distinct…

This book provides a resource for mathematics teachers to understanding the National Council of Teachers of Mathematics' (NCTM) standards and implementing these standards in their teaching. Five standards are overviewed: (1) number and operation; (2) algebra; (3) geometry; (4) measurement; and (5) data analysis and probability. Lesson plans are…

This book provides a resource for mathematics teachers to understanding the National Council of Teachers of Mathematics' (NCTM) standards and implementing these standards in their teaching. Five standards are overviewed: (1) number and operation; (2) algebra; (3) geometry; (4) measurement; and (5) data analysis and probability. Lesson plans are…

This book provides a resource for mathematics teachers to understanding the National Council of Teachers of Mathematics' (NCTM) standards and implementing these standards in their teaching. Five standards are overviewed: (1) number and operation; (2) algebra; (3) geometry; (4) measurement; and (5) data analysis and probability. Lesson plans are…

This book provides a resource for mathematics teachers to understanding the National Council of Teachers of Mathematics' (NCTM) standards and implementing these standards in their teaching. Five standards are overviewed: (1) number and operation; (2) algebra; (3) geometry; (4) measurement; and (5) data analysis and probability. Lesson plans are…

This book provides a resource for mathematics teachers to understanding the National Council of Teachers of Mathematics' (NCTM) standards and implementing these standards in their teaching. Five standards are overviewed: (1) number and operation; (2) algebra; (3) geometry; (4) measurement; and (5) data analysis and probability. Lesson plans are…

This book provides a resource for mathematics teachers to understanding the National Council of Teachers of Mathematics' (NCTM) standards and implementing these standards in their teaching. Five standards are overviewed: (1) number and operation; (2) algebra; (3) geometry; (4) measurement; and (5) data analysis and probability. Lesson plans are…