The ability to solve mathematical problems has been an interesting research topic for several decades. Intuition is considered a part of higher-level thinking that can help improve mathematical problem-solving abilities. Although many studies have been conducted on mathematical problem-solving, research on intuition as a bridge in mathematical…

This volume provides an in-depth, comparative examination of how primary mathematics education is influenced by national education reform, policy, local resources, and culture in three different countries. By drawing on first-hand observations and interviews, as well as analysis of policy documents and learning resources, the book considers the…

This latest book in the bestselling Mathematics Recovery® series gives mathematics educators a complete research-based framework for assessment, instruction and intervention in whole number arithmetic across grades K to 5. The integrated set of classroom tools includes: (1) Nine carefully designed schedules of assessment tasks; (2) Nine models of…

"The Effectiveness of Mathematics Teaching in Primary Schools: Lessons from England and China" provides a unique insight into the mathematics classrooms of these two countries and arrives at a time when the world is eager to know how Chinese learners consistently excel at learning mathematics and other core subjects. Showcasing the kinds…

Over the past several years, research teams have developed observational instruments to measure the quality of teachers' instructional practices. Instruments such as Framework for Teaching (FFT) and the Classroom Assessment Scoring System (CLASS) assess general teaching practices, including student-teacher interactions, behavior management, and…

Teaching English language learners has long presented challenges for teachers tasked with bringing these students to a level of language comprehension comparable to that of native speakers. These challenges and issues can lead to difficulty comprehending core academic topics for those learning the English language. "Optimizing Elementary…

This guidance report focuses on the teaching of mathematics to pupils in Key Stages 2 and 3. It is not intended to provide a comprehensive guide to mathematics teaching. We have made recommendations where there are research findings that schools can use to make a significant difference to pupils' learning, and have focused on the questions that…

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…

This fourth book in the Mathematics Recovery series equips teachers with detailed pedagogical knowledge and resources for teaching number to 7 to 11-year olds. Drawing on extensive programs of research, curriculum development, and teacher development, the book offers a coherent, up-to-date approach emphasizing computational fluency and the…

American students continue to struggle on measures of student achievement. This study employed Hierarchical Linear Modeling to estimate a two-level model and examine the influences of calculator use and teachers' instructional practices on student achievement in mathematics amongst first-grade students. The outcome variable was mathematics test…

This article presents a case study in which researcher-practitioner collaboration took place to promote effective use of technology in an urban elementary school mathematics classroom. Data were primarily gathered through classroom observations and interviews. The aim of this study was twofold. First, to increase our understanding of the effects…

In this Appendix, we provide details about the data used for the current study, the curricula used in the classrooms from which data were collected, and the current study's methodological approach. (Contains 14 tables and 5 footnotes.)[For full report, see ED544189.]

A logical analysis of word problems provides an hypothesis about the kinds of knowledge that may be necessary for solving multi-step word problems. This hypothesis is that knowledge of the overall pattern of relations in a problem may function in problem-solving apart from knowledge of the particular entities and the local relations in which they…

Fourth graders (n=204) and seventh graders (n=185) were given a prior-knowledge inventory, a graph test, and reading and achievement tests during four testing sessions. Significant predictors for graph comprehension were identified for both grade four and grade seven students. The results suggest that children should be involved in graphing…

A framework is presented for characterizing competence for cognitive tasks, with a detailed hypothesis about competence for counting by typical 5-year-old children. It is proposed that competence has three main components that are called conceptual, procedural, and utilizational competence. Conceptual competence, which is discussed in greatest…