This book contains a collection of fraction lessons that support curriculum and instruction. The goals of the lessons are to give all students the chance to learn how to: (1) name fractional parts of wholes and sets; (2) represent fractional parts using the standard notation including proper fractions, improper fractions, and mixed numbers, and…

In this research work we explored the nature of 9-12 year old pupils' responses to probabilistic problems with tree diagrams. It was found that a large percentage of pupils failed to respond correctly even to very simple problems that demanded the identification of "possible routes/paths" in figures with tree diagrams/mazes. The results…

For the past three years, we have been investigating the implications of testing on students in elementary mathematics classrooms throughout the state of NJ. Our research, and the work of others, indicates that the impact of testing depends on many factors, not the least of which involves how teachers prepare their students for the test. In this…

The National Assessment of Educational Progress (NAEP) is the nation's only ongoing representative sample survey of student achievement in core subject areas. In 2000, NAEP conducted a national mathematics assessment of fourth-, eighth-, and twelfth-grade students. State-level results were also collected at the fourth and eighth grades within…

Two grade 4 classes provided subjects for a study in the teaching of estimation in computation. A second study was conducted with two grade 5 and two grade 6 classes that supported the idea that estimation in whole number computation can be taught in a short period of time. (MP)

Several types of problems designed to provide opportunities for mathematically able students to do original and analytic thinking at grades 3 and 4 while reinforcing numeration and computation skills are presented. (MP)

Presents an instructional forum in which students and teachers work with researchers to engage in coordinated cycles of planning and implementing instruction and studying forms of students' thinking that emerged in the classroom. Reports on an 8-week teaching and learning study of elementary students' thinking about distribution, including their…

Presents a unit for fourth and fifth grades on fractions and mixed numbers in which students have to decrease and increase the number of servings of different recipes. Describes students' strategies for multiplying fractions, and discusses how the use of a ratio table facilitated their thinking. (ASK)

In this article, the authors would like to look at a range of solutions submitted by Year 4-5 teams in the 2003 "Naturally Mathematical Challenge" to a question that involves no more than the numbers 1 to 6 and possible arrangements of them. In the context of other competition questions and in their elaboration of mathematical process,…

Desiring to better encourage students' thinking and conceptual development, a fourth-grade teacher examines classroom discourse and written work during her students' analysis and description of basic geometric shapes.

This observational study involved literacy and mathematics instruction of 145 teachers in grades 3 through 5 in 20 low-income schools enrolled in the U.S. government's Comprehensive School Reform (CSR) Demonstration program. Observed curriculum and instructional practices were primarily and coherently focused on acquisition of basic facts and…

This booklet summarizes findings from data on mathematics achievement gathered on the 1992 National Assessment of Educational Progress (NAEP) for grades 4, 8, and 12. Approximately 26,000 4th, 8th, and 12th graders in 1,500 public and private schools participated in the national assessment. Information included in the report are: trends in…

A teacher's manual was developed for an elementary level mathematics course in Spanish as part of an immersion program for English speaking children. The Level E manual is designed for grade 4 pupils. Teaching procedures, conceptual and language objectives, vocabulary, structures, and learning activities are included. Activities are designed to…

Mathematics and the use of mathematical thinking should be much more than what has been traditional school arithmetic. Much of the mathematical reasoning can be developed and experienced out of school, particularly in the home. This material contains recording forms and worksheets for activities for the Level Four experiences. Pupils are to…

The major goal of the Comprehensive Instructional Management System for mathematics is to provide the classroom teacher in New York City with a well-structured, objective-based curriculum. This first part of the manual for Level 4 includes modules for 14 topics: (1) numbers and numeration; (2) addition of whole numbers; (3) subtraction of whole…