Surveys covering mathematical knowledge for teaching and teachers’ professional learning opportunities were administered to 461 middle school mathematics teachers in both 2005 and 2006. Results indicate that that teachers’ mathematical knowledge might have improved during this time period, and improvements may be linked to specific forms of professional learning. However, teacher-learning opportunities appear short and fragmented.

This ethnographic study explores the role that implicit and explicit questions played in encouraging mathematical thinking in a diverse elementary mathematics class taught by a reform-oriented teacher in an urban school.

This article explores the intersection of teacher learning and collegial interactions, reporting findings from a highly collaborative, improvement-oriented high school mathematics department. The author identifies discourse structures important to the representation and exploration of problems of practice.

This research examines the relationship between mathematics and science coursework patterns among high school graduates using data from the 2000 High School Transcript Study.

This inquiry raises questions about the manner in which the No Child Left Behind Act aims to improve mathematics education through continued reliance on standardized testing and mandated use of scientifically based teaching practices. Specifically, it is argued that this approach is tied to assumptions about intellectual ability and achievement that precipitated the dividing practices used to justify differential access to mathematics learning almost a century ago. An examination of so-called objective and scientific approaches to school mathematics suggests the need for more earnest reflection about the particular path toward educational progress privileged by this legislation.

The article describes results of a qualitative study of an elementary school as it enacted a variety of strategies to help students raise scores on a newly required state test designed to serve as an accountability tool.

Observations of the first days of school in eight sixth-grade classrooms identified three different classroom environments.

This study examined the effects of early acceleration of students in mathematics on the development of their attitude and anxiety toward mathematics across junior and senior high school, using data from the Longitudinal Study of American Youth (LSAY).

Drawing upon a teacher survey, this article proposes that successful instructional policies are themselves instructional: teachers’ opportunities to learn about and from policy influence both their practice and, at least indirectly, student achievement.

Drawing on the Longitudinal Study of American Youth, this study examines the effects of individual characteristics and different types of parental involvement on student participation in advanced mathematics.

The author evaluates and extends the literature demonstrating that gender differences on standardized tests of quantitative reasoning may reflect underlying differences in cognitive processing that might be explained in part by socialization patterns inherent in American culture.

Background to the key notions underlying the National Council of Teachers of Mathematics (NCTM) Curriculum and Evaluation Standards for School Mathematics

One mathematician's view of the NCTM standards document

A discussion of the danger of losing the essence of mathematics

The author explores further the areas of agreement and disagreement across the articles about the general issue of active learning, teaching for understanding, or, at the risk of raising a red flag, constructivism.

The authors have selected three trends as points of discussion for this special section of the Record featuring expert commentary on the condition of education in the nation. The trends address the following issues: (1) appraising the state of academic achievement among American elementary and secondary students, (2) improving the quality of the nation’s K-12 faculty, and (3) the march toward the expansion of higher education for all students.

One of two articles on academic achievement, this article discusses the performance of U.S. students on mathematics and science achievement tests compared to students in other countries. Recent data show they are performing better. This commentary examines the importance of meeting certain research conditions before drawing conclusions about achievement trends.

This article presents data on trends in mathematics and science achievement among U.S. students according to the National Assessment of Educational Progress and various international studies.

An examination of curriculum, instruction, and organizational formats in multi-grade and single-grade mathematics classes

This article focuses on opportunity-to-learn standards, which define a set of conditions that schools, districts, and states must meet in order to ensure students an equal opportunity to meet expectations for their performance.

The general tendency in the teaching of elementary mathematics at the present time seems to point first, toward the introduction of problems which have to do with the conditions of life in the sections where the pupils live; second, toward a kind of drill which shall make for greater speed and accuracy in the four fundamental processes; third, toward enlisting a broad-minded and self-dependent attitude in the pupil's approach to problems; and fourth, toward a familiarity with numbers through their daily use in manual arts and games.

The evolution of the teaching of primary arithmetic extends over a period of about two hundred years, although numerous sporadic efforts at teaching the science of number to young children had been made long before the founding of the Francke Institute at Halle.

OUTLINE PAGE I. THE SCOPE OF THE STUDY 9 1. Function of the Study to Trace General Tendencies 9 2. Teaching Method is a Mode of Presentation 9 3. Distinct Uniformities Exist Among its Variations 10 4. The Methods of Public Elementary Schools are Representative 10 5. Elementary Mathematics is Mainly Arithmetic 11

It is the function of this study to convey some notion of the methods employed in teaching mathematics in the first six grades of the American elementary school.

It has been suggested that all teaching methods represent adjustments to several variable factors in the school-room situation. Teaching method is never, or should not be, just one thing.

At the very beginning, it was suggested that many factors enter into the nature of our teaching methods. There was occasion to show the influence of varying aims on the spirit and manner of instruction, for differing aims inevitably amend any presentation of facts, in school or out.

The Tendency toward Shortening the Time Distribution Several decades ago arithmetic, as a formal subject, was begun in the first school year and continued throughout the grades to the last school year. This is no longer a characteristic condition, much less a uniform one.

THE DISTRIBUTION OF OBJECTIVE WORK Object Teaching is generally current: The use of objects in teaching arithmetic is current in the elementary school. Particularly is this true in the lowest grades of the school, in primary work.

The existing defects in objective teaching are not restricted to a false placing or distribution. The quality of the teaching use of objects is likewise open to serious criticism.

It has already been suggested that there has been considerable waste in the use of objective teaching in the lowest grades; and that the recent tendency has aimed to correct it.