Leading mathematics discussions requires both substantial teaching skill and mathematical knowledge that is usable in teaching. This article focuses on the conceptualization and design of mathematics teacher education that aims to support novices in learning to proficiently enact such teaching practices. Drawing on the elements of Grossman et al.’s (2009) framework for pedagogies of practice in professional education, we describe an approach to analyzing teaching practice that supports the design of teacher education in which novices to learn how to engage in leading a mathematics discussion and simultaneously develop a sense of why the work is done.
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.
In the spirit of deepening our understanding of the social conditions of everyday uses of mathematics, the authors studied 20 diverse families with a middle school child by interviewing family members together at home about their occasions of mathematics use.
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.
Mathematics enables us to fly to the moon, track our genetic codes, create beautiful music, design our cars, build our houses, and contact others around the world almost instantaneously. However, mathematics, that abstract language which helps us to access the relationships in our physical universe(s), is rarely invoked in the service of preparing young people for democratic participation. Deborah Ball and Hyman Bass take on the challenge of situating the highly revered, somewhat mystical discipline of mathematics as a key contributor to concepts of democracy.
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).
The first main section of the chapter, “The evolving content(s) of mathematics instruction,” discusses changes in the mathematics curriculum over the course of the century. The second main section, “On research: psychological, epistemological, and methodological issues,” describes the development of the discipline of research in mathematics education. A concluding discussion, “And next?,” discusses some of the evolutionary needs and pressures that may shape mathematics education in the early parts of the twenty-first century.
Our goal in this chapter is to provide an accurate characterization
of the current state of elementary and middle school mathematics education
in the United States and to highlight “crossroads” points where
crucial reevaluations are needed.
As one constructivist remarked, “In summary
then the term ‘constructivism’ appears to be fashionable, mostly
used loosely with no clear definition of the term, and is used without
clear links to an epistemological base.” Although there are countless
thousands of constructivist articles, it is rare to find ones with fully
worked out epistemology, learning theory, educational theory, or ethical
and political positions. This makes appraisal difficult.
In this chapter, we examine the construction of mathematical knowledge in classroom teaching and learning.
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.
Some mathematics should be taught to all students, but an adequate
presentation of a "common curriculum" for mathematics cannot
consist of a list of topics to be covered, however extensive and
carefully prepared. I use the word "curriculum" as a course of study,
its contents, and its organization, and my task in this chapter is to
consider four questions which shape an outline for a common curriculum
for mathematics. The questions to be examined are:
1. What does it mean to know mathematics?
2. Who decides on the mathematical tasks for students and for what
3. What should be the principles from which a common curriculum
can be built?
4. For this yearbook, how should individual differences be considered?
One of the most valuable types of intellectual talent for both
society and the individual is mathematical reasoning ability. It
undergirds much of current achievement in technology, science,
and social science. Usually this ability is poorly assessed by in-school
mathematics tests, because often they consist of a mixture of computation,
learned concepts, and reasoning. Also, it is difficult to
measure mathematical reasoning ability until the young student has
acquired enough knowledge of elementary general mathematics
with which to reason. The basic content of the test items must be
fairly well known so that reasoning can be the chief trait measured.
Both mathematicians and historians are familiar with the fact that
the evolution of counting was an extremely slow process. This has
been ascertained by piecing together remains of ancient cultures
turned up by archeologists and by observing the counting habits of
those primitive societies that still existed during the last century.