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February 2004
| Volume 61 | Number 5
Improving Achievement in Math and Science
Love and Hate for Math and Science
Marge Scherer
A Vision for Mathematics
William H. Schmidt
A common, coherent, and challenging curriculum can transform mathematics education in the United States. The No Child Left Behind Act's vision is to provide rigorous and demanding subject matter content for all students. As a crucial subject area, mathematics is vital to this effort. How can educators change the curriculum of mathematics to make it rigorous and accessible to all students? The author reviews the Third International Mathematics and Science Study (TIMSS) data showing significant curricular differences between the United States and other countries, especially in the degrees of standardization, coherence, and challenge. He examines briefly the role of teachers, noting that differences in subject matter background account for significantly different levels of achievement in different countries. The author argues that even the best teachers need an effective curriculum to be effective and that such a curriculum does not substantially threaten the U.S. commitment to local control of schools.
Improving Mathematics Teaching
James W. Stigler and James Hiebert
The TIMSS Video Study 1999 documents typical teaching practices in mathematics classrooms in seven countries: the United States, Japan, Australia, the Netherlands, the Czech Republic, Hong Kong, and Switzerland. By collecting and analyzing hundreds of videotapes of classroom process used by random samples of teachers in these countries, the researchers created a picture of what average teaching looks like in the different countries. This article reviews findings from the new video study and the original 1995 video study to arrive at several recommendations for improving mathematics instruction. The video studies showed that teaching methods within each country were strikingly homogeneous, but the differences among countries were equally striking. The researchers discuss two basic categories of math problems: those that call on students to use basic computational skills and procedures, and those that focus on concepts and connections among mathematical ideas. What was important was not just the percentage of each type of problem presented in math classes, but also the way in which teachers and students worked through the problems. Teachers in the United States turned most math problems into procedural exercises—even those problems that were intended to focus on making connections. Student achievement tended to be higher in countries in which making connections problems were implemented as they were intended.
A Deeper Look at Lesson Study
Catherine Lewis, Rebecca Perry and Jacqueline Hurd
Educators often attribute effective mathematics and science teaching in Japan to lesson study, a process in which teachers collaboratively study actual classroom lessons in view of improving the quality of their instruction. Teachers in the United States have few opportunities to observe their colleagues teaching lessons, yet the authors contend that the strategy is rich in possibilities for improving current mathematics and science instruction. Citing results from a successful teacher-led lesson study initiative, the authors show how teachers can benefit from increased knowledge of subject matter, increased knowledge of instruction, increased ability to observe students, stronger collegial networks, stronger connection of daily practice to long-term goals, stronger motivation and sense of efficacy, and improved quality of available lesson plans. The authors conclude that lesson study goes far beyond simply improving a lesson—it challenges teachers to improve their classroom instruction.
What Is High-Quality Instruction?
Iris R. Weiss and Joan D. Pasley
To assess the quality of mathematics and science instruction in U.S. classrooms, researchers at Horizon Research observed more than 350 representative lessons in grades K-12 and conducted follow-up interviews with teachers to explore their instructional decision making. Observers classified only 15 percent of the lessons as high in quality, 27 percent as medium, and 59 percent as low. The quality did not depend on whether the teacher used a “reform-oriented” approach or a traditional approach to instruction. Lessons rated as very effective shared some common characteristics: high student engagement with worthwhile content; a culture that combined respect and rigor; equal access for all students: effective questioning; and assistance in making sense of the content.
The Dangerous Intersection Project... and Other Scientific Inquiries
Kathleen Conn
Science instructed based on problem-solving activities and case studies can motivate students to seek out science information and become partners in their own learning. The author describes how teachers can use problem-solving lessons to stimulate students' need to know. For example, student teams in a physics class on kinematics and movement investigated potential improvements in dangerous road intersections, using physics equations to determine how fast a car would accelerate down a specific hill, what the safe turning radius for an exit ramp would be, and so on. The author provides additional examples, describes the problem-solving process, and asserts that “when teachers use the curriculum to suggest real-world problems, the curriculum comes to life and becomes rich in meaning.”
What Do Kids Know—and Misunderstand—About Science?
Cynthia Crockett
Children build their initial understandings about the world on primitive or incorrect information. On the basis of their limited experiences and their imaginations, children strive to construct usable ideas—those that help them explain events or phenomena. The science teacher's role, writes Crockett, is to help students identify their own ideas, recognize the ideas as something they have constructed themselves, and then challenge and modify those ideas. The author recommends that teachers make time for active classroom conversations and discussions to recognize and challenge student's misconceptions about science. She also discusses the limits of multiple-choice tests in revealing student misconceptions and conveying an accurate picture of student understanding. She describes a wide-scale study conducted by the Science Education Department at the Harvard-Smithsonian Center for Astrophysics, which found that the extent to which common misconceptions were included in test item response options determined the chances that students would select the correct answer. This finding demonstrates that, unless test items are carefully constructed, students will be able to answer correctly without really understanding the tested concepts.
Teaching Number Sense
Sharon Griffin
What is number sense? How does it develop? How can we teach number sense to students who start school without it? The author discusses recent research in the learning sciences that has found answers to each of these questions and offers new perspectives on what number sense is and how to teach it. She describes how Number Worlds, a program based on research and specifically designed to teach number sense, provides opportunities for making connections among the three worlds of math—real quantities, counting numbers, and formal symbols—and provides both a social context in which to explore and discuss the concepts and an appropriate sequence from prekindergarten to 2nd grade.
Marvelous Math!
Alfred S. Posamentier
If math is so wonderful, why are students the last to know? The author suggests enriching mathematics classrooms with fascinating mathematical facts and problems that will motivate both teachers and students. Take students on a journey into the past to discover the history of place value or pi. Show them the unexpected patterns and intriguing perspectives that make math truly marvelous.
The Networked Classroom
Jeremy Roschelle, William R. Penuel and Louis Abrahamson
In the typical mathematics or science class, a few students routinely answer most of the questions and share their work on a problem. Teachers rarely hear from the shy and less confident students. The networked classroom—handheld devices connecting to the teacher's laptop computer and integrated with a shared screen—can change all that. The authors describe recent research on how classroom networks can enhance communication in the classroom and improve student achievement. They also describe one such system in action.
The Arithmetic Gap
Tom Loveless and John Coughlan
Recent gains in U.S. students' performance on the National Assessment of Educational Progress in math have encouraged many researchers. The authors of this article, however, point out that these gains on the main NAEP mask a significant deficiency in students' mathematics performance: computation skills. The authors' problem-by-problem analysis of the long-term trend NAEP, a better assessment for reflecting change over time, reveals that student performance on computation problems has fallen in the 1990s for all age groups tested. The authors assert that computation skills are important because they lay the foundation for higher math and science learning. They suspect three major factors of contributing to the decline in computation skills: the poor preparation of teachers, the increased reliance on calculators in the early grades, and the math reform standards and curriculums that gained favor in the 1990s.
Why Mathematics Textbooks Matter
Barbara J. Reys, Robert E. Reys and Oscar Chávez
In mathematics classes, textbooks wield real power. They often dictate how teachers should sequence material, suggest the content teachers should teach, and provide activities and instructional ideas for engaging students. According to the authors, the great limitation of the traditional mathematics textbook is its presentation of mathematical ideas as facts to memorize rather than as a web of meaningful relationships. New models of mathematics textbooks, specifically those developed by the National Science Foundation, help correct this flaw. Using a common problem from a mathematics lesson—solving for the volume of a cylinder and a cone—the authors show that the new instructional approach challenges students to think and engages them in discovering the mathematical relationships that are at the heart of the discipline.
Math Acceleration for All
Carol Corbett Burris, Jay P. Heubert and Henry M. Levin
In 1995, South Side Middle School in Rockville Centre, New York, eliminated tracked math classes, adopted a universal accelerated math program starting in 6th grade, and instituted heterogeneous grouping, with dramatic results. After briefly reviewing studies that show the strong correlation of taking advanced math classes in high school and future success, the author reports on her longitudinal study that compared the last three cohorts before universal acceleration was instituted with the first three cohorts to receive universal acceleration. By every measure, all students—regardless of their initial level of achievement, socioeconomic background, or race—benefited from studying accelerated math in heterogeneously grouped classes; they were more likely to take advanced math classes in high school, and they demonstrated generally higher overall mathematics achievement. Because critics often complain that heterogeneous grouping occurs at the expense of high-achieving students, the study paid special attention to the achievement levels of this group. The study shows that high achievers did better, and more students became high achievers. The author concludes that we must not reserve accelerated courses in math and other subjects only for the most fortunate, but rather make rigorous courses accessible and available to all. The potential long-term benefits for students and for society are enormous.
Creating a Differentiated Mathematics Classroom
Richard Strong, Ed Thomas, Matthew Perini and Harvey Silver
Drawing on the work of Carol Ann Tomlinson and Robert J. Marzano, the authors propose a third alternative to differentiation in the mathematics classroom, a hybrid approach that incorporates both standards and differentiation. Students possess different mathematical learning styles. Teachers can facilitate student learning—and differentiate instruction in the mathematics classroom—by using a variety of research-based teaching strategies. The authors also suggest a new format that will make tests more thoughtful and fair.
The Rural Girls in Science Program
Angela B. Ginorio, Janice Fournier and Katie Frevert
Twelve years ago, the Rural Girls in Science Program at the University of Washington set out to foster an interest in science among high school girls in rural areas by showing them the relevance of science to issues in their communities. Targeting underrepresented populations of girls, primarily American Indian and Latina, the program provided a summer institute and mentored long-term research projects. Follow-up evaluations have found that the long-term research projects provided the greatest impetus for continued interest in science among the participants. The authors review the five crucial ingredients of these long-term projects: the research connected directly to the girls' interests and understanding of their communities; engaged them in the entire scientific process; tapped multiple expert resources; involved noncompetitive collaboration; and received the support of teachers, administrators, community members, and families. The authors describe ways to replicate the program and its lasting benefits.
Closing the Minority Achievement Gap in Math
John H. Holloway
Educational Leadership's Themes for 2004–2005
Web Wonders / Improving Achievement in Math and Science
Rick Allen
ASCD Community in Action
Anniversaries: Once More Once
Denis P. Doyle
EL Study Guide
Copyright © 2004 by Association for Supervision and Curriculum Development
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