What's happening with calculators in school's today? Are they being used? If so, by what students? How do teachers feel about using calculators in the mathematics program? Should calculators be used on standardized tests? Should use of calculators be integrated into basal mathematics textbooks? Accurate answers to such questions are essential in assessing the current status of calculator use in schools today and more importantly, preparing for calculator usage in the mathematics curriculum during the 1980s.
Robert E. Reys, Barbara J. Bestgen, James F. Rybolt and J. Wendell Wyatt
Robert E. Reys, Barbara J. Reys, Paul R. Trafton and Judy Zawojewski
Edited by Christian R. Hirsch
Robert E. Reys, Barbara J. Reys, Nobuhiko Nohda, Junichi Ishida, Shigeo Yoshikawa and Katsuhiko Shimizu
Four hundred and sixty-six fifth- and eighth-grade Japanese students were administered a computational estimation test. The fifth-grade mean was 7.39 and the eighth-grade mean was 11.15 on the 39-item open-ended test. Interviews with 21 students who had scored in the top 5% revealed that the Japanese students employed the three general cognitive processes outlined in a theoretical model based on interviews with United States students: reformulation, translation, and compensation. They also used many of the same strategies (front-end, compatible numbers, flexible rounding) utilized by American students. Few of the Japanese students could recall being taught to estimate in school. Japanese students demonstrated a greater degree of mental computation ability than American students, less frequently made order-of-magnitude errors, and were more reluctant to accept error. Japanese students tended to apply algorithmic computational procedures. Their tendency to use paper-and-pencil procedures mentally often interfered with the estimation process.
Kathryn B. Chval, Robert Reys, Barbara J. Reys, James E. Tarr and Óscar Chávez
The No Child Left Behind Act of 2001 (NCLB, 2002) elevates the importance of educational research and thereby provides opportunities for mathematics education researchers in its support for and funding of rigorous research studies and its requirement of effective, research-based practices. At the same time, by demanding more of overburdened teachers and administrators, NCLB may exacerbate a long-standing gulf between educational research and practice. We use our recent experiences with conducting school-based research to illustrate how educational research can be impeded by the added demands of NCLB and other factors in the current climate. In addition, we hope to begin a dialogue that will encourage researchers and practitioners to work together to capitalize on NCLB's increased emphasis on educational research to create a systematic approach to bridging the research-practice gulf.
James E. Tarr, Barbara J. Reys, David D. Barker and Rick Billstein
In this era of high-stakes testing and public accountability, school personnel are scrambling for ways to improve mathematics learning opportunities for all students. Although there is no single silver-bullet solution, Principles and Standards for School Mathematics (NCTM 2000) provides guidelines for designing high-quality school mathematics programs. One avenue for strengthening programs is through selecting and implementing high-quality curricular materials (textbooks).
Vena M. Long, Barbara Reys and Steven J. Osterlind
The content and emphasis of mathematics programs has been the subject of much discussion in recent years. Such technological advances as the increased availability and use of computers and calculators have caused a tremendous and sudden shift in the mathematical needs of today's citizens. Whereas twenty years ago mathematical operations using paper and pencil were the only means of doing tedious computation, today people use a hand-held calculator or computer to do such tasks as totaling grocery receipts, figuring interest payments, completing income tax forms, and balancing checkbooks.
Dung Tran, Barbara J. Reys, Dawn Teuscher, Shannon Dingman and Lisa Kasmer
This commentary highlights the contribution that careful and systematic analyses of curriculum or content standards can make to questions and issues important in the mathematics education field. We note the increased role that curriculum standards have played as part of a standards-based education reform strategy. We also review different methods used by researchers to compare and analyze the Common Core State Standards for Mathematics, each method designed for a particular purpose. Finally, we call upon mathematics education researchers to engage in careful analysis of curriculum standards and to share their findings in ways that can inform public debate as well as support education professionals in improving student learning opportunities.
Barbara J. Reys, Ok-Kyeong Kim and Jennifer M. Bay
The use of benchmarks, such as 0, 1/2, and 1, for comparing the size of fractions is not emphasized very often in instruction. Comparing fractions with 0, 1/2, or 1 by comparing the numerator with the denominator or by mentally modeling the fraction is a powerful tool for gauging the size of fractions, making quick estimates, and judging the reasonableness of computed results (Bezuk and Bieck 1992). If students are asked to compare 5/8 with 4/9, the traditional technique is to find the common denominator, convert both fractions to equivalent forms using this common denominator, then compare numerators. However, this problem can be solved more efficiently by comparing each fraction with 1/2: 5/8 is larger than 1/2, since it is larger than 4/8; and 4/9 is less than 1/2, since 4/9 is less than 4.5/9, or 1/2.
James E. Tarr, Robert E. Reys, Barbara J. Reys, Óscár Chavez, Jeffery Shih and Steven J. Osterlind
We examine student achievement of 2533 students in 10 middle schools in relation to the implementation of textbooks developed with funding from the National Science Foundation (NSF) or publisher-developed textbooks. Using hierarchical linear modeling (HLM), curriculum type was not a significant predictor of student achievement on the Balanced Assessment in Mathematics (BAM) or TerraNova Survey (TNS) after controlling for student-level variables. However, the Standards-Based Learning Environment (SBLE) moderated the effect of curriculum type. Students were positively impacted on the BAM by NSF-funded curricula when coupled with either Moderate or High levels of SBLE. There was no statistically significant impact of NSF-funded curricula on students in classrooms with a Low level of SBLE, and the relationship between publisher-developed textbooks and SBLE was not statistically significant. Moreover, there was no significant impact of either curriculum type when coupled with varying levels of SBLE on the TNS as the dependent measure.
Barbara J. Reys, Kathryn Chval, Shannon Dingman, Melissa McNaught, Troy P. Regis and Junko Togashi
The similarities and differences in grade-level learning expectations for fourth graders in ten different states that publish mathematics standards.