This paper very properly begins with a definition. Integration, as we all know, means to make into a whole, or to combine into a completely related unit. From the standpoint of a school program it means that the student not only has learned many things in school but he should also have acquired a unified idea of all the parts and of their relations to one another and to topics outside. It is an aim of education and a worthy one. Teachers everywhere hope that the individuals whom they teach will eventually be able to react to most life situations with intelligence and skill.

### David E. Williams

It is 1987. We have probed both far into space and to the depths of the oceans. Technology has enabled humans to walk on the moon several times; it has helped scientists to find the Titanic on the ocean's floor. Many of George Orwell's prophecies have come true, a number of them long before the year 1984. Technological advances have made the lives of many citizens easier and more productive. But elementary school students in classrooms across this country still are being taught the long-division algorithm using pencil and paper. Why?

### Douglas A. Grouws, James E. Tarr, Óscar Chávez, Ruthmae Sears, Victor M. Soria and Rukiye D. Taylan

This study examined the effect of 2 types of mathematics content organization on high school students' mathematics learning while taking account of curriculum implementation and student prior achievement. The study involved 2,161 students in 10 schools in 5 states. Within each school, approximately 1/2 of the students studied from an integrated curriculum (Course 1) and 1/2 studied from a subject-specific curriculum (Algebra 1). Hierarchical linear modeling with 3 levels showed that students who studied from the integrated curriculum were significantly advantaged over students who studied from a subject-specific curriculum on 3 end-of-year outcome measures: Test of Common Objectives, Problem Solving and Reasoning Test, and a standardized achievement test. Opportunity to learn and teaching experience were significant moderating factors.

### James E. Tarr, Douglas A. Grouws, Óscar Chávez and Victor M. Soria

We examined curricular effectiveness in high schools that offered parallel paths in which students were free to study mathematics using 1 of 2 content organizational structures, an integrated approach or a (traditional) subject-specific approach. The study involved 3,258 high school students, enrolled in either Course 2 or Geometry, in 11 schools in 5 geographically dispersed states. We constructed 3-level hierarchical linear models of scores on 3 end-of-year outcome measures: a test of common objectives, an assessment of problem solving and reasoning, and a standardized achievement test. Students in the integrated curriculum scored significantly higher than those in the subject-specific curriculum on the standardized achievement test. Significant student-level predictors included prior achievement, gender, and ethnicity. At the teacher level, in addition to Curriculum Type, the Opportunity to Learn and Classroom Learning Environment factors demonstrated significant power in predicting student scores, whereas Implementation Fidelity, Teacher Experience, and Professional Development were not significant predictors.

### Daniel F. McGaffrey, Laura S. Hamilton, Brian M. Stecher, Stephen P. Klein, Delia Bugliari and Abby Robyn

A number of recent efforts to improve mathematics instruction have focused on professional development activities designed to promote instruction that is consistent with professional standards such as those published by the National Council of Teachers of Mathematics. This paper describes the results of a study investigating the degree to which teachers' use of instructional practices aligned with these reforms is related to improved student achievement, after controlling for student background characteristics and prior achievement. In particular we focus on the effects of curriculum on the relationship between instructional practices and student outcomes. We collected data on tenth-grade students during the 1997–98 academic year. Some students were enrolled in integrated math courses designed to be consistent with the reforms, whereas others took the more traditional algebra and geometry sequence. Use of instructional practices was measured through a teacher questionnaire, and student achievement was measured using both the multiple-choice and open-ended components of the Stanford achievement tests. Use of standards-based or reform practices was positively related to achievement on both tests for students in integrated math courses, whereas use of reform practices was unrelated to achievement in the more traditional algebra and geometry courses. These results suggest that changes to instructional practices may need to be coupled with changes in curriculum to realize effects on student achievement.

### Michael R. Harwell, Thomas R. Post, Yukiko Maeda, Jon D. Davis, Arnold L. Cutler, Edwin Anderson and Jeremy A. Kahan

The current study examined the mathematical achievement of high school students enrolled for 3 years in one of three NSF funded *Standards*-based curricula (IMP, CMIC, MMOW). The focus was on traditional topics in mathematics as measured by subtests of a standardized achievement test and a criterion-referenced test of mathematics achievement. Students generally scored at or above the national mean on the achievement subtests. Hierarchical linear modeling results showed that prior mathematics knowledge was a significant but modest predictor of achievement, student SES had a moderate effect, and increasing concentrations of African American students in a classroom were associated with a stronger effect of attendance on achievement. No differences on the standardized achievement subtests emerged among the *Standards*-based curricula studied once background variables were taken into account. The two suburban districts providing data for the criterion-referenced test achieved well above the national norm.

### Thomas R. Post, Amanuel Medhanie, Michael Harwell, Ke Wu Norman, Danielle N. Dupuis, Thomas Muchlinski, Edwin Andersen and Debra Monson

This retrospective study examined the impact of prior mathematics achievement on the relationship between high school mathematics curricula and student postsecondary mathematics performance. The sample (*N* = 4,144 from 266 high schools) was partitioned into 3 strata by ACT mathematics scores. Students completing 3 or more years of a commercially developed curriculum, the University of Chicago School Mathematics Project curriculum, or National Science Foundation-funded curriculum comprised the sample. Of interest were comparisons of the difficulty level and grade in their initial and subsequent college mathematics courses, and the number of mathematics courses completed over 8 semesters of college work. In general, high school curriculum was not differentially related to the pattern of mathematics grades that students earned over time or to the difficulty levels of the students' mathematics course-taking patterns. There also was no relationship between high school curricula and the number of college mathematics courses completed.

### Jon R. Star, John P. Smith III and Amanda Jansen

Research on the impact of *Standards*-based mathematics and reform calculus curricula has largely focused on changes in achievement and attitudes, generally ignoring how students experience these new programs. This study was designed to address that deficit. As part of a larger effort to characterize students' transitions into and out of reform programs, we analyzed how 93 high school and college students perceived *Standards*-based and reform calculus programs as different from traditional ones. Results show considerable diversity across and even within sites. Nearly all students reported differences, but high-impact differences, like *Content*, were not always related to curriculum type (reform or traditional). Students' perceptions aligned moderately well with those of reform curriculum authors, e.g., concerning *Typical Problems*. These results show that students' responses to reform programs can be quite diverse and only partially aligned with adults' views.

### David E. Williams, Ann McAloon and G. Edith Robinson

In it “Position Statement on Calculators in the Mathematics Classroom” the National Council of Teachers of Mathematics recommends that calculators be integrated into all aspect of school mathematics, including class work, homework, and evaluation (NCTM 1986). This author cited the need for a comprehensive calculator proj ect encompassing all facet as of elementary mathematics education, a project that should include the development of a calculator-integrated curriculum. an extensive training program for teachers, the development of curriculum-support materials, change in textbook, workshops for parents and community group, and a change in evaluation of mathematics achievement (Williams 1987).

### William L. Rubink and Sylvia R. Taube

The middle school mathematics curriculum emphasizes integrated curriculum projects in response to the need to give students opportunities to explore and broaden areas of investigations. These interdisciplinary experiences help students understand the challenges faced by professionals. Although many educators concur that data analysis and statistics taught in the mathematics classroom should use data from real-world situations (NCTM 1989), mathematics teachers often need additional resources, both human and material, and must search beyond their textbooks for exciting activities. One way to breathe more life into mathematics teaching is to bring in ideas from other fields of study, particularly career opportunities that involve collecting and analyzing data. We describe a field-tested interdisciplinary-unit activity that involves collecting data about honeybees. In this activity, middle school students gain hands-on experiences with collecting, transforming, and analyzing data by using actual techniques employed by entomologists, the scientists who study insects. Ultimately, students acquire a sense of the methodology that scientists use to obtain a quantitative “view” of the world, one in which they conceptualize objects as things that can be measured (Thompson 1995).