Harold L. Schoen’s research while affiliated with University of Iowa and other places

We report results from a study of instructional practices that relate to student achievement in high school classrooms in which a standards-based curriculum (Core-Plus) was used. We used regression techniques to identify teachers' background characteristics, behaviors, and concerns that are associated with growth in student achievement and further described these associations via graphical representations and logical analysis. The sample consisted of 40 teachers and their 1,466 students in 26 schools. Findings support the importance of professional development specifically aimed at preparing to teach the curriculum. Generally, teaching behaviors that are consistent with the standards' recommendations and that reflect high mathematical expectations were positively related to growth in student achievement.

The level of preparation for college entrance tests, university mathematics placement tests, and beginning college mathematics courses was studied for students who completed the Standards-oriented curriculum "Contemporary Mathematics in Context" (A. Coxford, J. Fey, C. Hirsch, H. Schoen, E. Hart, B. Keller, and A. Watkins, 2001), the high school curriculum developed by the Core-Plus Mathematics Project (CPMP). Eight CPMP field test schools provided SAT scores for their students, and 15 test schools provided ACT results. A total of 164 CPMP students and 177 precalculus students took a college placement test used at a major university. Freshman college mathematics course grade data for each year from 1995-1996 through 1998-1999 were gathered for the graduates of two high schools, one of which used CPMP. Neither the SAT nor the ACT assessments were well aligned with the content goals of the CPMP curriculum, but CPMP course 3 (third year of the curriculum) students appeared to be as well prepared for SAT mathematics as other high school students, and CPMP course 4 students appeared to be better prepared. The ACT was more problematic for CPMP students through course 3, but even those students were not disadvantaged on the ACT. The pattern of success of CPMP students on the college placement test was somewhat better than that of traditional students, in spite of placement criteria that ignored students' conceptual understanding and facility with applications if their algebraic symbol manipulation skills were below criterion level. These results provide evidence in support of the feasibility of curricula that embody Standards recommendations. (Contains 22 references.) (SLD)

The classroom practices of 20 teachers were studied during the field test of course 1 of Contemporary Mathematics in Context (CPMP), the high school mathematics curriculum developed by the Core-Plus Mathematics Project. In each year of the CPMP curriculum, mathematics is developed along the interwoven strands of algebra and functions, geometry and trigonometry, statistics and probability, and discrete mathematics. Ten of the teachers were in the top quartile of field test teachers and the other 10 in the bottom quartile with respect to their students' growth in mathematics achievement over the 1-year course. The goal was to provide a description of the classroom practices and concerns of teachers whose students achieve at the highest levels using the practices and concerns of teachers of lower achieving students as a contrast. At the end of the school year, teachers completed a teacher concern survey. One the whole, teachers of first quartile students (first quartile teachers) perceived themselves as better informed about the CPMP curriculum and its use at their school. First quartile teachers expressed less concern about their ability to implement the CPMP curriculum and were less concerned about the impact on their students of using CPMP. These and other findings suggest that a teacher whose behavior is positively associated with growth in student achievement would have strong preparation in reform curriculum and teaching before teaching his or her first CPMP class or would have completed a workshop to prepare for the curriculum. The teacher would use the various parts of the CPMP curriculum in ways that align well with the developers' expectations and would not be likely to supplement the curriculum materials. (Contains 34 references.) (SLD)

The Core-Plus Mathematics Project (CPMP) has completed development and evaluation of student and teacher materials for an integrated 3-year high school mathematical sciences curriculum for all students. This paper provides a brief overview of the CPMP curriculum in terms of its design and theoretical framework as well as a profile of the mathematical achievement outcomes of students who participated in the national field test of the curriculum. Each CPMP course was field tested in 36 high schools. Students in CPMP courses after 1 year, 2 years, and 3 years illustrated better understanding of and ability to reason in quantitative situations than did students in more traditional mathematics courses and in the nationally representative norm group. The findings reported in this study are likely to be the result of CPMP students engaging frequently in class, homework, and assessment activities that provide them ample opportunity to cogitate on problems presented in realistic contexts about mathematical models for those problems, and seeing the connections among and patterns in various representations of those models. Contains 41 references. (ASK)

Current policy reports addressing mathematics education in American schools, such as Everybody Counts (NRC 1989), Curriculum and Evaluation Standards for School Mathematics (NCTM 1989), Professional Standards for Teaching Mathematics (NCTM 1991), and Assessment Standards for School Mathematics (NCTM 1995), call for sweeping reform in curricular, instructional, and assessment practices. Implementing the proposed reforms poses new opportunities and challenges for school districts, mathematics departments, and classroom teachers.

The performance of students in grades five through eight on test items in formats designed to measure various aspects of computational estimation was examined. Paper-pencil test data for 1376 students and interviews with 20 students were analyzed. Performance differed by item format, types of numbers and operations in the items, and grade level of students. Students tended to round numbers to the nearest leading power of 10 even when the items required other estimation processes.

The performance of students in grades five through eight on test items in formats designed to measure various aspects of computational estimation was examined. Paper-pencil test data for 1376 students and interviews with 20 students were analyzed. Performance differed by item format, types of numbers and operations in the items, and grade level of students. Students tended to round numbers to the nearest leading power of 10 even when the items required other estimation processes.