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A Longitudinal Study of Children in the Everyday Mathematics Curriculum
... Several studies have examined the effects of Everyday Mathematics on student achievement. Carroll (2001) conducted a longitudinal study of children using the Everyday Mathematics curriculum. The study compared Japanese, Chinese, traditionally taught U. S. students, and U.S. students taught Everyday Mathematics. ...
... The Everyday Mathematics first grade students performed higher than both the Chinese and the traditionally taught U.S. first graders, but below the Japanese students. This improvement in scores relative to the Chinese group indicated a positive effect of the curriculum (Carroll, 2001). Briars and Resnick (2000) examined the way Everyday Mathematics narrowed the achievement gap between African American and Caucasian students on the New Standards Mathematics Reference Exam (NSMRE). ...
International assessment data indicate American students are not competing with their counterparts in other countries. The mathematics curriculum and pedagogy are not preparing students to compete in a global economy. This study compared student achievement using sixth grade mathematics results from the Illinois Standards Achievement Test. Specifically, the study compared the results of students in three different rural school districts, all of whom were receiving instruction in three different mathematics curricula. In one district, students received seven years of the K-6 Everyday Mathematics curriculum which was compared with students who received seven years of instruction using a traditional mathematics curriculum in the second district and in the third district scores were compared with students who were taught using a traditional mathematics curriculum supplemented with Mountain Math. The results of this study indicate the constructivist K-6 elementary mathematics curriculum did not lead to higher levels in math achievement when compared with the traditional methods of instruction.
... The draft materials were revised on the basis of the evaluation studies and teacher feedback, and were commercially published. Finally, extensive summative evaluations of the published materials were carried out by UCSMP and by a group at Northwestern University, often focusing on issues identified as problematic during the field test (Arron, 1993; Carroll, 2000a Carroll, , 2000b Carroll, , 1999 Carroll, , 1998a Carroll, , 1998b Carroll, , 1997 Carroll, , 1996b Carroll, , 1996c Carroll, , 1996d Carroll, , 1995a Carroll, , 1993 Carroll & Fuson, 1998a, 1998b Carroll, Fuson, & Diamond, 2000; Carroll & Isaacs, in press; Carroll & Porter, 1998 Ding, 1997; Drueck, 1996; Drueck, Fuson, Carroll, & Bell, 1995; Fraivillig, 2001 Fraivillig, , 1996 Fraivillig, Murphy, & Fuson, 1999; Fuson, 1997; Fuson & Carroll, 1998; Fuson, Carroll, & Drueck, 2000; Fuson, Carroll, & Landis, 1996; Murphy, 1998). Because of this elaborate development process, the production of the first edition of EM took more than 10 years. ...
This article reviews research on the achievement outcomes of three types of approaches to improving elementary mathematics: mathematics curricula, computer-assisted instruction (CAI), and instructional process programs. Study inclusion requirements included use of a randomized or matched control group, a study duration of at least 12 weeks, and achievement measures not inherent to the experimental treatment. Eighty-seven studies met these criteria, of which 36 used random assignment to treatments. There was limited evidence supporting differential effects of various mathematics textbooks. Effects of CAI were moderate. The strongest positive effects were found for instructional process approaches such as forms of cooperative learning, classroom management and motivation programs, and supplemental tutoring programs. The review concludes that programs designed to change daily teaching practices appear to have more promise than those that deal primarily with curriculum or technology alone.
Ms. Smith, a first-grade teacher, asked her students how they could add thirty cents and twenty-seven cents. The students suggested several different solution methods. One student said that they could use the number grid to count. Ms. Smith asked where they should start, and the student said, “At thirty.” Together with the student, Ms. Smith counted twenty-seven more squares on the grid. After finishing, Ms. Smith asked whether the students knew a shortcut. Another student said to start on 27 and count by tens to end at 57.
In this study, about 200 middle school students solved an augmented-quotient division-with-remainders problem, and their solution processes and interpretations were examined. Based on earlier research, semantic-processing models were proposed to explain students' success or failure in solving division-with-remainder story problems on the basis of the presence or absence of an adequate interpretation provided by the solver after obtaining a numerical solution. In this study, students' solutions and their attempts and failures to "make sense" of their answers were analyzed for evidence that supported or refuted the hypothesized semantic-processing models. The results confirmed that the models provide a solid explanation of students' failure to solve division-with-remainder problems in school settings. More generally, the results indicated that student performance was adversely affected by their dissociation of sense making from the solution of school mathematics problems and their difficulty in providing written accounts of their mathematical thinking and reasoning.
Students using Everyday Mathematics (EM), developed to incorporate ideas from the NCTM Standards, were at normative U.S. levels on multidigit addition and subtraction symbolic computation on traditional, reform-based, and EM-specific test items. Heterogeneous EM 2nd graders scored higher than middle- to upper-middle-class U.S. traditional students on 2 number sense items, matched them on others, and were equivalent to a middle-class Japanese group. On a computation test, the EM 2nd graders outperformed the U.S. traditional students on 3 items involving 3-digit numbers and were outperformed on the 6 most difficult test items by the Japanese children. EM 3rd graders outscored traditional U.S. students on place value and numeration, reasoning, geometry, data, and number-story items.
The National Assessment of Educational Progress (NAEP) completed its fourth mathematics assessment during the 1985-86 school year and finished the analyses of the results in 1988. This monograph, prepared by an interpretive team of the National Council of Teachers of Mathematics, represents a comprehensive discussion of the results of the fourth assessment based on the analyses provided by NAEP. The monograph presents examples of the cognitive and affective items and summarizes the results of the individual items for the different grade levels and subgroups. Topics discussed include: (1) mathematical methods; (2) discrete mathematics; (3) organization and interpretation of data; (4) measurement; (5) geometry; (6) variables and relations; (7) number and operations; (8) the use of calculators; (9) attitudes toward mathematics; (10) math proficiency levels nationally and for demographic subgroups; and (11) minority and gender differences in mathematics. Bibliographies for the four NAEP assessments are listed. (YP)
This study compared the results of group tests of computational skills and tests of knowledge and skills in mathematics between three groups of first and fifth grade students from the United States, Japan, and Taiwan. The battery of tests were constructed after reviewing the mathematics textbooks used in each location and discussing the major goals of mathematics with mathematics educators. Tests administered to individuals included word problems, conceptual knowledge, mathematical operations, graphing, estimation, visualization, transformation or spatial relations, and mental calculations. Group tests were used to test computation skills. The results of the group testing and the individually administered tests are reported separately in two different sections. The methodology of the testing includes a description of the tests, selection of the sample, a description of the examiners, and the testing procedure. All items in each test, along with the percentages of students in each city responding correctly to each item, are presented in the appendixes. The results of the group tests appear in Appendix A and the individual tests in Appendix B. (KR)
National and international studies have found U.S. elementary students to be weak in their understandings and applications of geometric concepts. The University of Chicago School Mathematics Project's (UCMSP) Everyday Mathematics Program is one of the current reform-based elementary curricula incorporating geometry throughout the K-6 curriculum, with an emphasis on hands-on and problem-solving activities. In this study, the geometric knowledge of fifth and sixth graders using the UCSMP curriculum is compared to the knowledge of students using more traditional curricula. Because UCSMP students had been in the program since kindergarten, this research attempts to measure the longitudinal effects of such an approach. Along with an overall score, a subset of test items was used to assign each student a van Hiele level for geometric thinking, as well as a reasoning score. On all measures, UCSMP students substantially outperformed their counterparts, and nearly all differences were significant. Aspects of the UCSMP curriculum and the van Hiele model for learning geometry are discussed relative to these results.
Twelve classes using the reform-based curriculum, Everyday Mathematics (EM), were observed early in first grade. The two lessons observed involved students generating and solving addition and subtraction number stories. In these lessons, teachers were directed to help students link these number stories to representations (pictures or objects) and equations. Because this curriculum emphasizes invented procedures and number sense, the lessons also call for whole-class discussions of students' solutions. Further, the curriculum assumes that teachers will build upon and extend the children's mathematical thinking, highlighting these alternative solution methods and supporting the students' explanations. Results show that students were successful at making up, telling, and solving number stories and used a range of solution methods, including the mathematical representations available in the classrooms. However, only about three-quarters of the teachers established explicit links between the stories and mathematical representations, with fewer than half representing the stories as numbers and equations. Although student-based explanations play an important role in helping children develop solution procedures with understanding, solution methods were only elicited in half of the classes observed, and multiple methods in one-fourth of the classes. Implications for reform curricula, especially how they might clarify new goals for teachers, are discussed.
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