NCTM's Principles and Standards for School Mathematics (2000) identifies Data Analysis and Probability as one of the five content standards for pre-K–12 mathematics and delineates learning expectations at each of four grade bands. This standard places much more emphasis on data analysis than on probability, particularly for grades pre-K through 5. Indeed, only one of the four goals in the standard directly addresses probability, and no probability learning expectations are explicitly stated for grades pre-K through 2. The standard states, however, that “instructional programs from prekindergarten through grade 12 should enable all students to understand and apply basic concepts of probability” (p. 48).
James E. Tarr
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).
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.
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, 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.
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, Erica N. Walker, Karen F. Hollebrands, Kathryn B. Chval, Robert Q. Berry III, Chris L. Rasmussen, Cliff Konold and Karen King
During the past 2 decades, significant changes in mathematics curriculum standards and policies have brought greater attention to assessment instruments, practices, purposes, and results. In moving toward stronger accountability, the No Child Left Behind Act (NCLB) of 2001 (NCLB, 2002) mandates that school districts receiving funding under NCLB formulate and disseminate annual local report cards that include information on how students and each school in the district performed on state assessments. This mandate has not only facilitated a growth in state testing (Wilson, 2007) but also influenced the teaching of mathematics (Seeley, 2006). More recently, the National Governors Association Center for Best Practices (NGA Center) and the Council of Chief State School Officers (CCSSO) crafted and launched the Common Core State Standards for Mathematics (NGA Center & CCSSO, 2010), which have been formally adopted by the vast majority of U.S. states and territories. The Common Core State Standards for Mathematics (CCSSM) specifies standards for mathematical content by grade in K–8 and by conceptual categories at the secondary level and identifies key Standards for Mathematical Practice that should be present in K–12 instruction. The CCSSM represents an unprecedented initiative to raise academic standards in school mathematics that will inevitably influence the development of curriculum materials, teaching, and assessment practices.
Chris Rasmussen, Daniel J. Heck, James E. Tarr, Eric Knuth, Dorothy Y. White, Diana V. Lambdin, Patricia C. Baltzley, Judith Reed Quander and David Barnes
Daniel J. Heck, James E. Tarr, Karen F. Hollebrands, Erica N. Walker, Robert Q. Berry III, Patricia C. Baltzley, Chris L. Rasmussen and Karen D. King
The National Council of Teachers of Mathematics (NCTM) espouses priorities to foster stronger linkages between mathematics education research and teaching practice. Of the five foundational priorities, one is directly focused on research, indicating NCTM's commitment to “ensure that sound research is integrated into all activities of the Council” (NCTM, n.d.). Another priority specifically references the relationship between research and mathematics teaching; the priority on curriculum, instruction, and assessment states that NCTM pledges to “Provide guidance and resources for developing and implementing mathematics curriculum, instruction, and assessment that are coherent, focused, well-articulated, and consistent with research in the field [emphasis added], and focused on increasing student learning” (NCTM, n.d.).