You are a new teacher. You are excited, but also more than a little intimidated. What to do? What should be your priorities as a novice teacher? Of course, you cannot do it all, but where do you start? All of us who have taught mathematics have had a similar experience. And none of us can say that we know everything we should know about teaching.
Kathryn B. Chval and Óscar Chávez
A four-component process to teach mathematics to English language learners is explored. Research-based strategies within each example illustrate how research can be turned into practice.
Óscar Chávez and Robert E. Reys
Using spatial visualization to make connections among Zeno's paradox, geometry, fractions, infinite series and limits.
Óscar Chavez, Robert Reys, and Dusty Jones
Spatial Visualization Is An Important Skill that deserves instructional attention. Strong evidence supports the claim that “measures of mathematical ability tend to be strongly correlated with spatial ability” (Anderson 2000). Thus, there is every reason to believe that time spent helping students develop their spatial visualization skills will have additional benefits for their mathematical growth, perhaps even going so far as to improve test performance.
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.
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, 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.