The University of New Mexico

Description of Activity

Why do Native American and Hispanic children under-perform White children in mathematics learning? Differences in the academic performance of linguistically and culturally diverse children as measured by standardized tests has been fraught with debate up to the present. The goal of the proposed project is to provide an empirical foundation for an understanding of the role that cognitive diversity plays in mathematics performance. In particular, we are interested in examining how Native American, Hispanic, and White children in Grades 4-8 differ in their ways of learning and demonstrating learning in mathematics problem solving. To this end, we plan to use a mixed, longitudinal design to study the growth of mathematics learning for two cohorts of children over three years. We will collect data on hypothesized correlates of mathematics performance (e.g., SES, language proficiency, cognitive style, communication styles, domain-specific abilities, motivation, beliefs and perceptions) and examine the extent to which the correlates account for group and individual differences in math performance. In addition, we will estimate individual learning trajectories for each child and examine the extent to which the correlates are related to each child's mean mathematics achievement and to his/ her growth in mathematics learning over time. Aside from using the traditional standardized norm-referenced measures of mathematics learning, we plan to develop an innovative set of assessment instruments to tap the extensive cognitive processes involved in problem solving activities. The alternative assessment formats we develop will allow us to examine empirically the extent to which assessment characteristics such as cultural context, assessment format, and mode of delivery impact relative performance across the three studied groups of children.

Intellectual Merits and Broader Impact of the Research

This work will contribute to the understanding of cognitive and assessment conditions that support the demonstration of learning by culturally and linguistically diverse children. What we are proposing is the scientific analysis of prevailing myths about the etiology of differences in mathematics performance. Although we can find a patchwork of research studies investigating the relationship of one or two of these correlates of math achievement, our research program will be making a unique contribution by advancing knowledge and understanding in the field using sophisticated statistical analysis to explore the simultaneous effects of many correlates longitudinally. Moreover, by combining an extensive quantitative approach with strategic qualitative studies, we will be able to demonstrate triangulation for key variables and relationships among variables. Our research design allows us to provide answers to some fundamental questions often raised about cognitive diversity but rarely answered with scientific grounds.

Based on the data gathered during the three consecutive years, a set of guidelines for the development of research-based innovations will be generated that will enhance mathematics instruction and assessment for linguistically and culturally diverse children. By implementing a variety of formats, representations, styles, and contexts into our assessment design, we expect to be able to better serve linguistically and culturally diverse children in terms of both validly measured student achievement and usability of assessment data to inform instruction. By developing a wide range of evaluation methods, including technology-based methods, we will advance practice in mathematics assessment and instruction. The expected outcome of this project is to broaden the participation and success of underrepresented groups in mathematics and enhance our understanding of how these groups of children differ in their mathematics thinking and how we can best assess their performance.

One of the strengths of our proposal is that it is grounded in a strong theoretical framework that draws on cognitive science theory, constructivism, and socio-cultural theories of learning. To understand diversity in mathematics thinking, one must understand the interaction among cognitive processes and the cultural and social contexts from which new concepts and skills are constructed. Congruently, we will investigate the cognitive, socio-cultural, and linguistic processes that operate below the surface as students interpret and solve problems. We will also gain knowledge on how these processes are reflected in students’ performance and in the level and variability of their scores on each assessment format. This knowledge will contribute to improving both classroom-based and large-scale assessment practices.

 

 

 

 

 

Roxana Moreno, Principal Investigator

Dr. Roxana Moreno is an Associate Professor in Educational Psychology at the University of New Mexico. She earned her Ph.D. in psychology with an emphasis in cognitive science from the University of California, Santa Barbara, U.S.A. and her J.D. in law from the University of Buenos Aires, Argentina. Her research interests are in human memory, learning, and higher-order cognition with special interest in applying cognitive theories to educational technology and individual differences in learning. Before accepting a teaching position at the University of New Mexico, Dr. Moreno was awarded a Postdoctoral Fellowship in Science, Engineering, Mathematics, and Technology Education by the National Science Foundation to investigate the interaction of rich experiential and reflective interactions mediated by software pedagogical agents in virtual reality environments. Her investigations involve undergraduate students as well as elementary students from local schools who are culturally and linguistically diverse.

ROLE GRANT CONTACT INFORMATION
Office: 505.277.7115
Fax: 505.277.8361