What Is Quantitative Reasoning? Defining the Construct for Assessment Purposes

Abstract

In order to create fair and valid assessments, it is necessary to be clear about what is to be measured and how the resulting data should be interpreted. For a number of historical and practical reasons described in this paper, adequately detailed statements with both a theoretical and empirical base do not currently exist for the construct of quantitative reasoning for use in assessments. There is also no adequate explanation of the important differences between assessments that measure quantitative reasoning constructs and those that are intended to measure achievement in related mathematical content areas.The literature in psychology, psychometrics, philosophy, and education, while containing much that is relevant to the construct of quantitative reasoning, unfortunately does not provide materials that can be used in research and development to address such practical issues or to explain the basic nature of quantitative reasoning assessments. This paper briefly discusses the importance and use of constructs and the quantitative reasoning and standards literature. It then presents a statement about the construct of quantitative reasoning for assessment purposes within a construct validity framework that includes both a definition of the construct and threats to valid score interpretation. These threats are based on related but distinguishable constructs and other types of construct-irrelevant variance in the assessments.

Research on Validity Theory and Practice at ETS

“…For example, Dwyer et al (2003) defined quantitative reasoning as "the ability to analyze quantitative information" (p. 13) and specified that its domain would be restricted to quantitative tasks that would be new to the student (i.e., would not require methods that the test takers had been taught). They suggested that quantitative reasoning includes six more specific capabilities: (a) understanding quantitative information presented in various formats, (b) interpreting and drawing inferences from quantitative information, (c) solving novel quantitative problems, (d) checking the reasonableness of the results, (e) communicating quantitative information, and (f) recognizing the limitations of quantitative methods.…”

“…That is, broadly defined traits that are of practical interest may involve a number of more narrowly defined traits or factors that contribute to the test taker's performance. For example, as noted earlier, Dwyer et al (2003) defined the performance domain for quantitative reasoning in terms of six capabilities, including understanding quantitative information, interpreting quantitative information, solving quantitative problems, and estimating and checking answers for reasonableness. In addition, most trait measures require ancillary abilities (e.g., the ability to read) that are needed for effective performance in the assessment context.…”

Assessing Quantitative Literacy in Higher Education: An Overview of Existing Research and Assessments With Recommendations for Next‐Generation Assessment

“…Development of an operational or construct definition is “essential to validity and fairness to the scientific integrity of the inferences drawn from assessments” and helps to aid “decision‐making about assessment design, development, and interpretation” (Dwyer et al, , p. 1). Based on a synthesized review of the frameworks and definitions by national and international organizations, workforce initiatives, higher educational institutions and researchers, and K–12 theorists and practitioners, as well as existing assessments measuring quantitative literacy skills, we propose an operational definition for a next‐generation quantitative literacy assessment.…”

“…Dwyer et al () noted that to solve quantitative reasoning problems, mathematical content knowledge is needed. After examining and synthesizing the quantitative literacy literature and existing assessments, we identified four content areas important for assessing quantitative literacy in a higher education context: (a) number and operations, (b) algebra, (c) geometry and measurement, and (d) probability and statistics (see Table ).…”

Comparación Entre Los Promedios De La Prueba De Aptitud Académica Y La Prueba De Habilidades Cuantitativas De Los Estudiantes De La Universidad De Costa Rica

“…Estas capacidades permiten ejemplificar aún más que la habilidad cuantitativa no es conocimiento matemático, sino la habilidad asociada a la comprensión de la información cuantitativa (Dwyer, Gallagher, Levin y Morley, 2003). Siguiendo a estos autores, el razonamiento cuantitativo es "la capacidad de analizar la información cuantitativa, incluyendo la determinación de qué técnicas y procedimientos se pueden aplicar a un problema particular para llegar a su solución" (2003: 12); ellos hacen énfasis en que el razonamiento cuantitativo no se refiere a las habilidades de cálculo, sino a la capacidad para determinar cuál es la mejor estrategia de cálculo para resolver un problema y a la habilidad de inferir el grado de precisión requerido para estos cálculos.…”