RESUMEN

Research on mathematical cognition, learning, and instruction (MCLI) often takes cognition as its point of departure and considers instruction at a later point in the research cycle. In this article, we call for psychologists who study MCLI to reflect on the "status quo" of their research practices and to consider making instruction an earlier and more central aspect of their work. We encourage scholars of MCLI (a) to consider the needs of educators and schools when selecting research questions and developing interventions; (b) to compose research teams that are diverse in the personal, disciplinary, and occupational backgrounds of team members; (c) to make efforts to broaden participation in research and to conduct research in authentic settings; and (d) to communicate research in ways that are accessible to practitioners and to the general public. We argue that a more central consideration of instruction will lead to shifts that make research on MCLI more theoretically valuable, more actionable for educators, and more relevant to pressing societal challenges.

Asunto(s)

Cognición , Aprendizaje , Matemática , Humanos , Cognición/fisiología , Matemática/educación , Investigación , Enseñanza

RESUMEN

The recent development of satellite instruments that obtain spectrally resolved measurements of the atmosphere has highlighted the problem of how to determine the best subsets, or microwindows, of such spectra for retrievals of temperature and composition. A technique is described that maximizes the information content (or some other figure of merit) based on the modeling of the propagation of systematic as well as random error terms through the retrieval process. Apart from selecting microwindows, this technique can also prioritize existing microwindows for different circumstances and provides a full error analysis of the retrieval. A practical application is demonstrated for the Michelson Interferometer for Passive Atmospheric Sounding limb-viewing interferometer, but the technique is equally applicable to nadir-viewing instruments.