Proportional Reasoning in Nursing Practice
Celia Hoyles, Richard Noss, Stefano Pozzi
We investigate how expert nurses undertake the calculation of drug dosages on the ward. This calculation is error-critical in nursing practice and maps onto the concepts of ratio and proportion. Using episodes of actual drug administration gleaned from ethnographic study, we provide evidence that experienced nurses use a range of correct proportional-reasoning strategies based on the invariant of drug concentration to calculate dosage on the ward instead of the single taught method they describe outside of the practice. These strategies are tied to individual drugs, specific quantities and volumes of drugs, the way drugs are packaged, and the organization of clinical work.
Spatial-Mechanical Reasoning Skills Versus Mathematics Self-Confidence as Mediators of Gender Differences
M. Beth Casey, Ronald L. Nutall, Elizabeth Pezaris
For 187 Grade 8 students, we compared spatial-mechanical skills with mathematics self-confidence as mediators of gender differences in mathematics. Using items showing the largest male and female advantage, respectively, on the Third International Mathematics and Science Study (TIMSS) U.S. data, we created mathematics Male and Female subtests from items on the 8th-grade TIMSS. Using path-analytic techniques, we decomposed a significant gender/mathematics correlation, favoring males, on the TIMSS-Male subtest into direct and indirect effects. We found only indirect effects. A spatial-mechanical composite accounted for 74% of the total indirect effects, whereas mathematics self-confidence accounted for 26%. By 8th grade, girls' relatively poorer spatial-mechanical skills contribute to lower scores on types of mathematics at which boys typically excel.
The Effects of Curriculum on Achievement in Second-Year Algebra: The Example of the University of Chicago School Mathematics Project
Denise R. Thompson, Sharon L. Senk
We examine the performance of 8 pairs of 2nd-year algebra classes that had been matched on pretest scores. One class in each pair used the UCSMP Advanced Algebra curriculum, and the other used the 2nd-year-algebra text in place at the school. Achievement was measured by a multiple-choice posttest and a free-response posttest. Opportunity-to-learn (OTL) measures were used to ensure that items were fair to both groups of students. UCSMP students generally outperformed comparison students on multistep problems and problems involving applications or graphical representations. Both groups performed comparably on items testing algebraic skills. Hence, concerns that students studying from a Standards-oriented curriculum will achieve less than students studying from a traditional curriculum are not substantiated in this instance.
Experiencing Change: The Mathematics of Change in Multiple Environments
Tracy Noble, Ricardo Nemirovsky, Tracey Wright, Cornelia Tierney
In the SimCalc project and in the Mathematics of Change group at TERC, we are investigating how students from elementary through high school learn about the mathematics of change in multiple mathematical environments. As part of this research, we studied 5th-grade students doing mathematics-of-change activities from the Investigations curriculum (Russell, Tierney, Mokros, & Economopoulos, 1998) in multiple mathematical environments. This experience has led us to question the view that students connect experiences in different environments by recognizing a core mathematical structure that is common to all environments. We propose an alternative perspective on learning, in which students make mathematical environments into lived-in spaces for themselves and connect environments through the development of family resemblances across their experiences.