# The conceptual field of proportional reasoning researched through the lived experiences of nurses

## Keywords

Proportional reasoning; dosage calculation; medication errors; nursing; conceptual fields; lived experiences; multiplicative structures

## Abstract

Proportional reasoning instruction is prevalent in elementary, secondary, and post-secondary schooling. The concept of proportional reasoning is used in a variety of contexts for solving real-world problems. One of these contexts is the solving of dosage calculation proportional problems in the healthcare field. On the job, nurses perform drug dosage calculations which carry fatal consequences. As a result, nursing students are required to meet minimum competencies in solving proportion problems. The goal of this research is to describe the lived experiences of nurses in connection to their use of proportional reasoning in order to impact instruction of the procedures used to solve these problems. The research begins by clarifying and defining the conceptual field of proportional reasoning. Utilizing Vergnaud*s theory of conceptual fields and synthesizing the differing organizational frameworks used in the literature on proportional reasoning, the concept is organized and explicated into three components: concepts, procedures, and situations. Through the lens of this organizational structure, data from 44 registered nurses who completed a dosage calculation proportion survey were analyzed and connected to the framework of the conceptual field of proportional reasoning. Four nurses were chosen as a focus of in-depth study based upon their procedural strategies and ability to vividly describe their experiences. These qualitative results are synthesized to describe the lived experiences of nurses related to their education and use of proportional reasoning. Procedural strategies that are supported by textbooks, instruction, and practice are developed and defined. Descriptive statistics show the distribution of procedures used by nurses on a five question dosage calculation survey. The most common procedures used are the nursing formula, cross products, and dimensional analysis. These procedures correspond to the predominate procedures found in nursing dosage calculation texts. Instructional implications focus on the transition between elementary and secondary multiplicative structures, the confusion between equality and proportionality, and the difficulty that like quantities present in dealing with proportions.

2014

Fall

Dixon, Juli

## Degree

Doctor of Philosophy (Ph.D.)

## College

College of Education and Human Performance

## Degree Program

Education and Human Performance

application/pdf

CFE0005781

## URL

http://purl.fcla.edu/fcla/etd/CFE0005781

English

June 2015

None

## Access Status

Doctoral Dissertation (Open Access)

## Subjects

Dissertations, Academic -- Education and Human Performance; Education and Human Performance -- Dissertations, Academic

COinS