# Ratio and proportion: mapping the conceptual field

## Identifier

etd-07092009-100847

## Degree

Master of Natural Sciences (MNS)

## Department

Natural Sciences (Interdepartmental Program)

Thesis

## Abstract

Ratio and proportion are central to the middle school mathematics curriculum, but the full scope and extent of this topic is not described in detail in most state curriculum standards. In this thesis, numerous textbooks from the past one hundred years are sampled, along with several state‟s standards and the Louisiana state comprehensive curriculum. These sources are used to develop a more defined map of ratio and proportion as a conceptual field and a structured collection of problems. Proportional reasoning involves three phases: 1) the comparison of two magnitudes, expressed as ratio or rate, 2) the comparison of two ratios, called a proportion, and 3) the expression of proportional relationships as functions. As we follow this progression, proportional reasoning tasks change accordingly, through ratios, rates, missing-value proportions, similarity situations, and ultimately functions that express proportionality.

2009

## Document Availability at the Time of Submission

Release the entire work immediately for access worldwide.

COinS