Proportional Reasoning: Lessons from Research in Data and Chance


J. M. Watson
J. M. Shaughnessy
Author(s) Organizational Affiliation
University of Tasmania, Australia (Watson)
Portland State University (Shaughnessy)
Publication Year
Resource Type
Number of Pages

Proportionality is one of the major concepts connecting different topics in the mathematics curriculum at the middle school level (NRS levels 4-6). Students need to be helped to make explicit connections between proportions and data and chance.

This article describes two contexts where proportional reasoning is needed for a thorough understanding of the problem and the reactions of students to the tasks. One task focused on comparing groups and the second task focused on predictions from sampling. The authors also included “Lessons for the Classroom” for each of the two research tasks.
What the experts say

Adult learners are constantly bombarded with statistical information on TV, in newspapers and on the internet. Many learners lack understanding to make informed decisions about statistical data. The authors in this writing show teachers how students lack this statistical understanding.

Understanding how to think proportionally or use proportional reasoning is a mathematical strategy that has many uses. The authors give examples how proportional reasoning can help learners understand statistical data. They also share results of how learners might respond and how to correct learners' misconceptions about data sets using proportional reasoning.

While this study was done with middle school children, it could easily be adapted for adults at NRS levels 5 and 6. The skills of analyzing data and proportional reasoning are skills necessary for GED and college transition students.

This excellent article presents both a description of a research project and ideas for lessons to be taught in the ABE/GED math classroom. Although the students in the study were middle schoolers, their range of understanding, or lack thereof, might easily have been displayed by adults.

Jane Watson and Mike Shaughnessy identify proportionality as a major concept connecting different topics in the mathematics curriculum and express their concern that often "the statement of a problem is a giveaway that a proportion is involved." They believe that "teachers and students may overlook opportunities to make connections with applications of proportional reasoning in tasks such as comparisons of data sets or predictions of the compositions of samples." Their research involves two tasks meant to provide opportunities to make these connections.

For one task they present the students with four pairs of frequency charts representing classroom performance and ask them to determine if one class performed better than the other. Three of the pairs showed different performance results with equal number of students in each group. The fourth pair of charts is for classrooms that do not have equal number of students. Making visual comparisons or finding totals may have been successful strategies for equal sets, but a valid conclusion for the unequal sets requires some sort of proportional reasoning such as the use of the arithmetic mean.

In another task, the students were told the distribution of three different colored candies totaling 100 and were asked to predict, in a random sampling of 10, how many of a particular color would be likely.

The article provides detailed description of student responses, analysis of their cognitive development related to proportional reasoning, and facilitating questions for the teacher to use to help the student make explicit connections between proportions and data and chance.

Note: One reviewer felt that although this article is very informative about proportional reasoning, it is not of value to the field of adult education. Many adult learners seek to understand math and therefore, would probe further when being taught proportional reasoning. That is, many adults seek to find connections to real-life when introduced to new math concepts, something that is not often seen with younger learners.

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