QUANTITATIVE REASONING
Level II
All too often, quantitative data presented by the media are slanted, misleading, incomplete and/or inaccurate. For example, points of comparison in a table may minimize the dimensions of an overall decrease in crime. Income differentials between rich and poor are falsified when unearned income is excluded from a graph. An advertised sale price falsifies an item's original price. Financial advantages of a "free trade" agreement are exaggerated by omission of information on loss of U.S. jobs. Thus, our actions as workers, citizens, and consumers can often be strengthened through critical understanding of how quantitative information is used and misused.
Further, we can often understand important social issues more accurately by asking for quantitative data that are not initially presented. For example, a particular tax cut may have returned X amount of dollars to the people, but was that return equitably distributed? Yes, average family income increased Y percent in the 90's, but a breakdown of that average would show that only the wealthy significantly benefited from that increase. Thus, both as citizens and as agents of social change, we need to know not just what quantitative data show but what they don't show.
This competency will enable students to work more effectively on Core Knowledge and Skills competencies as well as competencies in their major, and it will prepare them for more effective work in their communities.Prerequisite: Understanding Arguments
Competency: Can use numerical information to gain insight and draw conclusions about public and community service issues.
Criteria:
1. Draw conclusions about public and community issues when dealing with quantitative information about those issues. In particular:
a. examine critically how public and community issues are presented in short arguments supported by quantitative reasoning
b. verify the calculations used in an argument about public and community issues that relies on quantitative reasoning
c. explain the information about public and community issue as presented in different kinds of charts and/or graphs
d. draw conclusions from quantitative information about public and community issues presented in other media other than articles or graphs/charts, such as political cartoons or advertisements
2. Use quantitative information about public and community issues to construct arguments about those issues.
3. Present numerical information about public and community issues in effective ways.
STANDARDS:
For all the criteria, use of a calculator or computer is encouraged.
1.
a. With respect to the arguments referred to in Criterion 1a, briefly discuss the main point, how the numerical information supports (or does not support) that point, and what other quantitative data you could examine to learn more about that point. Use the given numbers and your basic quantitative skills to gain more information about the situation (i.e., to create and solve some math problems that are meaningful to the analysis of the argument). Where appropriate, solve a math problem that involves making reasonable assumptions about rounding the data, choosing which given data are relevant, discussing which missing data would be relevant, and/or performing multiple operations with very large or very small numbers.
b. In the arguments referred to in Criterion 1b, show how each number was obtained from which previous data; or if some of the information is missing, state which information you would need and how you would go about verifying the calculations if that missing information were provided. Further, discuss possible sources from which you could find the missing information. Use the numerical and other evidence to evaluate the reasonableness of the argument.
c. Explain and evaluate the kinds of numerical questions that are answered by the graphs and charts referred to in Criterion 1c, identify the kinds of numerical questions that cannot be answered, and explain why. Solve problems by gathering information from one chart or graph to operate on the information from the other graphs/charts. Describe what kind of raw data was used to construct the graphs and charts. Draw conclusions from the information presented in the graphs and charts and indicate what other kinds of numerical data you would want in order to clarify or deepen the conclusions that can be drawn from the given graphs and charts.
d. Reason quantitatively about at least two media other than prose or graphs and charts. Describe the main argument and explain how the numbers support (or do not support) the point of the argument. Determine whether the use of numbers in the presentation (picture, TV show, etc.) clarifies or obscures the point of the argument.
2. For Criterion 2, Use “raw” numerical data approved or provided by an evaluator; in addition, collect and/or research a small amount of “raw” numerical data and then use them to construct an argument about a public and community service issue. Detail how the numerical data support the argument, and discuss what kinds of data might be collected that would further strengthen or challenge your argument.
3. For Criterion 3, critique others’ summaries of data and re-present the data in alternative graphs or charts. Present in clear forms one set of the data used for Criterion 2. ("Clear forms" refers to graphs or charts that summarize all the data in ways that clarify the main conclusions that can be drawn.)
4. In all the criteria, you must demonstrate clear reasoning as well as quantitative accuracy. This will involve demonstrating the ability to:
a. interpret and estimate quantities, including very large and very small values
b. extract quantitative information from graphs, tables, news stories, journal articles, or other media
c. present quantitative information in graphical, tabular or other written forms
d. compare quantities using differences, ratios, rates, and percents
e. interpret and apply descriptive statistical concepts appearing in various media, including measures of central tendency (mean, median, and mode), and the results of surveys
f. identify and pose real-world problems using and/or collecting quantitative data.
Examples of Demonstration:
1. Prior Learning: A student confident of her quantitative reasoning skills takes a brief quantitative reasoning diagnostic test. Based on her performance on the diagnostic, an evaluator determines that she may attempt to demonstrate the competency through prior learning. She then successfully responds to a proctored test and completes a 4-page response to an open-ended question that demonstrates her knowledge in relation to the competency.
2. Independent Learning: A student confident of his quantitative reasoning skills meets with an evaluator to review the competency criteria together. The meeting and a diagnostic test help determine that, because of his general quantitative reasoning skills and because of a few areas he still needs to study, Independent Learning is realistic. After studying the materials the evaluator suggested, the student successfully responds to a proctored test and completes a 4-page response to an open-ended question that demonstrates his knowledge in relation to the competency.
3. CPCS Instructional Activity: A student takes a course or workshop that addresses the Quantitative Reasoning competency.