# Quantative Literacy

## Operational Definition

Quantitative literacy is competence in the skills involved in the effective production, utilization and comprehension of quantitative information for the purposes of description, analysis, discovery, evaluation, reasoning, decision making, problem solving, and persuasion. Furthermore, quantitative literacy involves recognizing when such skills are needed and using them appropriately and ethically. The cultivation of quantitative literacy is essential for effective living skills, for informed citizenship and for personal enrichment.

## Objectives:

The following objectives are adapted from a framework for quantitative literacy developed by Christopher Wolfe (Wolfe, 1990; Wolfe & Haynes, 2002). Quantitative literacy can be broken down into four dimensions, each of which has assessable outcomes.

## Dimensions

# 1. Measurement, Data Collection and Interpretation

This category of skills involves quantitative description of phenomena, creation of a testable hypothesis, collection of accurate, valid quantitative data to address the hypothesis, and the analysis and interpretation of the data into usable information to test the hypothesis.

A student should:

- Be able to frame an important question in such a way that a suitable research method can be used to collect quantitative information that will address the question.
- Understand different scales of measurement and the implications for data analysis.
- Recognize the variety of research methods, appreciate their strengths and weaknesses, and understand how to select the best method for a given situation.
- Recognize the strengths and weaknesses of data based on the methods used to collect it.
- Recognize the importance of the characteristics of the sample on the validity of quantitative results and conclusions.
- Recognize relative levels of accuracy and precision in measurement and their implications for data analysis.

# 2. Quantitative Expression

This category of skills involves representing data in a graphical, tabular or abstracted form for the purposes of summarizing the data, revealing underlying trends and structure, and communicating the key meanings of the data.

A student should:

- Be able to produce appropriate visual representations of data that are clear, concise, accurate and valid for the purposes of description, analysis and communication.
- Be able to comprehend the critical features of quantitative information presented in graphs and tables
- Recognize the faults of misleading, inaccurate or improper graphs and tables when they are encountered.
- Understand how data sets may be summarized by means of mathematical methods, and to understand the strengths and weaknesses of these methods.
- Tailor the quantitative representation of data for optimal clarity and impact for a given audience.

# 3. Evaluating Evidence and Assertions

This category of skills involves the ability to evaluate evidence and assertions based on quantitative information and reasoning. This set of skills involves appropriately utilizing the precision of quantitative information and the rigor of quantitative reasoning for the purposes of prediction, decision making, and problem solving, as well as evaluating risk and uncertainty.

A student should:

- Be able to assess the strengths and weaknesses of quantitative evidence proffered in support of an assertion based on the source of the data, the methods used to collect and analyze the data, and the nature of the data itself.
- Evaluate the strengths and weaknesses of the chain of reasoning from data to conclusion.
- Be able to arrive at and defend his or her own interpretations and conclusions based on data.
- Appreciate uncertainty and error in data and in making measurements and drawing conclusions from data
- Recognize when data are incomplete, flawed or atypical.
- Translate a verbal assertion into quantitative expressions and then translate quantitative evidence and reasoning back into verbal assertions.
- Recognize that there are multiple ways to solve a given problem
- Choose the best method of computation to solve problems and solve them accurately
- Understand how to make predictions, decisions and conclusions about populations based on data from samples.
- Use data to evaluate risk, probabilities, costs and benefits.

# 4. Quantitative Intuition

Quantitative intuition refers to a person's ease in working with quantitative information and with a person's implicit sense of quantitative magnitude and estimation. First, it is amenability to working with quantitative data and conducting quantitative analyses. Second, it is a feel for orders of magnitude, and an implicit apprehension of whether numerical answers seem right or wrong without the conscious use of calculations or reasoning.

A student should:

- Be at ease when dealing with quantitative concepts, information and methods.
- Have a sense of the reasonableness or likelihood of quantitative solutions.
- Be able to estimate an approximate answer for quantitative problems.
- Develop an appropriate sense of scale and magnitude.
- Develop a sense of the probability or frequency of events (Stochastic intuition).
- Develop the appropriate use of heuristics.
- Recognize a logical line of evidence for a hypothesis.

# Assessment Examples

- Assessing QLA
- Self Assessments
- Information on the Quant-Q
- QLA Assessment amenable to disciplinary differences
- Measures of a student's ability to measure, collect, & interpret data
- Measures of a student's ability for quantitative expression
- Measures of a student's ability for evaluating evidence & assertions
- Measures of a student's ability in quantitative intuition
- Measures of a student's process of acquiring skills over a period of time (portfolio)

# Article of Interest

- A Mathematician's Proposal (Change 10/31/2007)