What is QL/QR?

The term quantititave literacy (QL) and its cousins quantitative reasoning (QR), mathematical literacy, and numeracy have been getting a lot of use lately. And I suspect that, at least in some circles, they will become even more familiar in the near future. The good side is that the vital topic of QL is getting some attention and awareness of QL is on the rise. The bad side is that these terms are on the verge of becoming meaningless buzzwords. This brief page may not change any of this. But it does provide some answers and opinions about ... what is QL/QR?

Many long answers to this question are given in the two recent and excellent monographs, Why Numbers Count: Quantitative Literacy for Tomorrow's America (The College Board, 1997) and Mathematics and Democracy: The Case for Quantitative Literacy (National Council on Education and the Disciplines, Lynn Arthur Steen, ed., 2001). Many of the more concise definitions given below are taken from those volumes. A list of various numeracies is also given by Lynn Steen.

For example, the term numerate appeared in a British report (Mathematics Counts, W.H. Cockcroft, Her Majesty's Stationery Office, 1982):

We would wish the term numerate to imply the possession of two attributes. The first of these is an "at homeness" with numbers and an ability to make use of mathematical skills which enables an individual to cope with the practical demands of everyday life. The second is an ability to have some appreciation and understanding of information which is presented in mathematical terms.

The National Adult Literacy Survey (National Center for Education Statistics, 1993) defined QL as

The knowledge and skills required to apply arithmetic operations, either alone or sequentially, using numbers embedded in printed material (for example, balancing a checkbook or completing an order form).

The International Life Skills Survey (Policy Research Initiative, Statistics Canada, 2000) claims that QL is

an aggregate of skills, knowledge, beliefs, dispositions, habits of mind, communication capabilities, and problem solving skills that people need in order to engage effectively in quantitative situations arising in life and work.

The Programme for International Assessment (Organization for Economic Cooperation and Development, 2000) defines mathematics literacy as

an individual's capacity to identify and understand the role that mathematics plays in the world, to make well-founded mathematical judgments and to engage in mathematics in ways that meet the needs of that individual's current and future life as a constructive, concerned and reflective citizen.

Lynn Steen, in the Case for Quantitative Literacy (Mathematics and Democracy: The Case for Quantitative Literacy), identifies the following elements of QL (with elaboration):

confidence in mathematics, cultural appreciation, interpreting data, logical thinking, making decisions, mathematics in context, number sense, practical skills, prerequisite knowledge, symbol sense.

Contributors to the volume Why Numbers Count were asked to offer many their views of quantitative literacy. Here are the results:

Quantitative literacy involves understanding the role of numbers in the world. It provides the ability to see below the surface and to demand enough information to get at the real issues.
-- Ted Porter, historian

Beyond arithmetic and geometry, quantitative literacy also requires logic, data analysis, and probability.... It enables individuals to analyze evidence, to read graphs, to understand logical arguments, to detect logical fallacies, to understand evidence, and to evaluate risks. Quantitative literacy means knowing how to reason and how to think.
-- Gina Kolata, journalist

Quantitative literacy can be defined as the level of mathematical knowledge and skills required of all citizens. It includes the ability to apply aspects of mathematics (including measurement, data representation, number sense, variables geometric shapes, spatial visualization, and chance) to understand, predict, and control routine events in people's lives.
-- John Dossey, mathematics educator

Quantitative literacy requires one to understand the nature of mathematics and its role in scientific inquiry and technological progress; to grasp sufficient mathematics to understand important scientific and engineering concepts; and to possess quantitative skills sufficient for responding critically to scientific issues in the media and public life.
-- F. James Rutherford, physics educator

The heart of quantitative literacy is real world problem solving--the use of mathematics in everyday life, on the job, and as an intelligent citizen. Problem solving must be both mathematically defensible and useful in the real world.
-- Henry Pollak, applied mathematician

Numeracy is not the same as mathematics. It is an aggregation of skills, knowledge, beliefs, dispositions, habits of mind, communication capabilities, and problem solving skills that people need in order to engage effectively and autonomously in quantitative situations arising in life and work.
-- Iddo Gal, cognitive scientist

Practices are the habitual patterns of actions engaged in routinely by people, usually without thought; they include standard patterns, routines, procedures, processes, and habits. Quantitative practices deal with numbers, uncertainty, errors in data, design of experiments, creation of models, validations, inferences, making tradeoffs, etc.
-- Peter Denning, computer scientist

Quantitative reasoning as an interpretive activity that takes place within a deductively structured framework. It involves a tapestry of meaning provided by a warp of abstract patterns and a weft of context and story line. In quantitative reasoning, context provides meaning.
-- George Cobb, statistician

Important quantitative competencies are those that can be used to solve problems people would frequently encounter on the job or in their roles as citizens or parents. Quantitative competencies require identifying and solving problems not in algebra and geometry, but in the five SCANS competency domains such as planning, information, and systems analysis.
-- Arnold Packer, economist

Quantitative literacy involves understanding the mathematical concepts and skills that are necessary for everyday life. It includes computation, interpretation, inquiry, and application of mathematical concepts that are critical for life in the contemporary world.
-- Glenda Price, college provost