## Different Views on Quantitative Literacy

Contributors to "Why Numbers Count" offer many different views of quantitative literacy, as well as several variations on the term itself--including numeracy, quantitative practices, quantitative reasoning, mathematical literacy, problem solving, quantitative competencies.

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

Contrasting views were expressed by mathematicians who were asked to reflect on the definitions offered by these authors. Mathematicians distinguished rather sharply between "quantitative" and "mathematical" literacy:

Quantitative literacy involves reasoning with numbers (Jim Lewis); reading, interpreting and making simple applications (Carole Lacampagne); understanding operations on rational numbers (Jack Price); constructing and recognizing a sound argument (Keith Devlin); and understanding variability and how to quantify it (Gail Burrill).

In contrast, mathematical literacy offers a big-picture view of how to work with numbers, relationships, and patterns (Jim Lewis); higher order thinking, including all the goals of the NCTM Standards (Jack Price); mostly qualitative issues, not quantitative ones (Keith Devlin); the language of algebra as well as geometric and spatial experience (Zal Usiskin).

-- Mathematicians and mathematics educators